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VII: THEORY OF ELECTRICAL IMAGES", "pages": [ "098", "107" ], "concepts": [ "concept/conductor", "concept/electrical-earth", "concept/electrical-image", "concept/equipotential-surface", "concept/induced-electrification", "concept/induced-electrification-of-the-first-species", "concept/induced-electrification-of-the-second-species", "concept/inverse-points", "concept/inverse-points-with-respect-to-a-sphere", "concept/neutral-line", "concept/optical-image", "concept/sphere", "law/coulomb-s-law", "method/method-of-electric-images", "person/sim-on-denis-poisson", "person/william-thomson", "quantity/electric-charge", "quantity/electric-energy", "quantity/electric-potential", "quantity/surface-charge-density", "theorem/electric-field-of-a-uniformly-electrified-sphere" ], "excerpts": [ "maxwell-elementary-treatise-electricity-1888/x-a65a4c7dec", "maxwell-elementary-treatise-electricity-1888/x-9744a43ca8", "maxwell-elementary-treatise-electricity-1888/x-7eddc05411", "maxwell-elementary-treatise-electricity-1888/x-4858de6d8d", "maxwell-elementary-treatise-electricity-1888/x-a46db30ced", "maxwell-elementary-treatise-electricity-1888/x-2578e5b493", "maxwell-elementary-treatise-electricity-1888/x-3748d57246", "maxwell-elementary-treatise-electricity-1888/x-bb2b10ed6e", "maxwell-elementary-treatise-electricity-1888/x-9c382e9081", "maxwell-elementary-treatise-electricity-1888/x-e356d0cfd5", "maxwell-elementary-treatise-electricity-1888/x-4ffe54a311", "maxwell-elementary-treatise-electricity-1888/x-45524471da" ], "equations": [ "maxwell-elementary-treatise-electricity-1888/eq-4848cfcebd", "maxwell-elementary-treatise-electricity-1888/eq-861bb630c8", "maxwell-elementary-treatise-electricity-1888/eq-6aa66a3f46", "maxwell-elementary-treatise-electricity-1888/eq-c0cf6a49d4", "maxwell-elementary-treatise-electricity-1888/eq-14fc81cfad", "maxwell-elementary-treatise-electricity-1888/eq-2a169a5a96", "maxwell-elementary-treatise-electricity-1888/eq-3a3045c436", "maxwell-elementary-treatise-electricity-1888/eq-3de372884b", "maxwell-elementary-treatise-electricity-1888/eq-7f2cc10557", "maxwell-elementary-treatise-electricity-1888/eq-795dd232e3", "maxwell-elementary-treatise-electricity-1888/eq-27185acbea", "maxwell-elementary-treatise-electricity-1888/eq-577e5a8e6f", "maxwell-elementary-treatise-electricity-1888/eq-a3d61257ed", "maxwell-elementary-treatise-electricity-1888/eq-eef64e9514", "maxwell-elementary-treatise-electricity-1888/eq-6f45be4433", "maxwell-elementary-treatise-electricity-1888/eq-64bd1bcc1c", "maxwell-elementary-treatise-electricity-1888/eq-c5d1ee7bfb", "maxwell-elementary-treatise-electricity-1888/eq-3bd272abd1", "maxwell-elementary-treatise-electricity-1888/eq-9048db91fa", "maxwell-elementary-treatise-electricity-1888/eq-b771914988", "maxwell-elementary-treatise-electricity-1888/eq-641dcaed8d" ], "exercise_sets": [] }, { "id": "maxwell-elementary-treatise-electricity-1888/ch-viii", "number": "VIII", "title": "ON ELECTROSTATIC CAPACITY", "name": "Maxwell 1888, ch. VIII: ON ELECTROSTATIC CAPACITY", "pages": [ "107", "114" ], "concepts": [ "concept/conductor", "concept/electrical-earth", "concept/electrification", "concept/electrode", "instrument/condenser", "instrument/electrometer", "instrument/leyden-jar", "instrument/parallel-disk-condenser", "instrument/voltaic-battery", "instrument/wheatstone-s-bridge", "method/comparison-of-two-condensers", "method/condenser-bridge", "method/discharging-a-conductor", "person/alessandro-volta", "person/william-thomson", "quantity/capacity", "quantity/coefficient-of-induction", "quantity/electric-charge", "quantity/electric-energy", "quantity/electric-potential", "quantity/electromotive-force", "theorem/condenser-bridge-balance-condition" ], "excerpts": [ "maxwell-elementary-treatise-electricity-1888/x-3898cbdd03", "maxwell-elementary-treatise-electricity-1888/x-d6dc070f66", "maxwell-elementary-treatise-electricity-1888/x-22f08942cb", "maxwell-elementary-treatise-electricity-1888/x-de4e81e77b", "maxwell-elementary-treatise-electricity-1888/x-15850818bd", "maxwell-elementary-treatise-electricity-1888/x-c03465d138", "maxwell-elementary-treatise-electricity-1888/x-ef4897b436", "maxwell-elementary-treatise-electricity-1888/x-93594939a7", "maxwell-elementary-treatise-electricity-1888/x-d650224a0f" ], "equations": [ "maxwell-elementary-treatise-electricity-1888/eq-ba8287018e", "maxwell-elementary-treatise-electricity-1888/eq-b7538c7c44", "maxwell-elementary-treatise-electricity-1888/eq-dcedd21e9f", "maxwell-elementary-treatise-electricity-1888/eq-31be88cd1e", "maxwell-elementary-treatise-electricity-1888/eq-b34956cafd", "maxwell-elementary-treatise-electricity-1888/eq-bc144d0269", "maxwell-elementary-treatise-electricity-1888/eq-aaf0e2683b", "maxwell-elementary-treatise-electricity-1888/eq-b3a4853c56", "maxwell-elementary-treatise-electricity-1888/eq-a111219051", "maxwell-elementary-treatise-electricity-1888/eq-15f5747cb8", "maxwell-elementary-treatise-electricity-1888/eq-3b38c6e471", "maxwell-elementary-treatise-electricity-1888/eq-ee099e4ac7", "maxwell-elementary-treatise-electricity-1888/eq-9fe54f8926", "maxwell-elementary-treatise-electricity-1888/eq-9539378b27", "maxwell-elementary-treatise-electricity-1888/eq-9be60f31cf", "maxwell-elementary-treatise-electricity-1888/eq-23dca126d4", "maxwell-elementary-treatise-electricity-1888/eq-0107660d5c", "maxwell-elementary-treatise-electricity-1888/eq-4e95d4778c", "maxwell-elementary-treatise-electricity-1888/eq-738d3c1502", "maxwell-elementary-treatise-electricity-1888/eq-3c0f77dde6", "maxwell-elementary-treatise-electricity-1888/eq-ae8310db6c", "maxwell-elementary-treatise-electricity-1888/eq-6248eca347", "maxwell-elementary-treatise-electricity-1888/eq-a653d55727", "maxwell-elementary-treatise-electricity-1888/eq-204ec80eaa", "maxwell-elementary-treatise-electricity-1888/eq-3a6ae9ec79", "maxwell-elementary-treatise-electricity-1888/eq-57b10d2396", "maxwell-elementary-treatise-electricity-1888/eq-3d973a64e0", "maxwell-elementary-treatise-electricity-1888/eq-0f829495e9", "maxwell-elementary-treatise-electricity-1888/eq-7c42fa0c4c", "maxwell-elementary-treatise-electricity-1888/eq-3550752c46", "maxwell-elementary-treatise-electricity-1888/eq-5d880364aa", "maxwell-elementary-treatise-electricity-1888/eq-212db2de95", "maxwell-elementary-treatise-electricity-1888/eq-e329b44aa5", "maxwell-elementary-treatise-electricity-1888/eq-d6fdc1e1db", "maxwell-elementary-treatise-electricity-1888/eq-015e300532" ], "exercise_sets": [] }, { "id": "maxwell-elementary-treatise-electricity-1888/ch-ix", "number": "IX", "title": "THE ELECTRIC CURRENT", "name": "Maxwell 1888, ch. IX: THE ELECTRIC CURRENT", "pages": [ "140", "147" ], "concepts": [ "concept/anode", "concept/cathode", "concept/conduction", "concept/conduction-current", "concept/conductivity-of-gases", "concept/convection-current", "concept/dielectric", "concept/disruptive-discharge", "concept/electric-absorption", "concept/electric-brush", "concept/electric-current", "concept/electric-discharge", "concept/electric-displacement", "concept/electric-glow", "concept/electric-polarity", "concept/electric-spark", "concept/electric-tension", "concept/electric-wind", "concept/electrical-brittleness", "concept/electrode", "concept/electrolysis", "concept/electrolyte", "concept/electrolytic-convection", "concept/heat", "concept/insulator", "concept/ion", "concept/kinetic-theory-of-heat", "concept/linear-conductor", "concept/magnetic-action-of-an-electric-current", "concept/metal", "concept/molecular-agitation", "concept/polarization", "concept/pyroelectricity", "concept/residual-discharge", "concept/spectrum", "concept/steady-current", "concept/tourmaline", "concept/transient-current", "experiment/tube-and-piston-model-of-a-dielectric", "instrument/daniell-s-cell", "instrument/electrometer", "instrument/galvanometer", "instrument/quadrant-electrometer", "instrument/spectroscope", "instrument/voltaic-battery", "law/faraday-s-laws-of-electrolysis", "law/joule-s-law", "law/kirchhoff-s-circuit-laws", "law/kirchhoff-s-laws", "law/ohm-s-law", "person/friedrich-kohlrausch", "person/georg-simon-ohm", "person/gustav-robert-kirchhoff", "person/hans-christian-oersted", "person/hermann-von-helmholtz", "person/james-prescott-joule", "person/michael-faraday", "person/norman-lockyer", "person/rudolf-clausius", "person/william-thomson", "quantity/conductivity", "quantity/electric-potential", "quantity/electric-strength", "quantity/electrochemical-equivalent", "quantity/electromotive-force", "quantity/resistance", "quantity/specific-inductive-capacity", "quantity/specific-resistance", "quantity/surface-charge-density", "theorem/resistance-of-a-uniform-wire", "theorem/resistance-of-conductors-in-multiple-arc", "theorem/resistance-of-conductors-in-series" ], "excerpts": [ "maxwell-elementary-treatise-electricity-1888/x-840f8469df", "maxwell-elementary-treatise-electricity-1888/x-aa5597dfca", "maxwell-elementary-treatise-electricity-1888/x-1c83b24150", "maxwell-elementary-treatise-electricity-1888/x-ac8fa0ec8d", "maxwell-elementary-treatise-electricity-1888/x-47a8589b5b", "maxwell-elementary-treatise-electricity-1888/x-1e2fb6ba36", "maxwell-elementary-treatise-electricity-1888/x-5aab6e6aa7", "maxwell-elementary-treatise-electricity-1888/x-80838f83da", "maxwell-elementary-treatise-electricity-1888/x-f9974b7304", "maxwell-elementary-treatise-electricity-1888/x-ab0c29f4b6", "maxwell-elementary-treatise-electricity-1888/x-3d25fe9cde", "maxwell-elementary-treatise-electricity-1888/x-750a9ff9fb", "maxwell-elementary-treatise-electricity-1888/x-56d37af88f", "maxwell-elementary-treatise-electricity-1888/x-9975884361", "maxwell-elementary-treatise-electricity-1888/x-49126f1b1c", "maxwell-elementary-treatise-electricity-1888/x-89baee262c", "maxwell-elementary-treatise-electricity-1888/x-a88ff6f3dc", "maxwell-elementary-treatise-electricity-1888/x-9c4282e3ea", "maxwell-elementary-treatise-electricity-1888/x-01f0144770", "maxwell-elementary-treatise-electricity-1888/x-d53ae7e1a4", "maxwell-elementary-treatise-electricity-1888/x-2b6bdabfc4", "maxwell-elementary-treatise-electricity-1888/x-01a1737dc7", "maxwell-elementary-treatise-electricity-1888/x-19dff27e54", "maxwell-elementary-treatise-electricity-1888/x-727f22574b", "maxwell-elementary-treatise-electricity-1888/x-ac0f7fad20", "maxwell-elementary-treatise-electricity-1888/x-f4ae0d887c", "maxwell-elementary-treatise-electricity-1888/x-db66f774a6", "maxwell-elementary-treatise-electricity-1888/x-e822105e35", "maxwell-elementary-treatise-electricity-1888/x-30e1952f50", "maxwell-elementary-treatise-electricity-1888/x-aa6ba317fd", "maxwell-elementary-treatise-electricity-1888/x-97ceed394c", "maxwell-elementary-treatise-electricity-1888/x-141cd554c9", "maxwell-elementary-treatise-electricity-1888/x-b5971c646d", "maxwell-elementary-treatise-electricity-1888/x-511d649c00" ], "equations": [ "maxwell-elementary-treatise-electricity-1888/eq-184170045b", "maxwell-elementary-treatise-electricity-1888/eq-ee127e023d", "maxwell-elementary-treatise-electricity-1888/eq-5d62bfe413", "maxwell-elementary-treatise-electricity-1888/eq-f5613a74fa", "maxwell-elementary-treatise-electricity-1888/eq-c46a61d7b6", "maxwell-elementary-treatise-electricity-1888/eq-b81327c95f", "maxwell-elementary-treatise-electricity-1888/eq-c7bc23ee13", "maxwell-elementary-treatise-electricity-1888/eq-6eeb6b1493", "maxwell-elementary-treatise-electricity-1888/eq-acfc970331", "maxwell-elementary-treatise-electricity-1888/eq-9e6da24093", "maxwell-elementary-treatise-electricity-1888/eq-0cdb2617b2", "maxwell-elementary-treatise-electricity-1888/eq-4961708d1f", "maxwell-elementary-treatise-electricity-1888/eq-baf87a6468", "maxwell-elementary-treatise-electricity-1888/eq-176abcfeb8" ], "exercise_sets": [] }, { "id": "maxwell-elementary-treatise-electricity-1888/ch-x", "number": "X", "title": "PHENOMENA OF AN ELECTRIC CURRENT WHICH FLOWS THROUGH HETEROGENEOUS MEDIA", "name": "Maxwell 1888, ch. 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"theorem/common-potential-after-contact" ], "excerpts": [ "maxwell-elementary-treatise-electricity-1888/x-bbe6c7add1", "maxwell-elementary-treatise-electricity-1888/x-5d18e17163", "maxwell-elementary-treatise-electricity-1888/x-ffee7d32a9", "maxwell-elementary-treatise-electricity-1888/x-c4f2368c14", "maxwell-elementary-treatise-electricity-1888/x-808eebec61", "maxwell-elementary-treatise-electricity-1888/x-407d2d5dbf", "maxwell-elementary-treatise-electricity-1888/x-2504f2dea7", "maxwell-elementary-treatise-electricity-1888/x-14c680b43f", "maxwell-elementary-treatise-electricity-1888/x-922f36ed8a", "maxwell-elementary-treatise-electricity-1888/x-293ae86c2c", "maxwell-elementary-treatise-electricity-1888/x-10ac65d8a8", "maxwell-elementary-treatise-electricity-1888/x-64fc2c6286", "maxwell-elementary-treatise-electricity-1888/x-1c734f3b86", "maxwell-elementary-treatise-electricity-1888/x-a453ad3e17", "maxwell-elementary-treatise-electricity-1888/x-a12903328e", 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"maxwell-elementary-treatise-electricity-1888/eq-cf7bf3881e", "maxwell-elementary-treatise-electricity-1888/eq-60e4a6043b", "maxwell-elementary-treatise-electricity-1888/eq-c6b8c744d0", "maxwell-elementary-treatise-electricity-1888/eq-6d6590beb4", "maxwell-elementary-treatise-electricity-1888/eq-3b301c71ac", "maxwell-elementary-treatise-electricity-1888/eq-0c4daf0b3a", "maxwell-elementary-treatise-electricity-1888/eq-e65f588127", "maxwell-elementary-treatise-electricity-1888/eq-288eb0bcb0", "maxwell-elementary-treatise-electricity-1888/eq-adea4180e5", "maxwell-elementary-treatise-electricity-1888/eq-7481ab0506", "maxwell-elementary-treatise-electricity-1888/eq-0310e4cdfb", "maxwell-elementary-treatise-electricity-1888/eq-9b0a6c7b47", "maxwell-elementary-treatise-electricity-1888/eq-16a09aaac1", "maxwell-elementary-treatise-electricity-1888/eq-1af5b2593f", "maxwell-elementary-treatise-electricity-1888/eq-324b4c6e29", "maxwell-elementary-treatise-electricity-1888/eq-8fbe8426c8", "maxwell-elementary-treatise-electricity-1888/eq-f01c164397", "maxwell-elementary-treatise-electricity-1888/eq-378c477504", "maxwell-elementary-treatise-electricity-1888/eq-d876ae1035", "maxwell-elementary-treatise-electricity-1888/eq-7034dcff4a", "maxwell-elementary-treatise-electricity-1888/eq-36acb3d76e", "maxwell-elementary-treatise-electricity-1888/eq-fdf305cdc2", "maxwell-elementary-treatise-electricity-1888/eq-99cd191488", "maxwell-elementary-treatise-electricity-1888/eq-f923256305", "maxwell-elementary-treatise-electricity-1888/eq-43b029a35d", "maxwell-elementary-treatise-electricity-1888/eq-25ff1430f1", "maxwell-elementary-treatise-electricity-1888/eq-66eb24d4a1", "maxwell-elementary-treatise-electricity-1888/eq-cdbc851e26", "maxwell-elementary-treatise-electricity-1888/eq-1ff057ea96", "maxwell-elementary-treatise-electricity-1888/eq-d8e2fdaef0", "maxwell-elementary-treatise-electricity-1888/eq-15304f59ef", "maxwell-elementary-treatise-electricity-1888/eq-b91787a4c5", 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"maxwell-elementary-treatise-electricity-1888/eq-cfb3423057", "maxwell-elementary-treatise-electricity-1888/eq-155e956d4f", "maxwell-elementary-treatise-electricity-1888/eq-5f7a73da2f", "maxwell-elementary-treatise-electricity-1888/eq-ef872efefc", "maxwell-elementary-treatise-electricity-1888/eq-a46b771fc2", "maxwell-elementary-treatise-electricity-1888/eq-0cf23e8fdd", "maxwell-elementary-treatise-electricity-1888/eq-e44bdd033f", "maxwell-elementary-treatise-electricity-1888/eq-87be207383", "maxwell-elementary-treatise-electricity-1888/eq-b068590bb6", "maxwell-elementary-treatise-electricity-1888/eq-d69896bcb5", "maxwell-elementary-treatise-electricity-1888/eq-ba61ae24b2", "maxwell-elementary-treatise-electricity-1888/eq-41c016ab5c", "maxwell-elementary-treatise-electricity-1888/eq-b59162bc3d", "maxwell-elementary-treatise-electricity-1888/eq-6bff70ac2b", "maxwell-elementary-treatise-electricity-1888/eq-d1de377c70", "maxwell-elementary-treatise-electricity-1888/eq-e0107d09ec", 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XIII: ON THE ELECTRIC RESISTANCE OF SUBSTANCES", "pages": [ "215", "227" ], "concepts": [ "concept/alloy", "concept/conductor", "concept/current-through-a-rarefied-gas", "concept/dielectric", "concept/disruptive-discharge", "concept/electric-tension", "concept/electrode", "concept/electrolysis", "concept/electrolyte", "concept/mercury", "concept/polarization", "concept/residual-discharge", "concept/siemens-s-formula-for-metal-resistance", "concept/transient-current", "instrument/galvanometer", "instrument/influence-machine", "instrument/leyden-jar", "instrument/resistance-coil", "instrument/wheatstone-s-bridge", "law/kirchhoff-s-second-law", "law/ohm-s-law", "method/cycle-rule-for-linear-circuits", "method/paalzow-s-siphon-method", "person/augustus-matthiessen", "person/c-f-varley", "person/c-w-siemens", "person/gustav-robert-kirchhoff", "person/michael-faraday", "person/william-thomson", "quantity/absolute-temperature", "quantity/capacity", "quantity/conductivity", "quantity/electric-current", "quantity/electromotive-force", "quantity/resistance", "quantity/specific-resistance", "quantity/temperature", "quantity/temperature-coefficient-of-resistance", "unit/ohm" ], "excerpts": [ "maxwell-elementary-treatise-electricity-1888/x-9f3ec35fcd", "maxwell-elementary-treatise-electricity-1888/x-68a8313e38", "maxwell-elementary-treatise-electricity-1888/x-ad7bee4e88", "maxwell-elementary-treatise-electricity-1888/x-961c9e9dca", "maxwell-elementary-treatise-electricity-1888/x-b51d67aae3", "maxwell-elementary-treatise-electricity-1888/x-4696da793a", "maxwell-elementary-treatise-electricity-1888/x-a101d83262", "maxwell-elementary-treatise-electricity-1888/x-39bffe1e9e", "maxwell-elementary-treatise-electricity-1888/x-cb854a1911", "maxwell-elementary-treatise-electricity-1888/x-58c84fe670", "maxwell-elementary-treatise-electricity-1888/x-31d0c395dd", "maxwell-elementary-treatise-electricity-1888/x-53180185a2", "maxwell-elementary-treatise-electricity-1888/x-6465b38914" ], "equations": [ "maxwell-elementary-treatise-electricity-1888/eq-0c2541ef19", "maxwell-elementary-treatise-electricity-1888/eq-6fa9caabb2", "maxwell-elementary-treatise-electricity-1888/eq-1c10bf3661", "maxwell-elementary-treatise-electricity-1888/eq-c70d5f336b", "maxwell-elementary-treatise-electricity-1888/eq-45c9d1f410", "maxwell-elementary-treatise-electricity-1888/eq-a5e80daab9", "maxwell-elementary-treatise-electricity-1888/eq-24dc874c31", "maxwell-elementary-treatise-electricity-1888/eq-9d52bb38e0", "maxwell-elementary-treatise-electricity-1888/eq-2edecd0101", "maxwell-elementary-treatise-electricity-1888/eq-d1b8647405", "maxwell-elementary-treatise-electricity-1888/eq-2ac0395ca5", "maxwell-elementary-treatise-electricity-1888/eq-5518a7e0ae", "maxwell-elementary-treatise-electricity-1888/eq-63c64b3508", "maxwell-elementary-treatise-electricity-1888/eq-bd97b7d277", "maxwell-elementary-treatise-electricity-1888/eq-e2e6655f2b", "maxwell-elementary-treatise-electricity-1888/eq-901085aa7b", "maxwell-elementary-treatise-electricity-1888/eq-d803c495fa" ], "exercise_sets": [] } ], "excerpts": [ { "id": "maxwell-elementary-treatise-electricity-1888/x-b5c74a1dd0", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-i", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 21", "location": "Electrification by Friction", "latex": "\\textit{Whatever produces or tends to produce a transfer of Electrification is called Electromotive Force.}", "markdown": "*Whatever produces or tends to produce a transfer of Electrification is called Electromotive Force.*", "why": "A short, exact definition that a learner can memorise and check against the path-dependence discussion that follows.", "use": [ "lesson" ], "concepts": [ "quantity/electromotive-force" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/x-352310df7e", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-i", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 22", "location": "Electrification by Friction", "latex": "The electromotive force from any point, along a path drawn in air, to a certain point chosen as a point of reference, is called the Electric Potential at that point.", "markdown": "The electromotive force from any point, along a path drawn in air, to a certain point chosen as a point of reference, is called the Electric Potential at that point.", "why": "It defines potential as a reference-relative quantity, which is the idea a learner most needs before any calculation.", "use": [ "lesson" ], "concepts": [ "quantity/electric-potential" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/x-692b6bf64f", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-i", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 20", "location": "Electrification by Friction", "latex": "Hence bodies when electrified in the same way are repelled from each other, but when they are electrified in opposite ways they are attracted to each other.", "markdown": "Hence bodies when electrified in the same way are repelled from each other, but when they are electrified in opposite ways they are attracted to each other.", "why": "It states the rule of like repelling and unlike attracting in one sentence, grounded in a simple pith-ball experiment.", "use": [ "lesson", "website" ], "concepts": [ "concept/negative-electrification", "concept/positive-electrification" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/x-6e763f8234", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-i", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 19", "location": "Electrification by Friction", "latex": "Bodies may therefore be divided into two classes: conductors, or those which transmit the discharge, and non-conductors, through which the discharge does not take place.", "markdown": "Bodies may therefore be divided into two classes: conductors, or those which transmit the discharge, and non-conductors, through which the discharge does not take place.", "why": "It gives the operational test that separates conductors from insulators, using the spark and the knuckle.", "use": [ "lesson" ], "concepts": [ "concept/conductor", "concept/insulator" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/x-ca597c7300", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-i", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 17", "location": "Electrification by Friction", "latex": "The shreds of paper will move, the lighter ones will raise themselves on one end, and some of them will leap up to the sealing-wax.", "markdown": "The shreds of paper will move, the lighter ones will raise themselves on one end, and some of them will leap up to the sealing-wax.", "why": "It opens the chapter with a home experiment that a learner can repeat at a table, with no apparatus.", "use": [ "website", "lesson" ], "concepts": [ "concept/electric-field", "concept/electrification" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/x-85a1e2e16c", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-i", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 24", "location": "Electrification by Friction", "latex": "We must also remember that temperature corresponds to a real physical state, whereas potential is a mere mathematical quantity, the value of which depends on the point of reference which we may choose.", "markdown": "We must also remember that temperature corresponds to a real physical state, whereas potential is a mere mathematical quantity, the value of which depends on the point of reference which we may choose.", "why": "It warns learners where the heat analogy fails, so they do not treat potential as a physical substance.", "use": [ "lesson" ], "concepts": [ "quantity/electric-potential" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/x-a4280ba3e0", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-i", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 23", "location": "Electrification by Friction", "latex": "No two different equipotential surfaces can cut one another, for no point can have two different potentials.", "markdown": "No two different equipotential surfaces can cut one another, for no point can have two different potentials.", "why": "A one-line proof from the definition of potential that makes equipotential surfaces easy to picture and reason about.", "use": [ "lesson" ], "concepts": [ "concept/equipotential-surface" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/x-8eef3cc182", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-i", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 17", "location": "Electrification by Friction", "latex": "\\textsc{Take} a stick of sealing-wax, rub it on woollen cloth or\nflannel, and then bring it near to some shreds of paper strewed on\nthe table. The shreds of paper will move, the lighter ones will\nraise themselves on one end, and some of them will leap up to the\nsealing-wax.", "markdown": "Take a stick of sealing-wax, rub it on woollen cloth or flannel, and then bring it near to some shreds of paper strewed on the table. The shreds of paper will move, the lighter ones will raise themselves on one end, and some of them will leap up to the sealing-wax.", "why": "A simple kitchen-table experiment that opens the subject with something a learner can try and watch.", "use": [ "lesson", "website" ], "concepts": [ "concept/electric-field", "concept/electrification" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/x-7e1328646a", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-i", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 18", "location": "Electrification by Friction", "latex": "The fact that certain bodies after being rubbed appear to attract\nother bodies was known to the ancients. In modern times many\nother phenomena have been observed, which have been found to be\nrelated to these phenomena of attraction.", "markdown": "The fact that certain bodies after being rubbed appear to attract other bodies was known to the ancients. In modern times many other phenomena have been observed, which have been found to be related to these phenomena of attraction.", "why": "Gives the historical background of electric phenomena, going back to the ancients.", "use": [ "history", "website" ], "concepts": [ "concept/electrification", "concept/electromagnetism" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/x-9e7224e572", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-i", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 19", "location": "Electrification by Friction", "latex": "The discharge, therefore, takes place through metals\nand through the human body, but not through glass, sealing-wax,\nor gutta-percha. Bodies may therefore be divided into two\nclasses: conductors, or those which transmit the discharge, and\nnon-conductors, through which the discharge does not take place.", "markdown": "The discharge, therefore, takes place through metals and through the human body, but not through glass, sealing-wax, or gutta-percha. Bodies may therefore be divided into two classes: conductors, or those which transmit the discharge, and non-conductors, through which the discharge does not take place.", "why": "Shows how an experimental observation leads to the division of bodies into conductors and non-conductors.", "use": [ "lesson" ], "concepts": [ "concept/conductor", "concept/insulator", "method/discharging-a-conductor" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/x-b952d6d72c", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-i", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 20", "location": "Electrification by Friction", "latex": "This is a\nmatter of mere convention, but the convention is a useful one,\nprovided we remember that it is a convention as arbitrary as\nthat adopted in the diagrams of analytical geometry of calling\nhorizontal distances positive or negative according as they are\nmeasured towards the right or towards the left of the point of\nreference.", "markdown": "This is a matter of mere convention, but the convention is a useful one, provided we remember that it is a convention as arbitrary as that adopted in the diagrams of analytical geometry of calling horizontal distances positive or negative according as they are measured towards the right or towards the left of the point of reference.", "why": "Reminds a learner that calling one kind of electrification positive is a choice of naming, like the sign convention on a graph's axis.", "use": [ "lesson", "website" ], "concepts": [ "concept/negative-electrification", "concept/positive-electrification" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/x-cc21851e0d", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-i", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 23", "location": "Electrification by Friction", "latex": "If two vessels containing the same or different fluids are put into\ncommunication by means of a pipe, fluid will flow from the vessel\nin which the pressure is greater into that in which it is less till the\npressure is equalized.", "markdown": "If two vessels containing the same or different fluids are put into communication by means of a pipe, fluid will flow from the vessel in which the pressure is greater into that in which it is less till the pressure is equalized.", "why": "Offers a concrete fluid picture that makes the idea of potential difference driving a transfer easier to grasp.", "use": [ "lesson" ], "concepts": [ "concept/physical-analogy", "concept/pressure", "quantity/electric-potential" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/x-ff262b6808", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-i", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 24", "location": "Electrification by Friction", "latex": "To raise a body to a high temperature may melt or\nvolatilize it. To raise a body, together with the vessel which surrounds\nit, to a high potential produces no physical effect whatever\non the body.", "markdown": "To raise a body to a high temperature may melt or volatilize it. To raise a body, together with the vessel which surrounds it, to a high potential produces no physical effect whatever on the body.", "why": "Shows where the temperature analogy fails: potential depends on the chosen reference point and has no physical effect of its own.", "use": [ "lesson" ], "concepts": [ "concept/physical-analogy", "concept/temperature", "quantity/electric-potential" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/x-b389bf993b", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-i", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 24", "location": "Electrification by Friction", "latex": "And here we may introduce\nonce for all the common phrase \\textit{The Electric Fluid} for the purpose\nof warning our readers against it. It is one of those phrases,\nwhich, having been at one time used to denote an observed fact,\nwas immediately taken up by the public to connote a whole system\nof imaginary knowledge.", "markdown": "And here we may introduce once for all the common phrase *The Electric Fluid* for the purpose of warning our readers against it. It is one of those phrases, which, having been at one time used to denote an observed fact, was immediately taken up by the public to connote a whole system of imaginary knowledge.", "why": "A warning from the author against turning a useful analogy into a belief about what electricity is.", "use": [ "lesson", "website", "history" ], "concepts": [ "concept/electric-fluid", "concept/physical-analogy" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/x-38968ba637", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-ii", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 36", "location": "ON THE CHARGES OF ELECTRIFIED BODIES", "latex": "For if the process of electrification is conducted within the closed vessel, however intense the electrification of the parts of the system may be, the electrification of the whole, as indicated by the electroscope connected with the vessel, remains zero.", "markdown": "For if the process of electrification is conducted within the closed vessel, however intense the electrification of the parts of the system may be, the electrification of the whole, as indicated by the electroscope connected with the vessel, remains zero.", "why": "It gives the argument that charge creation inside a closed, connected vessel leaves the net charge zero, which is the basis of the third law.", "use": [ "lesson", "history" ], "concepts": [ "concept/closed-conducting-surface", "concept/electrification", "instrument/electroscope" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/x-fac737735c", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-ii", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 36", "location": "ON THE CHARGES OF ELECTRIFIED BODIES", "latex": "The total electrification or charge of a body or system of bodies remains always the same, except in so far as it receives electrification from, or gives electrification to other bodies.", "markdown": "The total electrification or charge of a body or system of bodies remains always the same, except in so far as it receives electrification from, or gives electrification to other bodies.", "why": "It is the first law of electrical phenomena, stated so that a learner can see what 'conservation' means for an isolated system.", "use": [ "lesson", "website" ], "concepts": [ "law/conservation-of-electric-charge", "quantity/electric-charge" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/x-6e5681eae9", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-ii", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 36", "location": "ON THE CHARGES OF ELECTRIFIED BODIES", "latex": "If an electrified body or system of bodies be placed within a closed conducting surface (which may consist of the floor, walls, and ceiling of the room in which the experiment is made), the interior electrification of this surface is equal and opposite to the electrification of the body or system of bodies.", "markdown": "If an electrified body or system of bodies be placed within a closed conducting surface (which may consist of the floor, walls, and ceiling of the room in which the experiment is made), the interior electrification of this surface is equal and opposite to the electrification of the body or system of bodies.", "why": "It makes the induced-charge result concrete by naming the room itself as the enclosing conductor, so a learner can picture the experiment.", "use": [ "lesson" ], "concepts": [ "concept/closed-conducting-surface", "concept/electrification" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/x-34226c5841", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-ii", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 33", "location": "ON THE CHARGES OF ELECTRIFIED BODIES", "latex": "The electrification of the gold leaves when tested is found to be of the \\textit{same} kind as that of the ball.", "markdown": "The electrification of the gold leaves when tested is found to be of the *same* kind as that of the ball.", "why": "It highlights the sign question, that the leaves carry the same kind of charge as the ball in the first part of the experiment, which a learner often gets wrong.", "use": [ "lesson" ], "concepts": [ "concept/negative-electrification", "concept/positive-electrification", "instrument/gold-leaf-electroscope" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/x-8ae2582822", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-ii", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 32", "location": "ON THE CHARGES OF ELECTRIFIED BODIES", "latex": "This statement, which is approximately true for any deep vessel, is rigorously true for a closed vessel.", "markdown": "This statement, which is approximately true for any deep vessel, is rigorously true for a closed vessel.", "why": "It separates the approximate result for open vessels from the exact result for closed ones.", "use": [ "lesson" ], "concepts": [ "concept/closed-conducting-surface", "experiment/faraday-s-ice-pail-experiment", "instrument/electroscope" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/x-e808f1945d", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-ii", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 33", "location": "ON THE CHARGES OF ELECTRIFIED BODIES", "latex": "Their electrification however will be found to be of the \\textit{opposite} kind from that of the ball.", "markdown": "Their electrification however will be found to be of the *opposite* kind from that of the ball.", "why": "It states the surprising outcome that the vessel's charge has the opposite sign once the ball is withdrawn after the vessel has been earthed.", "use": [ "lesson" ], "concepts": [ "concept/negative-electrification", "concept/positive-electrification", "experiment/faraday-s-ice-pail-experiment" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/x-50d930adc1", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-ii", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 33", "location": "ON THE CHARGES OF ELECTRIFIED BODIES", "latex": "Since whatever be the position of the electrified bodies within the vessel its external electrification is the same, it must depend on the total electrification of the bodies within it, and not on the distribution of that electrification.", "markdown": "Since whatever be the position of the electrified bodies within the vessel its external electrification is the same, it must depend on the total electrification of the bodies within it, and not on the distribution of that electrification.", "why": "It shows how an observation leads to the idea that charge is a total, not a pattern.", "use": [ "lesson", "website" ], "concepts": [ "method/comparing-charges", "quantity/electric-charge" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/x-3789e32da9", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-ii", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 34", "location": "ON THE CHARGES OF ELECTRIFIED BODIES", "latex": "When an electrified body is placed within a closed vessel and then put into electrical connection with the vessel, the body is completely discharged.", "markdown": "When an electrified body is placed within a closed vessel and then put into electrical connection with the vessel, the body is completely discharged.", "why": "It gives a clean experimental statement of complete discharge by internal contact.", "use": [ "lesson" ], "concepts": [ "concept/closed-conducting-surface", "method/discharging-a-conductor" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/x-13102932a5", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-ii", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 35", "location": "ON THE CHARGES OF ELECTRIFIED BODIES", "latex": "We have thus a method of comparing the electric charges of different bodies without discharging them, of producing charges equal to that of a given electrified body, and either of the same or of opposite signs, and of adding any number of such charges together.", "markdown": "We have thus a method of comparing the electric charges of different bodies without discharging them, of producing charges equal to that of a given electrified body, and either of the same or of opposite signs, and of adding any number of such charges together.", "why": "It sums up what the vessel experiments achieve: comparing, copying and adding charges.", "use": [ "lesson", "website" ], "concepts": [ "method/charging-a-vessel-with-multiples-of-a-given-charge", "method/comparing-charges", "quantity/electric-charge" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/x-41d0d23337", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-ii", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 36", "location": "ON THE CHARGES OF ELECTRIFIED BODIES", "latex": "In all electrical experiments the electrification of bodies is found to change, but it is always found that this change arises from defective insulation, and that as the means of insulation are improved, the loss of electrification becomes less. We may therefore assert that the electrification of a body cut off from electrical communication with all other bodies by a perfectly insulating medium would remain absolutely constant.", "markdown": "In all electrical experiments the electrification of bodies is found to change, but it is always found that this change arises from defective insulation, and that as the means of insulation are improved, the loss of electrification becomes less. We may therefore assert that the electrification of a body cut off from electrical communication with all other bodies by a perfectly insulating medium would remain absolutely constant.", "why": "It models how a conservation law is inferred from experiments that approach an ideal limit.", "use": [ "lesson", "history" ], "concepts": [ "concept/insulator", "law/conservation-of-electric-charge" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/x-a507850337", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-ii", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 37", "location": "ON THE CHARGES OF ELECTRIFIED BODIES", "latex": "By means of Thomson's Quadrant Electrometer it is easy to measure the electrification of a body when it is a million times less than when charged to an amount convenient for experiment. Hence the experimental evidence for the above statements shews that they cannot be erroneous to the extent of one-millionth of the principal electrifications concerned.", "markdown": "By means of Thomson’s Quadrant Electrometer it is easy to measure the electrification of a body when it is a million times less than when charged to an amount convenient for experiment. Hence the experimental evidence for the above statements shews that they cannot be erroneous to the extent of one-millionth of the principal electrifications concerned.", "why": "It shows how instrument sensitivity sets the precision with which a law is tested.", "use": [ "lesson", "history" ], "concepts": [ "instrument/quadrant-electrometer", "law/conservation-of-electric-charge", "person/william-thomson", "quantity/electric-charge" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/x-55bff8b0ed", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-iii", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 44", "location": "ON ELECTRICAL WORK AND ENERGY", "latex": "Since an electrified system is subject to the law of Conservation of Energy, the work expended in charging it is entirely stored up in the system in the form of electrical energy.", "markdown": "Since an electrified system is subject to the law of Conservation of Energy, the work expended in charging it is entirely stored up in the system in the form of electrical energy.", "why": "It shows how conservation of energy turns the work of charging into stored electrical energy.", "use": [ "lesson", "history" ], "concepts": [ "law/conservation-of-energy", "quantity/electric-energy" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/x-0e4a37480d", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-iii", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 40", "location": "ON ELECTRICAL WORK AND ENERGY", "latex": "If the electrified body is moved in such a way as to remain on the same equipotential surface, no work is done by the electric forces or against them.", "markdown": "If the electrified body is moved in such a way as to remain on the same equipotential surface, no work is done by the electric forces or against them.", "why": "It explains why the electric force is perpendicular to equipotential surfaces, a point learners often find hard to see.", "use": [ "lesson" ], "concepts": [ "concept/equipotential-surface", "quantity/electromotive-force" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/x-571157f51f", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-iii", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 48", "location": "ON ELECTRICAL WORK AND ENERGY", "latex": "There are many such reciprocal relations. They occur in every branch of science, and they often enable us to deduce the solution of new electrical problems from those of simpler problems with which we are already familiar.", "markdown": "There are many such reciprocal relations. They occur in every branch of science, and they often enable us to deduce the solution of new electrical problems from those of simpler problems with which we are already familiar.", "why": "It presents reciprocity as a general method for turning hard problems into easier ones.", "use": [ "history", "lesson" ], "concepts": [ "theorem/reciprocity-of-potentials" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/x-83c4c72316", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-iii", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 39", "location": "ON ELECTRICAL WORK AND ENERGY", "latex": "Thus when a fish has swallowed the angler's hook and swims off, the angler following him for fear his line should break, the fish is doing work against the angler, but when the fish becomes tired and the angler draws him to shore, the angler is doing work against the fish.", "markdown": "Thus when a fish has swallowed the angler’s hook and swims off, the angler following him for fear his line should break, the fish is doing work against the angler, but when the fish becomes tired and the angler draws him to shore, the angler is doing work against the fish.", "why": "A vivid, memorable picture of which side does work when the forces of a system resist or assist a change.", "use": [ "lesson", "website" ], "concepts": [ "concept/energy", "concept/work" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/x-bce7ac4e29", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-iii", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 39", "location": "ON ELECTRICAL WORK AND ENERGY", "latex": "Work is always measured by the product of the change of configuration into the force which resists that change. Thus, when a man lifts a heavy body, the change of configuration is measured by the increase of distance between the body and the earth, and the force which resists it is the weight of the body. The product of these measures the work done by the man. If the man, instead of lifting the heavy body vertically upwards, rolls it up an inclined plane to the same height above the ground, the work done against gravity is precisely the same; for though the heavy body is moved a greater distance, it is only the vertical component of that distance which coincides in direction with the force of gravity acting on the body.", "markdown": "Work is always measured by the product of the change of configuration into the force which resists that change. Thus, when a man lifts a heavy body, the change of configuration is measured by the increase of distance between the body and the earth, and the force which resists it is the weight of the body. The product of these measures the work done by the man. If the man, instead of lifting the heavy body vertically upwards, rolls it up an inclined plane to the same height above the ground, the work done against gravity is precisely the same; for though the heavy body is moved a greater distance, it is only the vertical component of that distance which coincides in direction with the force of gravity acting on the body.", "why": "Gives a concrete worked example of measuring work and shows why only the component along the force counts.", "use": [ "lesson" ], "concepts": [ "concept/work" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/x-6aa340f4db", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-iii", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 38", "location": "ON ELECTRICAL WORK AND ENERGY", "latex": "In fact, this doctrine is the one generalised statement which is found to be consistent with fact, not in one physical science only, but in all. When once apprehended it furnishes to the physical enquirer a principle on which he may hang every known law relating to physical actions, and by which he may be put in the way to discover the relations of such actions in new branches of science.", "markdown": "In fact, this doctrine is the one generalised statement which is found to be consistent with fact, not in one physical science only, but in all. When once apprehended it furnishes to the physical enquirer a principle on which he may hang every known law relating to physical actions, and by which he may be put in the way to discover the relations of such actions in new branches of science.", "why": "Explains why conservation of energy matters across all of science, in Maxwell's own phrasing.", "use": [ "website", "history" ], "concepts": [ "law/conservation-of-energy" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/x-d7a6135267", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-iii", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 40", "location": "ON ELECTRICAL WORK AND ENERGY", "latex": "\\textit{The electric potential at a given point of the field is measured by the amount of work which must be done by an external agent in carrying one unit of positive electricity from a place where the potential is zero to the given point.}", "markdown": "*The electric potential at a given point of the field is measured by the amount of work which must be done by an external agent in carrying one unit of positive electricity from a place where the potential is zero to the given point.*", "why": "States potential as work per unit charge, the working definition a learner needs.", "use": [ "lesson", "website" ], "concepts": [ "concept/work", "quantity/electric-potential" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/x-84f53cfdb2", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-iii", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 40", "location": "ON ELECTRICAL WORK AND ENERGY", "latex": "Hence the magnitude of the electric force may be found by dividing the difference of the potentials of two neighbouring equipotential surfaces by the distance between them, the distance being, of course, very small, and measured perpendicularly to either surface.", "markdown": "Hence the magnitude of the electric force may be found by dividing the difference of the potentials of two neighbouring equipotential surfaces by the distance between them, the distance being, of course, very small, and measured perpendicularly to either surface.", "why": "Shows how to get the strength of the electric force from potential differences and distance.", "use": [ "lesson" ], "concepts": [ "concept/equipotential-surface", "quantity/electric-potential", "quantity/electromotive-force" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/x-3c9d9afd10", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-iii", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 42", "location": "ON ELECTRICAL WORK AND ENERGY", "latex": "By increasing without limit the number of equal parts into which the charge is divided, the breadth of the parallelograms will be diminished without limit. In the limit, therefore, the difference of the two values of the work vanishes, and either value becomes ultimately equal to the area \\(CAFGHBD\\), bounded by the curve, the extreme ordinates, and the base line.", "markdown": "By increasing without limit the number of equal parts into which the charge is divided, the breadth of the parallelograms will be diminished without limit. In the limit, therefore, the difference of the two values of the work vanishes, and either value becomes ultimately equal to the area CAFGHBD, bounded by the curve, the extreme ordinates, and the base line.", "why": "Shows the squeeze between lower and upper sums that turns work into an area, an early picture of integration.", "use": [ "lesson" ], "concepts": [ "concept/indicator-diagram", "concept/limit", "theorem/work-done-in-charging-a-conductor" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/x-306183a6ed", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-iii", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 48", "location": "ON ELECTRICAL WORK AND ENERGY", "latex": "This is the first instance we have met with of the \\textit{reciprocal} relation of two bodies. There are many such reciprocal relations. They occur in every branch of science, and they often enable us to deduce the solution of new electrical problems from those of simpler problems with which we are already familiar.", "markdown": "This is the first instance we have met with of the *reciprocal* relation of two bodies. There are many such reciprocal relations. They occur in every branch of science, and they often enable us to deduce the solution of new electrical problems from those of simpler problems with which we are already familiar.", "why": "Tells the learner why reciprocity is useful: a solved problem gives a solution to its mirror image.", "use": [ "lesson", "website" ], "concepts": [ "theorem/reciprocity-of-potentials" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/x-a8403d00af", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-iii", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 51", "location": "ON ELECTRICAL WORK AND ENERGY", "latex": "Hence, when the potential of each conductor is maintained constant during a displacement in which a quantity of work, \\(W\\), is done, the voltaic batteries which are employed to keep the potentials constant must do an amount of work equal to \\(2W\\). Of this energy supplied to the system, half is spent in increasing the energy of the system, and the other half appears as mechanical work.", "markdown": "Hence, when the potential of each conductor is maintained constant during a displacement in which a quantity of work, W, is done, the voltaic batteries which are employed to keep the potentials constant must do an amount of work equal to 2W. Of this energy supplied to the system, half is spent in increasing the energy of the system, and the other half appears as mechanical work.", "why": "A surprising energy-accounting result: holding potential constant means the batteries supply twice the mechanical work.", "use": [ "lesson" ], "concepts": [ "instrument/voltaic-battery", "law/conservation-of-energy", "theorem/work-done-in-displacing-conductors-at-constant-potential" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/x-5fe580a502", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-iv", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 52", "location": "THE ELECTRIC FIELD", "latex": "Finally, when we contemplate the region occupied by the medium as being a part of space in which electric phenomena may be observed, we shall call this region the Electric Field.", "markdown": "Finally, when we contemplate the region occupied by the medium as being a part of space in which electric phenomena may be observed, we shall call this region the Electric Field.", "why": "It gives a clear definition of the electric field as a region of space rather than an object.", "use": [ "lesson", "website" ], "concepts": [ "concept/dielectric", "concept/electric-field" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/x-059299b19c", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-iv", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 53", "location": "THE ELECTRIC FIELD", "latex": "Since, therefore, the force which acts on the ball depends partly on the charge of the ball and partly on its position and on the electrification of the system, it is convenient to regard this force as the product of two factors, one being the charge of the ball, and the other \\textit{the electromotive force at that point of the field which is occupied by the centre of the ball}.", "markdown": "Since, therefore, the force which acts on the ball depends partly on the charge of the ball and partly on its position and on the electrification of the system, it is convenient to regard this force as the product of two factors, one being the charge of the ball, and the other *the electromotive force at that point of the field which is occupied by the centre of the ball*.", "why": "It shows the learner why the field strength is defined separately from the charge that feels it.", "use": [ "lesson" ], "concepts": [ "concept/electrification", "quantity/electromotive-force" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/x-3190a27d3d", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-iv", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 54", "location": "THE ELECTRIC FIELD", "latex": "This shews that there has been an actual transference of electricity from the one disk to the other, the direction of this transference being that of the electromotive force.", "markdown": "This shews that there has been an actual transference of electricity from the one disk to the other, the direction of this transference being that of the electromotive force.", "why": "It links a measurable transfer of charge directly to the direction of the field.", "use": [ "lesson" ], "concepts": [ "concept/electrification", "quantity/electromotive-force" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/x-5ec99e2ae0", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-iv", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 55", "location": "THE ELECTRIC FIELD", "latex": "The force with which they tend to separate is proportional to the area of the disks, and it increases as the electromotive force increases, not, however, in the simple ratio of that force, but in the ratio of the square of the electromotive force.", "markdown": "The force with which they tend to separate is proportional to the area of the disks, and it increases as the electromotive force increases, not, however, in the simple ratio of that force, but in the ratio of the square of the electromotive force.", "why": "It warns learners that the mechanical force grows as the square of the field, not linearly.", "use": [ "lesson" ], "concepts": [ "concept/electric-tension", "quantity/electromotive-force" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/x-6e9055148e", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-iv", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 56", "location": "THE ELECTRIC FIELD", "latex": "The fact that the electromotive force at a point close to the surface of a conductor is perpendicular to the surface and proportional to the density of the electrification at that point was first established experimentally by Coulomb, and it is generally referred to as Coulomb's Law.", "markdown": "The fact that the electromotive force at a point close to the surface of a conductor is perpendicular to the surface and proportional to the density of the electrification at that point was first established experimentally by Coulomb, and it is generally referred to as Coulomb’s Law.", "why": "It names the law, states its two parts, and credits its experimental origin.", "use": [ "lesson", "history" ], "concepts": [ "law/coulomb-s-law", "quantity/electromotive-force", "quantity/surface-charge-density" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/x-6bf5d06fa9", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-iv", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 58", "location": "THE ELECTRIC FIELD", "latex": "All these points lie on a certain surface, which is called an equipotential surface. On one side of this surface the potential is higher, on the other it is lower, than at the surface itself.", "markdown": "All these points lie on a certain surface, which is called an equipotential surface. On one side of this surface the potential is higher, on the other it is lower, than at the surface itself.", "why": "It explains how equipotential surfaces arise from points of equal potential, the basis for mapping a field.", "use": [ "lesson" ], "concepts": [ "concept/equipotential-surface", "quantity/electric-potential" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/x-b2c0669ac6", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-iv", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 60", "location": "THE ELECTRIC FIELD", "latex": "A line of force in every part of its course passes from places of higher to places of lower potential.", "markdown": "A line of force in every part of its course passes from places of higher to places of lower potential.", "why": "It gives the direction rule that ties lines of force to falling potential.", "use": [ "lesson", "website" ], "concepts": [ "concept/line-of-electric-force", "quantity/electric-potential" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/x-67f7c95606", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-iv", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 52", "location": "THE ELECTRIC FIELD", "latex": "In every case, wherever we find an electrified insulated body, we are sure to find at the boundaries of the insulating medium, wherever they may be, an equal amount of electrification of the opposite kind.", "markdown": "In every case, wherever we find an electrified insulated body, we are sure to find at the boundaries of the insulating medium, wherever they may be, an equal amount of electrification of the opposite kind.", "why": "Shows why attention shifts from the charged bodies to the medium between them.", "use": [ "lesson", "website" ], "concepts": [ "concept/dielectric", "concept/electric-field" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/x-a1d52e74bb", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-iv", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 52", "location": "THE ELECTRIC FIELD", "latex": "We call it an \\textit{insulating} medium when we regard it simply as retaining the charge on the surface of the electrified body. When we consider it as taking an important part in the manifestation of electric phenomena we shall use Faraday's expression, and call it a \\textit{dielectric} medium. Finally, when we contemplate the region occupied by the medium as being a part of space in which electric phenomena may be observed, we shall call this region the Electric Field.", "markdown": "We call it an *insulating* medium when we regard it simply as retaining the charge on the surface of the electrified body. When we consider it as taking an important part in the manifestation of electric phenomena we shall use Faraday’s expression, and call it a *dielectric* medium. Finally, when we contemplate the region occupied by the medium as being a part of space in which electric phenomena may be observed, we shall call this region the Electric Field.", "why": "Separates three names for the same space, each stressing a different way of thinking about it.", "use": [ "lesson", "history" ], "concepts": [ "concept/dielectric", "concept/electric-field" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/x-d75087b88c", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-iv", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 54", "location": "THE ELECTRIC FIELD", "latex": "The measurement of small forces is always a difficult operation, and becomes almost impossible when the weight of the body acted on forms a disturbing force and has to be got rid of by the adjustment of counterpoises. The measurement of the charges of the disks, on the other hand, is much more simple.", "markdown": "The measurement of small forces is always a difficult operation, and becomes almost impossible when the weight of the body acted on forms a disturbing force and has to be got rid of by the adjustment of counterpoises. The measurement of the charges of the disks, on the other hand, is much more simple.", "why": "Explains why a good experimenter prefers measuring charges to measuring tiny forces.", "use": [ "lesson" ], "concepts": [ "experiment/exploring-the-field-with-two-disks", "quantity/electromotive-force" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/x-40fcd7b44a", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-iv", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 55", "location": "THE ELECTRIC FIELD", "latex": "The electrification of each disk is proportional to the electromotive force, and the mechanical force on the disk is proportional to its electrification and the electromotive force conjointly, that is, to the \\textit{square} of the electromotive force.", "markdown": "The electrification of each disk is proportional to the electromotive force, and the mechanical force on the disk is proportional to its electrification and the electromotive force conjointly, that is, to the *square* of the electromotive force.", "why": "Gives the reasoning behind the square law for electric tension.", "use": [ "lesson" ], "concepts": [ "concept/electric-tension", "quantity/electromotive-force" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/x-6d6c074272", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-iv", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 56", "location": "THE ELECTRIC FIELD", "latex": "Let \\(e\\) be the electrification of the first sphere, and let the charge removed by the segment be \\(ne\\), then the charge remaining on the sphere is \\((1 - n)e\\). The charge of the first sphere is then divided with the second sphere, and becomes \\(\\tstrut\\frac{1}{2}(1 - n)e\\).", "markdown": "Let e be the electrification of the first sphere, and let the charge removed by the segment be ne, then the charge remaining on the sphere is (1 - n)e. The charge of the first sphere is then divided with the second sphere, and becomes [-1.5ex]0pt4.2ex12(1 - n)e.", "why": "Begins a worked example where repeated halving of charge turns a null result into a proof.", "use": [ "lesson" ], "concepts": [ "experiment/proof-plane-segment-and-spheres-experiment", "instrument/coulomb-s-proof-plane" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/x-5529ee5480", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-iv", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 57", "location": "THE ELECTRIC FIELD", "latex": "A convenient way of determining the direction of the electromotive force is to suspend a small elongated conductor with its middle point at the given point of the field. The two ends of the short conductor will become oppositely electrified, and will then be drawn in opposite directions by the electromotive force, so that the axis of the conductor will place itself in the direction of the force at that point.", "markdown": "A convenient way of determining the direction of the electromotive force is to suspend a small elongated conductor with its middle point at the given point of the field. The two ends of the short conductor will become oppositely electrified, and will then be drawn in opposite directions by the electromotive force, so that the axis of the conductor will place itself in the direction of the force at that point.", "why": "Shows how a simple thread can reveal the direction of an invisible force.", "use": [ "lesson", "website" ], "concepts": [ "concept/electric-field", "quantity/electromotive-force" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/x-db1620b383", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-iv", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 57", "location": "THE ELECTRIC FIELD", "latex": "Place one of the spheres at a fixed point, and move the other about till, on connecting the spheres with a wire as before, no charge is found on either sphere. The potentials of the field at the points occupied by the centres of the spheres must now be the same.", "markdown": "Place one of the spheres at a fixed point, and move the other about till, on connecting the spheres with a wire as before, no charge is found on either sphere. The potentials of the field at the points occupied by the centres of the spheres must now be the same.", "why": "Shows how equal potential is found by a null test: no charge flows, so the potentials match.", "use": [ "lesson" ], "concepts": [ "concept/equipotential-surface", "method/determining-equipotential-surfaces-with-an-exploring-sphere", "quantity/electric-potential" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/x-7ac03379f6", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-iv", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 60", "location": "THE ELECTRIC FIELD", "latex": "Since the electric force is everywhere perpendicular to the equipotential surfaces, the lines of force cut these surfaces everywhere at right angles. The lines of force which meet the surface of a conductor are therefore at right angles to it.", "markdown": "Since the electric force is everywhere perpendicular to the equipotential surfaces, the lines of force cut these surfaces everywhere at right angles. The lines of force which meet the surface of a conductor are therefore at right angles to it.", "why": "Links lines of force to equipotential surfaces, which helps in reading field diagrams.", "use": [ "lesson", "website" ], "concepts": [ "concept/conductor", "concept/equipotential-surface", "concept/line-of-electric-force" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/x-218d927df8", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-v", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 61", "location": "FARADAY'S LAW OF LINES OF INDUCTION", "latex": "If we consider a portion of an electrified surface as cut off from the rest by the bounding line which surrounds it, and if from every point of this bounding line we draw a line of force, producing it till it meets the surface of some other body in a point which is said to \\textit{correspond} to the point of the body from which the line was drawn, these lines will form a tubular surface, and will cut off a certain portion from the surface of the other body corresponding to the portion of the surface of the first body, and the total electrifications of the two corresponding portions are equal in numerical magnitude but opposite in kind.", "markdown": "If we consider a portion of an electrified surface as cut off from the rest by the bounding line which surrounds it, and if from every point of this bounding line we draw a line of force, producing it till it meets the surface of some other body in a point which is said to *correspond* to the point of the body from which the line was drawn, these lines will form a tubular surface, and will cut off a certain portion from the surface of the other body corresponding to the portion of the surface of the first body, and the total electrifications of the two corresponding portions are equal in numerical magnitude but opposite in kind.", "why": "It states Faraday's law of lines of induction in one sentence, which a learner can check against the tube picture that follows.", "use": [ "lesson" ], "concepts": [ "concept/electrification", "concept/line-of-electric-force", "law/faraday-s-law-of-lines-of-induction" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/x-da33720093", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-v", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 62", "location": "FARADAY'S LAW OF LINES OF INDUCTION", "latex": "A system of lines of force forming a tubular surface closed at the one end by a portion of the positively electrified surface and at the other by the corresponding portion of the negative surface, is called by Faraday a \\textit{Tube of Induction}, because electric induction, according to Faraday, is that condition of the dielectric by which the electrifications of the opposed surfaces are placed in that physical relation to one another, which we express by saying that their electrifications are equal and opposite.", "markdown": "A system of lines of force forming a tubular surface closed at the one end by a portion of the positively electrified surface and at the other by the corresponding portion of the negative surface, is called by Faraday a *Tube of Induction*, because electric induction, according to Faraday, is that condition of the dielectric by which the electrifications of the opposed surfaces are placed in that physical relation to one another, which we express by saying that their electrifications are equal and opposite.", "why": "It gives the name and the physical meaning of the tube of induction in the terms a learner needs to picture it.", "use": [ "lesson" ], "concepts": [ "concept/dielectric", "concept/electric-induction", "concept/tube-of-induction" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/x-0bb1f8ee2d", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-v", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 67", "location": "FARADAY'S LAW OF LINES OF INDUCTION", "latex": "The similarity which constitutes the analogy is not between the phenomena themselves, but between the relations of these phenomena.", "markdown": "The similarity which constitutes the analogy is not between the phenomena themselves, but between the relations of these phenomena.", "why": "It gives the single rule a learner must hold when using an analogy between two physical subjects.", "use": [ "lesson" ], "concepts": [ "concept/physical-analogy" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/x-199a25977a", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-v", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 63", "location": "FARADAY'S LAW OF LINES OF INDUCTION", "latex": "Hence in this simple case the number of cells is double the number of units of energy in the system.", "markdown": "Hence in this simple case the number of cells is double the number of units of energy in the system.", "why": "It states the cell-counting result that leads to the idea of energy stored in the dielectric.", "use": [ "lesson" ], "concepts": [ "concept/unit-cell", "quantity/electric-energy" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/x-6c5a5458a8", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-v", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 73", "location": "FARADAY'S LAW OF LINES OF INDUCTION", "latex": "It follows from (2) that the potential at the beginning of a tube is higher than at the end of it. Hence, no tube can return into itself, for in that case the same point would have two different potentials, which is impossible.", "markdown": "It follows from (2) that the potential at the beginning of a tube is higher than at the end of it. Hence, no tube can return into itself, for in that case the same point would have two different potentials, which is impossible.", "why": "It shows a learner how the direction of potential rules out closed tubes of induction, a common point of confusion.", "use": [ "lesson" ], "concepts": [ "concept/line-of-electric-force", "concept/tube-of-induction", "quantity/electric-potential" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/x-9584a2e9d6", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-v", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 77", "location": "FARADAY'S LAW OF LINES OF INDUCTION", "latex": "The boundary between these two regions forms what is called the neutral line, the form and position of which depend on the form and position of \\(A\\) and \\(B\\).", "markdown": "The boundary between these two regions forms what is called the neutral line, the form and position of which depend on the form and position of A and B.", "why": "It names the boundary where the surface charge changes sign and shows that its shape depends on the geometry of both bodies.", "use": [ "lesson", "website" ], "concepts": [ "concept/neutral-line", "quantity/surface-charge-density" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/x-796308f33a", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-v", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 76", "location": "FARADAY'S LAW OF LINES OF INDUCTION", "latex": "Under the action of the inductor \\(B\\) part of its surface, on the side next to \\(B\\), will become electrified oppositely to \\(B\\); but since the algebraic sum of its electrification is zero, some other part of its surface must be electrified similarly to \\(B\\).", "markdown": "Under the action of the inductor B part of its surface, on the side next to B, will become electrified oppositely to B; but since the algebraic sum of its electrification is zero, some other part of its surface must be electrified similarly to B.", "why": "It explains why an insulated body near a charge carries charges of both signs, which is the core idea of induction.", "use": [ "lesson", "website" ], "concepts": [ "concept/electric-induction", "concept/induced-electrification-of-the-second-species" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/x-3cd99de070", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-v", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 74", "location": "FARADAY'S LAW OF LINES OF INDUCTION", "latex": "\\textit{If the same system is electrified in three different ways, then if the potential at any point in the third case is the sum of the potentials in the first and second cases, the electrification of any part of the system in the third case will be the sum of the electrifications of the same part in the first and second cases.}", "markdown": "*If the same system is electrified in three different ways, then if the potential at any point in the third case is the sum of the potentials in the first and second cases, the electrification of any part of the system in the third case will be the sum of the electrifications of the same part in the first and second cases.*", "why": "States the principle of superposition in full and precisely.", "use": [ "lesson", "website" ], "concepts": [ "law/superposition-of-electric-effects", "quantity/electric-potential" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/x-72ae084f7c", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-v", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 74", "location": "FARADAY'S LAW OF LINES OF INDUCTION", "latex": "If the electric field under consideration consist of a finite portion of a dielectric medium, and if at every point of the boundary of this region the potential is given, and if the distribution of electrification within the region be also given, then the potential at any point within the region can have one and only one value consistent with these conditions.", "markdown": "If the electric field under consideration consist of a finite portion of a dielectric medium, and if at every point of the boundary of this region the potential is given, and if the distribution of electrification within the region be also given, then the potential at any point within the region can have one and only one value consistent with these conditions.", "why": "Gives the uniqueness theorem that the rest of the chapter relies on.", "use": [ "lesson", "website" ], "concepts": [ "theorem/uniqueness-theorem-for-electric-potential" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/x-2d00c81bfc", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-v", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 75", "location": "FARADAY'S LAW OF LINES OF INDUCTION", "latex": "If in any case we can find a distribution of potential which satisfies the given conditions, then by this theorem we are assured that this distribution is the only possible solution of the problem. Hence the importance of this theorem in the theory of electricity.", "markdown": "If in any case we can find a distribution of potential which satisfies the given conditions, then by this theorem we are assured that this distribution is the only possible solution of the problem. Hence the importance of this theorem in the theory of electricity.", "why": "Shows why uniqueness matters: any solution you find is the solution.", "use": [ "lesson", "website" ], "concepts": [ "theorem/uniqueness-theorem-for-electric-potential" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/x-2db70327d4", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-v", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 75", "location": "FARADAY'S LAW OF LINES OF INDUCTION", "latex": "Hence the potential at every point outside of \\(B\\) \\textit{may}, consistently with the conditions, be the same as before. By our theorem, therefore, the potential at every point outside \\(B\\) \\textit{must} be the same, when, instead of the body \\(A\\), we have a conducting surface \\(B\\), raised to the potential \\(P\\).", "markdown": "Hence the potential at every point outside of B *may*, consistently with the conditions, be the same as before. By our theorem, therefore, the potential at every point outside B *must* be the same, when, instead of the body A, we have a conducting surface B, raised to the potential P.", "why": "Shows the move from 'may be' to 'must be' that uniqueness allows.", "use": [ "lesson" ], "concepts": [ "concept/equipotential-surface", "theorem/thomson-s-theorem", "theorem/uniqueness-theorem-for-electric-potential" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/x-0fc09cd76a", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-v", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 75", "location": "FARADAY'S LAW OF LINES OF INDUCTION", "latex": "The charge of every part of the surface of a conductor is of the same sign as its potential, unless there is another body in the field whose potential is of the same sign but numerically greater.", "markdown": "The charge of every part of the surface of a conductor is of the same sign as its potential, unless there is another body in the field whose potential is of the same sign but numerically greater.", "why": "Gives a rule for the sign of surface charge, with its exception.", "use": [ "lesson" ], "concepts": [ "quantity/electric-charge", "quantity/electric-potential", "theorem/sign-of-surface-charge-follows-potential" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/x-ea5c793bc6", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-v", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 76", "location": "FARADAY'S LAW OF LINES OF INDUCTION", "latex": "If an uninsulated conductor is placed in the same field with a charged conductor, the charge on every part of the surface of the uninsulated conductor is of the opposite sign to the charge of the charged conductor.", "markdown": "If an uninsulated conductor is placed in the same field with a charged conductor, the charge on every part of the surface of the uninsulated conductor is of the opposite sign to the charge of the charged conductor.", "why": "States the result for an earthed conductor near a charged one, which the following argument proves.", "use": [ "lesson" ], "concepts": [ "concept/induced-electrification-of-the-first-species", "concept/inductor", "concept/line-of-electric-force" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/x-56416d81c9", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-v", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 76", "location": "FARADAY'S LAW OF LINES OF INDUCTION", "latex": "Next, let us suppose that the body, \\(A\\), instead of being uninsulated is insulated, but originally without charge. Under the action of the inductor \\(B\\) part of its surface, on the side next to \\(B\\), will become electrified oppositely to \\(B\\); but since the algebraic sum of its electrification is zero, some other part of its surface must be electrified similarly to \\(B\\).", "markdown": "Next, let us suppose that the body, A, instead of being uninsulated is insulated, but originally without charge. Under the action of the inductor B part of its surface, on the side next to B, will become electrified oppositely to B; but since the algebraic sum of its electrification is zero, some other part of its surface must be electrified similarly to B.", "why": "Explains why an insulated, uncharged body has charge of both signs on its surface.", "use": [ "lesson", "website" ], "concepts": [ "concept/induced-electrification-of-the-second-species", "concept/inductor", "concept/neutral-line" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/x-44420f9031", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-v", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 63", "location": "FARADAY'S LAW OF LINES OF INDUCTION", "latex": "We have seen that the electric field is divided by the equipotential surfaces into a series of shells, like the coats of an onion, the thickness of each shell at any point being inversely as the electric force at that point.", "markdown": "We have seen that the electric field is divided by the equipotential surfaces into a series of shells, like the coats of an onion, the thickness of each shell at any point being inversely as the electric force at that point.", "why": "The onion-shell picture gives a learner a concrete image of equipotential surfaces and of how their spacing shows the strength of the force.", "use": [ "lesson", "website" ], "concepts": [ "concept/electric-field", "concept/equipotential-surface" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/x-a5bd52aeb9", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-v", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 62", "location": "FARADAY'S LAW OF LINES OF INDUCTION", "latex": "By an imaginary surface is meant a surface which has no physical existence, but which may be imagined to exist in space without interfering with the physical properties of the substance which occupies that space. Thus we may imagine a vertical plane dividing a man's head longitudinally into two equal parts, and by means of this imaginary surface we may render our ideas of the form of his head more precise, though any attempt to convert this imaginary surface into a physical one would be criminal.", "markdown": "By an imaginary surface is meant a surface which has no physical existence, but which may be imagined to exist in space without interfering with the physical properties of the substance which occupies that space. Thus we may imagine a vertical plane dividing a man’s head longitudinally into two equal parts, and by means of this imaginary surface we may render our ideas of the form of his head more precise, though any attempt to convert this imaginary surface into a physical one would be criminal.", "why": "A vivid, humorous example shows why we may draw surfaces in thought to count tubes or flows without disturbing anything.", "use": [ "lesson", "website" ], "concepts": [ "concept/imaginary-surface" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/x-dfb160d6f5", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-v", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 64", "location": "FARADAY'S LAW OF LINES OF INDUCTION", "latex": "This remarkable correspondence between the number of cells into which the tubes of induction are cut by the equipotential surfaces, and the electrical energy of the system, leads us to enquire whether the electrical energy may not have its true seat in the dielectric medium which is thus cut up into cells, each cell being a portion of the medium in which half a unit of energy is stored up.", "markdown": "This remarkable correspondence between the number of cells into which the tubes of induction are cut by the equipotential surfaces, and the electrical energy of the system, leads us to enquire whether the electrical energy may not have its true seat in the dielectric medium which is thus cut up into cells, each cell being a portion of the medium in which half a unit of energy is stored up.", "why": "It shows how a counting result prompts the idea that energy is stored in the medium between charged bodies.", "use": [ "lesson", "history" ], "concepts": [ "concept/dielectric", "concept/unit-cell", "quantity/electric-energy" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/x-a0e2373410", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-v", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 65", "location": "FARADAY'S LAW OF LINES OF INDUCTION", "latex": "It is probable that the actual motion of displacement is exceedingly small, in which case we must suppose the quantity of electricity in a cubic inch of the medium to be exceedingly great. If this is really the case the actual velocity of electricity in a telegraph wire may be very small, less, say, than the hundredth of an inch in an hour, though the signals which it transmits may be propagated with great velocity.", "markdown": "It is probable that the actual motion of displacement is exceedingly small, in which case we must suppose the quantity of electricity in a cubic inch of the medium to be exceedingly great. If this is really the case the actual velocity of electricity in a telegraph wire may be very small, less, say, than the hundredth of an inch in an hour, though the signals which it transmits may be propagated with great velocity.", "why": "It separates how fast a signal travels from how far the electricity itself moves, and shows the author hedging with 'probable'.", "use": [ "lesson", "history" ], "concepts": [ "concept/electric-current", "concept/electric-displacement" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/x-1493b3e287", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-v", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 67", "location": "FARADAY'S LAW OF LINES OF INDUCTION", "latex": "To begin with a case of extreme simplicity;---a person slow at arithmetic having to find the price of 52 yards of cotton at 7 pence a yard, if he happened to remember that there are 52 weeks and a day in a year of 365 days, might at once give the answer, 364 pence, without performing the calculation. Here there is no resemblance whatever between the quantities themselves---the weeks and the yards of cotton,---the sole resemblance is between the arithmetical relations of these quantities to others in the same question.", "markdown": "To begin with a case of extreme simplicity;---a person slow at arithmetic having to find the price of 52 yards of cotton at 7 pence a yard, if he happened to remember that there are 52 weeks and a day in a year of 365 days, might at once give the answer, 364 pence, without performing the calculation. Here there is no resemblance whatever between the quantities themselves---the weeks and the yards of cotton,---the sole resemblance is between the arithmetical relations of these quantities to others in the same question.", "why": "A homely arithmetic example makes clear that an analogy is a likeness of relations, not of things.", "use": [ "lesson", "website" ], "concepts": [ "concept/physical-analogy" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/x-0b1bbd7e3b", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-v", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 68", "location": "FARADAY'S LAW OF LINES OF INDUCTION", "latex": "We must not conclude from the partial similarity of some of the relations of the phenomena of heat and electricity that there is any real physical similarity between the causes of these phenomena. The similarity is a similarity between relations, not a similarity between the things related.", "markdown": "We must not conclude from the partial similarity of some of the relations of the phenomena of heat and electricity that there is any real physical similarity between the causes of these phenomena. The similarity is a similarity between relations, not a similarity between the things related.", "why": "It warns learners against over-reading an analogy, which is a common mistake.", "use": [ "lesson", "website" ], "concepts": [ "concept/electrostatics-heat-analogy", "concept/physical-analogy" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/x-55ce425952", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-v", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 69", "location": "FARADAY'S LAW OF LINES OF INDUCTION", "latex": "`I went into this cube,' he says, `and lived in it, but though I used lighted candles, electrometers, and all other tests of electrical states, I could not find the least influence upon them, or indication of anything particular given by them, though all the time the outside of the cube was powerfully charged and large sparks and brushes were starting off from every part of its outer surface.'", "markdown": "‘I went into this cube,’ he says, ‘and lived in it, but though I used lighted candles, electrometers, and all other tests of electrical states, I could not find the least influence upon them, or indication of anything particular given by them, though all the time the outside of the cube was powerfully charged and large sparks and brushes were starting off from every part of its outer surface.’", "why": "Faraday's first-hand account of living in a charged cube shows vividly that potential changes alone have no physical effect.", "use": [ "lesson", "website", "history" ], "concepts": [ "concept/conductor", "experiment/faraday-s-cube-experiment", "quantity/electric-potential" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/x-937e72bab9", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-vi", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 80", "location": "PARTICULAR CASES OF ELECTRIFICATION", "latex": "\\textit{Definition}.---The electric or electromotive force at a point is the force which would be experienced by a small body charged with the unit of positive electricity and placed at that point, the electrification of the system being supposed to remain undisturbed by the presence of this unit of electricity.", "markdown": "*Definition*.---The electric or electromotive force at a point is the force which would be experienced by a small body charged with the unit of positive electricity and placed at that point, the electrification of the system being supposed to remain undisturbed by the presence of this unit of electricity.", "why": "It gives the learner a precise operational meaning of electric force before any formula is used.", "use": [ "lesson" ], "concepts": [ "quantity/electromotive-force" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/x-dfe6e79875", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-vi", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 79", "location": "PARTICULAR CASES OF ELECTRIFICATION", "latex": "Hence the idea of an electrified point is a mere mathematical fiction which can never be realised in nature.", "markdown": "Hence the idea of an electrified point is a mere mathematical fiction which can never be realised in nature.", "why": "It warns learners that the point-charge idealisation is a useful model and not a physical object.", "use": [ "lesson" ], "concepts": [ "concept/electrification" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/x-240d7a8fd9", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-vi", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 92", "location": "PARTICULAR CASES OF ELECTRIFICATION", "latex": "But in the vulgar language of the time when dynamical science was unknown, all the words relating to exertion, such as force, energy, power, \\&c., were confounded with each other, though some of the schoolmen endeavoured to introduce a greater precision into their language.", "markdown": "But in the vulgar language of the time when dynamical science was unknown, all the words relating to exertion, such as force, energy, power, &c., were confounded with each other, though some of the schoolmen endeavoured to introduce a greater precision into their language.", "why": "It shows how the everyday sense of force differs from the physicist's, which helps learners separate force, energy and power.", "use": [ "history", "website" ], "concepts": [ "quantity/electromotive-force" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/x-d3817b9374", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-vi", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 84", "location": "PARTICULAR CASES OF ELECTRIFICATION", "latex": "Now the electric capacity of a body in a given field is measured by the charge which raises its potential to unity. Hence the electric capacity of a conducting sphere placed in air at a considerable distance from any other conductor is numerically equal to the radius of the sphere.", "markdown": "Now the electric capacity of a body in a given field is measured by the charge which raises its potential to unity. Hence the electric capacity of a conducting sphere placed in air at a considerable distance from any other conductor is numerically equal to the radius of the sphere.", "why": "It gives a concrete, checkable case of capacity that learners can work through with a sphere.", "use": [ "lesson" ], "concepts": [ "quantity/capacity", "quantity/electric-potential" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/x-deb06d63a6", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-vi", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 80", "location": "PARTICULAR CASES OF ELECTRIFICATION", "latex": "or the electric force close to the surface of an electrified sphere is at right angles to the surface and is equal to the surface-density multiplied by \\(4 \\pi\\).", "markdown": "or the electric force close to the surface of an electrified sphere is at right angles to the surface and is equal to the surface-density multiplied by 4 .", "why": "It states the link between surface density and force at a conductor's surface in one memorable result.", "use": [ "lesson" ], "concepts": [ "quantity/electromotive-force", "quantity/surface-charge-density" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/x-228b4a1c97", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-vi", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 91", "location": "PARTICULAR CASES OF ELECTRIFICATION", "latex": "This circle is an example of a line of equilibrium, for the resultant force vanishes at every point of this line.", "markdown": "This circle is an example of a line of equilibrium, for the resultant force vanishes at every point of this line.", "why": "It shows a striking case where opposing charges cancel the force along a whole curve, which invites visual exploration.", "use": [ "website" ], "concepts": [ "quantity/electromotive-force" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/x-7fb3c4dd6e", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-vi", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 85", "location": "PARTICULAR CASES OF ELECTRIFICATION", "latex": "The smaller the distance between the surfaces and the greater the area of the surfaces, the greater the capacity of the jar.", "markdown": "The smaller the distance between the surfaces and the greater the area of the surfaces, the greater the capacity of the jar.", "why": "It states the design rule behind the Leyden jar in plain terms that a learner can test with a model.", "use": [ "lesson" ], "concepts": [ "instrument/leyden-jar", "quantity/capacity" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/x-8fd8eccd6a", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-vi", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 93", "location": "PARTICULAR CASES OF ELECTRIFICATION", "latex": "Now the quantity of electricity in a body is measured, according to Faraday's ideas, by the \\textit{number} of lines of force, or rather of induction, which proceed from it. These lines of force must all terminate somewhere, either on bodies in the neighbourhood, or on the walls and roof of the room, or on the earth, or on the heavenly bodies, and wherever they terminate there is a quantity of electricity exactly equal and opposite to that on the part of the body from which they proceeded.", "markdown": "Now the quantity of electricity in a body is measured, according to Faraday’s ideas, by the *number* of lines of force, or rather of induction, which proceed from it. These lines of force must all terminate somewhere, either on bodies in the neighbourhood, or on the walls and roof of the room, or on the earth, or on the heavenly bodies, and wherever they terminate there is a quantity of electricity exactly equal and opposite to that on the part of the body from which they proceeded.", "why": "A vivid picture of charge as counted lines of force that end on equal and opposite charge elsewhere.", "use": [ "website", "history", "lesson" ], "concepts": [ "concept/line-of-electric-force", "person/michael-faraday", "quantity/electric-charge" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/x-62582858e7", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-vi", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 79", "location": "PARTICULAR CASES OF ELECTRIFICATION", "latex": "We must bear in mind, however, that it is physically impossible to charge the small sphere with more than a certain quantity of electricity on each unit of area of its surface. If the surface-density exceed this limit, electricity will fly off in the form of the brush discharge. Hence the idea of an electrified point is a mere mathematical fiction which can never be realised in nature.", "markdown": "We must bear in mind, however, that it is physically impossible to charge the small sphere with more than a certain quantity of electricity on each unit of area of its surface. If the surface-density exceed this limit, electricity will fly off in the form of the brush discharge. Hence the idea of an electrified point is a mere mathematical fiction which can never be realised in nature.", "why": "Warns a learner that the point charge is an idealisation, and says why a real conductor cannot be shrunk to a point.", "use": [ "lesson", "website" ], "concepts": [ "concept/electrical-image", "quantity/surface-charge-density" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/x-57561648de", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-vi", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 79", "location": "PARTICULAR CASES OF ELECTRIFICATION", "latex": "If we suppose the radius of the inner sphere to become very small till at last the sphere cannot be distinguished from a point, we may imagine the whole charge concentrated at this point, and we may then express our result by saying that the electric action of a uniformly electrified sphere at any point outside the sphere is the same as that of the whole charge of the sphere would be if concentrated at the centre of the sphere.", "markdown": "If we suppose the radius of the inner sphere to become very small till at last the sphere cannot be distinguished from a point, we may imagine the whole charge concentrated at this point, and we may then express our result by saying that the electric action of a uniformly electrified sphere at any point outside the sphere is the same as that of the whole charge of the sphere would be if concentrated at the centre of the sphere.", "why": "States the key result that lets a charged sphere be treated as a point charge from outside.", "use": [ "lesson" ], "concepts": [ "concept/electrical-image", "theorem/field-of-a-uniformly-electrified-sphere" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/x-71a00414bf", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-vi", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 81", "location": "PARTICULAR CASES OF ELECTRIFICATION", "latex": "The electric potential at any point is the work which must be expended in order to bring a body charged with unit of electricity from an infinite distance to that point.", "markdown": "The electric potential at any point is the work which must be expended in order to bring a body charged with unit of electricity from an infinite distance to that point.", "why": "Gives a clear, work-based definition of potential that a learner can picture.", "use": [ "lesson", "website" ], "concepts": [ "quantity/electric-potential" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/x-ecd1ec5390", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-vi", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 85", "location": "PARTICULAR CASES OF ELECTRIFICATION", "latex": "This example may serve to illustrate the principle of the Leyden jar, which consists of two metallic surfaces separated by insulating material. The smaller the distance between the surfaces and the greater the area of the surfaces, the greater the capacity of the jar.", "markdown": "This example may serve to illustrate the principle of the Leyden jar, which consists of two metallic surfaces separated by insulating material. The smaller the distance between the surfaces and the greater the area of the surfaces, the greater the capacity of the jar.", "why": "Connects the capacity formula for concentric spheres to a real device and says how its capacity can be increased.", "use": [ "lesson", "website" ], "concepts": [ "instrument/leyden-jar", "quantity/capacity" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/x-3098e75c30", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-vi", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 93", "location": "PARTICULAR CASES OF ELECTRIFICATION", "latex": "Very few, however, even of scientific men, are careful to observe these distinctions; hence we often hear of the force of a cannon-ball when either its energy or its momentum is meant, and of the force of an electrified body when the quantity of its electrification is meant.", "markdown": "Very few, however, even of scientific men, are careful to observe these distinctions; hence we often hear of the force of a cannon-ball when either its energy or its momentum is meant, and of the force of an electrified body when the quantity of its electrification is meant.", "why": "Warns about the common mistake of using 'force' for energy, momentum or charge.", "use": [ "lesson", "history" ], "concepts": [ "quantity/force" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/x-fdced0d763", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-vi", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 89", "location": "PARTICULAR CASES OF ELECTRIFICATION", "latex": "In other cases we cannot afford to despise the humbler method of actually drawing tentative figures on paper, and selecting that which appears least unlike the figure we require.", "markdown": "In other cases we cannot afford to despise the humbler method of actually drawing tentative figures on paper, and selecting that which appears least unlike the figure we require.", "why": "Shows the working physicist's honest, practical method of sketching when exact solutions are out of reach.", "use": [ "website", "history" ], "concepts": [ "concept/equipotential-surface", "concept/inverse-problem-of-electrostatics" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/x-a65a4c7dec", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-vii", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 101", "location": "THEORY OF ELECTRICAL IMAGES", "latex": "The point \\(B\\) with its imaginary charge is called the \\textit{electric image} of \\(A\\).", "markdown": "The point B with its imaginary charge is called the *electric image* of A.", "why": "It states the definition of an electric image in one sentence the learner can carry away.", "use": [ "lesson" ], "concepts": [ "concept/electrical-image" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/x-9744a43ca8", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-vii", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 106", "location": "THEORY OF ELECTRICAL IMAGES", "latex": "It can only exist when \\(A\\) is insulated, and it is everywhere of the same sign as \\(P_a\\).", "markdown": "It can only exist when A is insulated, and it is everywhere of the same sign as P_a.", "why": "It shows that the second species of induced electrification needs an insulated body, a condition a learner could easily forget.", "use": [ "lesson" ], "concepts": [ "concept/induced-electrification-of-the-second-species" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/x-7eddc05411", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-vii", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 106", "location": "THEORY OF ELECTRICAL IMAGES", "latex": "the negative electrification is more concentrated than the positive, so that the neutral line which separates the positive from the negative electrification is not the equator of the sphere, but lies nearer to \\(B\\).", "markdown": "the negative electrification is more concentrated than the positive, so that the neutral line which separates the positive from the negative electrification is not the equator of the sphere, but lies nearer to B.", "why": "It warns that the neutral line is not simply the equator, a tempting mistake for a learner picturing symmetry.", "use": [ "lesson" ], "concepts": [ "concept/neutral-line" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/x-4858de6d8d", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-vii", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 98", "location": "THEORY OF ELECTRICAL IMAGES", "latex": "This method has the great advantage of being intelligible by the aid of the most elementary mathematical reasoning, especially when it is considered in connection with the diagrams of equipotential surfaces described in Arts.\\ 93-96.", "markdown": "This method has the great advantage of being intelligible by the aid of the most elementary mathematical reasoning, especially when it is considered in connection with the diagrams of equipotential surfaces described in Arts. 93-96.", "why": "It tells the learner that the image method rests on elementary reasoning and on pictures of equipotential surfaces.", "use": [ "history", "website" ], "concepts": [ "concept/electrical-image", "concept/equipotential-surface" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/x-a46db30ced", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-vii", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 99", "location": "THEORY OF ELECTRICAL IMAGES", "latex": "But if we stand in front of a plane mirror and make observations on the apparent direction of the objects reflected therein, we find that these observations are consistent with the hypothesis that there is no mirror, but that certain objects exist in the region beyond the plane of the mirror. These hypothetical objects are geometrically related to certain real objects in front of the plane of the mirror, and they are called the \\textit{images} of these objects.", "markdown": "But if we stand in front of a plane mirror and make observations on the apparent direction of the objects reflected therein, we find that these observations are consistent with the hypothesis that there is no mirror, but that certain objects exist in the region beyond the plane of the mirror. These hypothetical objects are geometrically related to certain real objects in front of the plane of the mirror, and they are called the *images* of these objects.", "why": "Builds the idea of an image from the familiar mirror before any electricity is introduced.", "use": [ "lesson", "website" ], "concepts": [ "concept/electrical-image", "concept/optical-image" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/x-2578e5b493", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-vii", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 99", "location": "THEORY OF ELECTRICAL IMAGES", "latex": "When Adams and Leverrier discovered the hitherto unknown planet Neptune, they did so by ascertaining the direction and magnitude of the gravitating force due to the unseen planet at certain points of space.", "markdown": "When Adams and Leverrier discovered the hitherto unknown planet Neptune, they did so by ascertaining the direction and magnitude of the gravitating force due to the unseen planet at certain points of space.", "why": "Shows that deducing hidden bodies from their measured effects is a real scientific habit, not just a trick of electricity.", "use": [ "history", "lesson" ], "concepts": [ "concept/electrical-image" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/x-3748d57246", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-vii", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 100", "location": "THEORY OF ELECTRICAL IMAGES", "latex": "It appears, therefore, that when a spherical surface is uniformly electrified, the electric phenomena in the region outside the sphere are exactly the same as if the spherical surface had been removed, and a very small body placed at the centre of the sphere, having the same electric charge as the sphere.", "markdown": "It appears, therefore, that when a spherical surface is uniformly electrified, the electric phenomena in the region outside the sphere are exactly the same as if the spherical surface had been removed, and a very small body placed at the centre of the sphere, having the same electric charge as the sphere.", "why": "States the simplest case of an image: a whole charged sphere acts like one point charge at its centre.", "use": [ "lesson", "website" ], "concepts": [ "concept/sphere", "method/method-of-electric-images", "quantity/electric-potential", "theorem/electric-field-of-a-uniformly-electrified-sphere" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/x-bb2b10ed6e", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-vii", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 100", "location": "THEORY OF ELECTRICAL IMAGES", "latex": "This is a simple instance in which the phenomena in a certain region are consistent with a false hypothesis as to what exists beyond that region.", "markdown": "This is a simple instance in which the phenomena in a certain region are consistent with a false hypothesis as to what exists beyond that region.", "why": "Gives the central idea in one sentence: an image is useful because it gives right answers in one region even though it is not really there.", "use": [ "lesson", "website" ], "concepts": [ "concept/electrical-image", "method/method-of-electric-images" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/x-9c382e9081", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-vii", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 101", "location": "THEORY OF ELECTRICAL IMAGES", "latex": "Hence, if an electrified point \\(A\\) be placed outside a spherical conductor which is at potential zero, the electrical action at all points outside the sphere will be equivalent to that due to the point \\(A\\) together with another point, \\(B\\), within the sphere, which is the inverse point to \\(A\\), and whose charge is to that of \\(A\\) as \\(-1\\) is to \\(m\\). The point \\(B\\) with its imaginary charge is called the \\textit{electric image} of \\(A\\).", "markdown": "Hence, if an electrified point A be placed outside a spherical conductor which is at potential zero, the electrical action at all points outside the sphere will be equivalent to that due to the point A together with another point, B, within the sphere, which is the inverse point to A, and whose charge is to that of A as -1 is to m. The point B with its imaginary charge is called the *electric image* of A.", "why": "Gives the central result of the chapter: where the image lies and what charge it carries.", "use": [ "lesson", "website" ], "concepts": [ "concept/conductor", "concept/electrical-earth", "concept/electrical-image", "concept/inverse-points" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/x-e356d0cfd5", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-vii", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 98", "location": "THEORY OF ELECTRICAL IMAGES", "latex": "By this method he has solved problems in electricity which have never been attempted by any other method, and which, even after the solution has been pointed out, no other method seems capable of attacking.", "markdown": "By this method he has solved problems in electricity which have never been attempted by any other method, and which, even after the solution has been pointed out, no other method seems capable of attacking.", "why": "Gives Maxwell's own assessment of how powerful Thomson's method was.", "use": [ "history", "website" ], "concepts": [ "method/method-of-electric-images", "person/william-thomson" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/x-4ffe54a311", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-vii", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 106", "location": "THEORY OF ELECTRICAL IMAGES", "latex": "The surface-density is negative on the side next to \\(B\\) and positive on the side furthest from \\(B\\), but though the total quantities of positive and negative electrification are equal, the negative electrification is more concentrated than the positive, so that the neutral line which separates the positive from the negative electrification is not the equator of the sphere, but lies nearer to \\(B\\).", "markdown": "The surface-density is negative on the side next to B and positive on the side furthest from B, but though the total quantities of positive and negative electrification are equal, the negative electrification is more concentrated than the positive, so that the neutral line which separates the positive from the negative electrification is not the equator of the sphere, but lies nearer to B.", "why": "Corrects the natural guess that an insulated sphere near a charged body is split evenly at its equator.", "use": [ "lesson" ], "concepts": [ "concept/induced-electrification", "concept/neutral-line", "quantity/surface-charge-density" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/x-45524471da", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-vii", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 104", "location": "THEORY OF ELECTRICAL IMAGES", "latex": "When the potentials of the two spheres are equal the force is always repulsive.", "markdown": "When the potentials of the two spheres are equal the force is always repulsive.", "why": "A short, checkable statement of when two conducting spheres repel rather than attract.", "use": [ "lesson" ], "concepts": [ "quantity/electric-energy", "quantity/electric-potential" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/x-3898cbdd03", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-viii", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 107", "location": "ON ELECTROSTATIC CAPACITY", "latex": "the amount of the charge is the greater the nearer the disks are placed to each other, being approximately inversely as the distance between them.", "markdown": "the amount of the charge is the greater the nearer the disks are placed to each other, being approximately inversely as the distance between them.", "why": "It states the approximate inverse dependence of charge on separation, a relation a learner can test with two parallel disks.", "use": [ "lesson" ], "concepts": [ "instrument/condenser", "quantity/electric-charge" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/x-d6dc070f66", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-viii", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 108", "location": "ON ELECTROSTATIC CAPACITY", "latex": "In this case the capacity of the inner conductor is almost or altogether independent of everything but the outer conductor. This is the case in the Leyden jar, and in a cable with a copper core surrounded by an insulator the outside of which is protected by a sheathing of iron wires.", "markdown": "In this case the capacity of the inner conductor is almost or altogether independent of everything but the outer conductor. This is the case in the Leyden jar, and in a cable with a copper core surrounded by an insulator the outside of which is protected by a sheathing of iron wires.", "why": "It shows that a conductor enclosed by another has a capacity that depends almost only on the outer one, which explains the Leyden jar's design.", "use": [ "lesson" ], "concepts": [ "concept/conductor", "instrument/leyden-jar", "quantity/capacity" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/x-22f08942cb", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-viii", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 107", "location": "ON ELECTROSTATIC CAPACITY", "latex": "An apparatus consisting of two insulated conductors, each presenting\na large surface to the other with a small distance between\nthem, is called a \\textit{condenser}, because a small electromotive force is\nable to charge such an apparatus with a large quantity of electricity.", "markdown": "An apparatus consisting of two insulated conductors, each presenting a large surface to the other with a small distance between them, is called a *condenser*, because a small electromotive force is able to charge such an apparatus with a large quantity of electricity.", "why": "Defines a condenser and explains the reason for its name.", "use": [ "lesson", "website" ], "concepts": [ "concept/conductor", "instrument/condenser", "quantity/electromotive-force" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/x-de4e81e77b", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-viii", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 107", "location": "ON ELECTROSTATIC CAPACITY", "latex": "If we now remove one of the disks from the other we\ndo work against the electric attraction which draws them together,\nand we may thus increase the energy of the system so much that,\nthough the original electromotive force was only that of a single\nvoltaic cell, either of the disks when separated may be raised to so\nhigh a potential that the gold leaves of an electrometer connected\nwith it are deflected.", "markdown": "If we now remove one of the disks from the other we do work against the electric attraction which draws them together, and we may thus increase the energy of the system so much that, though the original electromotive force was only that of a single voltaic cell, either of the disks when separated may be raised to so high a potential that the gold leaves of an electrometer connected with it are deflected.", "why": "Shows how pulling charged disks apart does work and turns a weak cell's charge into a high, measurable potential.", "use": [ "lesson", "website" ], "concepts": [ "instrument/electrometer", "instrument/parallel-disk-condenser", "instrument/voltaic-battery", "quantity/electric-energy", "quantity/electric-potential" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/x-15850818bd", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-viii", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 107", "location": "ON ELECTROSTATIC CAPACITY", "latex": "\\textsc{The} capacity of a conductor is measured by the charge of\nelectricity which will raise its potential to the value unity, the\npotential of all other conductors in the field being kept at zero.", "markdown": "The capacity of a conductor is measured by the charge of electricity which will raise its potential to the value unity, the potential of all other conductors in the field being kept at zero.", "why": "Gives the precise definition of capacity, including the condition that all other conductors are held at zero potential.", "use": [ "lesson", "website" ], "concepts": [ "quantity/capacity", "quantity/electric-charge", "quantity/electric-potential" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/x-c03465d138", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-viii", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 108", "location": "ON ELECTROSTATIC CAPACITY", "latex": "It was in this way that Volta demonstrated that the electrification\ndue to a voltaic cell is of the same kind as that due to friction,\nthe copper electrode being positive with respect to the zinc electrode.", "markdown": "It was in this way that Volta demonstrated that the electrification due to a voltaic cell is of the same kind as that due to friction, the copper electrode being positive with respect to the zinc electrode.", "why": "A historical remark on how the condenser let Volta show that cell electricity and frictional electricity are the same kind.", "use": [ "history", "website" ], "concepts": [ "concept/electrification", "concept/electrode", "person/alessandro-volta" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/x-ef4897b436", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-viii", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 108", "location": "ON ELECTROSTATIC CAPACITY", "latex": "There are other forms of condensers, however, in which one of\nthe conductors is almost or altogether surrounded by the other.\nIn this case the capacity of the inner conductor is almost or altogether\nindependent of everything but the outer conductor. This is\nthe case in the Leyden jar, and in a cable with a copper core surrounded\nby an insulator the outside of which is protected by a\nsheathing of iron wires.", "markdown": "There are other forms of condensers, however, in which one of the conductors is almost or altogether surrounded by the other. In this case the capacity of the inner conductor is almost or altogether independent of everything but the outer conductor. This is the case in the Leyden jar, and in a cable with a copper core surrounded by an insulator the outside of which is protected by a sheathing of iron wires.", "why": "Connects the Leyden jar to a real cable and shows why surrounding one conductor with another fixes its capacity.", "use": [ "lesson", "website" ], "concepts": [ "instrument/condenser", "instrument/leyden-jar", "quantity/capacity" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/x-93594939a7", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-viii", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 109", "location": "ON ELECTROSTATIC CAPACITY", "latex": "The following method, by which the existence of a determinate\nrelation between the capacities of four condensers may be\nverified, has been employed by Sir W. Thomson.\\footnote{Gibson and Barclay.} It corresponds\nin electrostatics to Wheatstone's Bridge in current electricity.", "markdown": "The following method, by which the existence of a determinate relation between the capacities of four condensers may be verified, has been employed by Sir W. Thomson.% 0.14emGibson and Barclay. It corresponds in electrostatics to Wheatstone’s Bridge in current electricity.", "why": "Introduces the four-condenser balance method and the analogy with the Wheatstone bridge.", "use": [ "lesson", "history" ], "concepts": [ "instrument/condenser", "instrument/wheatstone-s-bridge", "method/condenser-bridge", "person/william-thomson", "quantity/capacity" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/x-d650224a0f", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-viii", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 109", "location": "ON ELECTROSTATIC CAPACITY", "latex": "From this it appears that if we connect first the one and then\nthe other conductor with the earth the values of the potentials and\ncharges will be diminished in the ratio of \\(\\dfrac{K^2}{(K+H)(K+h)}\\) to\nunity.", "markdown": "From this it appears that if we connect first the one and then the other conductor with the earth the values of the potentials and charges will be diminished in the ratio of K^2(K+H)(K+h) to unity.", "why": "States the result of alternate earthing: potentials and charges shrink by a fixed ratio each cycle.", "use": [ "lesson" ], "concepts": [ "concept/electrical-earth", "method/discharging-a-conductor", "quantity/capacity" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/x-840f8469df", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-ix", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 118", "location": "THE ELECTRIC CURRENT", "latex": "This operation, in which a compound body is decomposed by an electric current, is called Electrolysis, and the mode in which the current is transmitted is called Electrolytic Conduction.", "markdown": "This operation, in which a compound body is decomposed by an electric current, is called Electrolysis, and the mode in which the current is transmitted is called Electrolytic Conduction.", "why": "It names the process and its mode of conduction in one sentence, so the learner sees how electrolysis differs from conduction in a metal.", "use": [ "lesson" ], "concepts": [ "concept/electrolysis", "concept/electrolyte" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/x-aa5597dfca", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-ix", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 114", "location": "THE ELECTRIC CURRENT", "latex": "There will thus be a transference of positive electricity from \\(A\\) to \\(B\\) along the path travelled over by the pith ball, and this is what occurs in every electric current, namely, the passage of electricity along a definite direction.", "markdown": "There will thus be a transference of positive electricity from A to B along the path travelled over by the pith ball, and this is what occurs in every electric current, namely, the passage of electricity along a definite direction.", "why": "It gives the learner a concrete picture of what an electric current is: charge carried along a definite path, shown by a pith ball moving between two charged bodies.", "use": [ "lesson" ], "concepts": [ "concept/convection-current", "concept/electric-current" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/x-1c83b24150", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-ix", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 117", "location": "THE ELECTRIC CURRENT", "latex": "The ratio of the numerical value of the electromotive force to that of the current is called the Resistance of the conductor.", "markdown": "The ratio of the numerical value of the electromotive force to that of the current is called the Resistance of the conductor.", "why": "It gives a clear definition of resistance as a ratio, which the learner can check against Ohm's law.", "use": [ "lesson" ], "concepts": [ "quantity/electromotive-force", "quantity/resistance" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/x-ac8fa0ec8d", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-ix", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 117", "location": "THE ELECTRIC CURRENT", "latex": "The whole work done by the external electromotive force in urging electricity through the body is therefore spent in generating heat.", "markdown": "The whole work done by the external electromotive force in urging electricity through the body is therefore spent in generating heat.", "why": "It states the energy argument behind Joule's law in plain terms: electrical work becomes heat.", "use": [ "lesson" ], "concepts": [ "law/joule-s-law", "quantity/electromotive-force" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/x-47a8589b5b", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-ix", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 122", "location": "THE ELECTRIC CURRENT", "latex": "According to the theory of molecular motion of which he has himself been the chief founder, every molecule of the fluid is moving in an exceedingly irregular manner, being driven first one way and then another by the impacts of other molecules which are also in a state of agitation.", "markdown": "According to the theory of molecular motion of which he has himself been the chief founder, every molecule of the fluid is moving in an exceedingly irregular manner, being driven first one way and then another by the impacts of other molecules which are also in a state of agitation.", "why": "It gives a vivid historical picture of molecular agitation that Clausius used to explain electrolytic conduction.", "use": [ "history" ], "concepts": [ "concept/electrolysis", "person/rudolf-clausius" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/x-1e2fb6ba36", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-ix", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 128", "location": "THE ELECTRIC CURRENT", "latex": "This analogy is so complete that we may make use of the same terms in describing the behaviour of media under the action of electromotive force as we apply to bodies under the action of stress.", "markdown": "This analogy is so complete that we may make use of the same terms in describing the behaviour of media under the action of electromotive force as we apply to bodies under the action of stress.", "why": "It tells the learner that the whole chapter runs on an analogy between a dielectric under stress and a solid under load, so the terms carry over.", "use": [ "lesson", "history" ], "concepts": [ "concept/disruptive-discharge", "concept/physical-analogy", "quantity/electromotive-force" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/x-5aab6e6aa7", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-ix", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 129", "location": "THE ELECTRIC CURRENT", "latex": "The excess of water in the tube \\(D\\) may be taken to represent a positive charge of electricity on one side of the dielectric, and the excess of mercury in the tube \\(A\\) may represent the negative charge on the other side.", "markdown": "The excess of water in the tube D may be taken to represent a positive charge of electricity on one side of the dielectric, and the excess of mercury in the tube A may represent the negative charge on the other side.", "why": "It shows a concrete mapping from the tube apparatus to the two electricities on either side of a dielectric.", "use": [ "lesson" ], "concepts": [ "concept/dielectric", "concept/electric-displacement", "concept/physical-analogy" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/x-80838f83da", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-ix", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 131", "location": "THE ELECTRIC CURRENT", "latex": "The electric strength of a dielectric medium depends on the nature of the medium and its density and temperature.", "markdown": "The electric strength of a dielectric medium depends on the nature of the medium and its density and temperature.", "why": "It states plainly that electric strength is a property of the particular medium and its condition, not a fixed constant.", "use": [ "lesson" ], "concepts": [ "concept/dielectric", "quantity/electric-strength" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/x-f9974b7304", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-ix", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 139", "location": "THE ELECTRIC CURRENT", "latex": "The light of the spark or other discharge is made to fall on the slit of the collimator of the spectroscope, and after being analysed by the prisms is observed through the telescope.", "markdown": "The light of the spark or other discharge is made to fall on the slit of the collimator of the spectroscope, and after being analysed by the prisms is observed through the telescope.", "why": "It describes the apparatus path step by step, so a learner sees how a spark is turned into a spectrum.", "use": [ "lesson" ], "concepts": [ "concept/spectrum", "instrument/spectroscope" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/x-ab0c29f4b6", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-ix", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 140", "location": "THE ELECTRIC CURRENT", "latex": "But there are methods by which the difference of potential of the conductors may be maintained constant, in which case the current will continue to flow with uniform strength as a Steady Current.", "markdown": "But there are methods by which the difference of potential of the conductors may be maintained constant, in which case the current will continue to flow with uniform strength as a Steady Current.", "why": "It gives the learner the defining condition of a steady current: a constant potential difference keeps the current constant.", "use": [ "lesson" ], "concepts": [ "concept/steady-current" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/x-3d25fe9cde", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-ix", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 142", "location": "THE ELECTRIC CURRENT", "latex": "Thus we see that the electric current has a magnetic action which is exerted outside the current, and by which its existence can be ascertained and its intensity measured without breaking the circuit or introducing anything into the current itself.", "markdown": "Thus we see that the electric current has a magnetic action which is exerted outside the current, and by which its existence can be ascertained and its intensity measured without breaking the circuit or introducing anything into the current itself.", "why": "It explains why a current can be detected and measured from outside the wire, a point that frames the whole discussion of galvanometers.", "use": [ "history" ], "concepts": [ "concept/electric-current", "concept/magnetic-action-of-an-electric-current" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/x-750a9ff9fb", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-ix", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 142", "location": "THE ELECTRIC CURRENT", "latex": "The galvanometer is the most convenient instrument for measuring the strength of electric currents. We shall therefore assume the possibility of constructing such an instrument in studying the laws of these currents, and when we say that an electric current is of a certain strength we suppose that the measurement is effected by the galvanometer.", "markdown": "The galvanometer is the most convenient instrument for measuring the strength of electric currents. We shall therefore assume the possibility of constructing such an instrument in studying the laws of these currents, and when we say that an electric current is of a certain strength we suppose that the measurement is effected by the galvanometer.", "why": "Shows how current strength is operationally defined by an instrument.", "use": [ "lesson" ], "concepts": [ "concept/electric-current", "instrument/galvanometer" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/x-56d37af88f", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-ix", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 143", "location": "THE ELECTRIC CURRENT", "latex": "The Resistance of a conductor is defined to be the ratio of the electromotive force to the strength of the current which it produces. The introduction of this term would have been of no scientific value unless Ohm had shewn, as he did experimentally, that it corresponds to a real physical quantity, that is, that it has a definite value which is altered only when the nature of the conductor is altered.", "markdown": "The Resistance of a conductor is defined to be the ratio of the electromotive force to the strength of the current which it produces. The introduction of this term would have been of no scientific value unless Ohm had shewn, as he did experimentally, that it corresponds to a real physical quantity, that is, that it has a definite value which is altered only when the nature of the conductor is altered.", "why": "Explains why resistance is a useful idea: it is a definite property of the conductor, established by experiment.", "use": [ "lesson", "history", "website" ], "concepts": [ "law/ohm-s-law", "person/georg-simon-ohm", "quantity/resistance" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/x-9975884361", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-ix", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 128", "location": "THE ELECTRIC CURRENT", "latex": "If the wire, when the force is removed, returns to its former shape and becomes completely untwisted it is said to be elastic. Such a wire corresponds to a dielectric which acts as a perfect insulator with respect to the electromotive force employed.", "markdown": "If the wire, when the force is removed, returns to its former shape and becomes completely untwisted it is said to be elastic. Such a wire corresponds to a dielectric which acts as a perfect insulator with respect to the electromotive force employed.", "why": "Gives a mechanical picture, the twisted wire, for how a dielectric holds electric displacement without conducting.", "use": [ "lesson", "website" ], "concepts": [ "concept/dielectric", "concept/electric-displacement", "quantity/electromotive-force" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/x-49126f1b1c", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-ix", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 128", "location": "THE ELECTRIC CURRENT", "latex": "If no such permanent twist can be given to the wire by a force which is not sufficient to break it, the wire is called brittle. In like manner we may speak of those dielectrics such as air, which will not transmit electricity except by the disruptive discharge, as electrically brittle.", "markdown": "If no such permanent twist can be given to the wire by a force which is not sufficient to break it, the wire is called brittle. In like manner we may speak of those dielectrics such as air, which will not transmit electricity except by the disruptive discharge, as electrically brittle.", "why": "Uses the idea of a brittle wire to explain why air carries electricity only by sudden breakdown.", "use": [ "lesson", "website" ], "concepts": [ "concept/dielectric", "concept/disruptive-discharge", "concept/electrical-brittleness" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/x-89baee262c", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-ix", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 131", "location": "THE ELECTRIC CURRENT", "latex": "In this way we may construct a mechanical illustration of the properties of a dielectric of any kind, in which the two electricities are represented by two real fluids, and the electric potential is represented by fluid pressure. Charge and discharge are represented by the motion of the piston \\(P\\), and electromotive force by the resultant force on the piston.", "markdown": "In this way we may construct a mechanical illustration of the properties of a dielectric of any kind, in which the two electricities are represented by two real fluids, and the electric potential is represented by fluid pressure. Charge and discharge are represented by the motion of the piston P, and electromotive force by the resultant force on the piston.", "why": "Sums up the tube model by mapping each electrical quantity to a mechanical one.", "use": [ "lesson" ], "concepts": [ "concept/dielectric", "experiment/tube-and-piston-model-of-a-dielectric", "quantity/electric-potential", "quantity/electromotive-force" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/x-a88ff6f3dc", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-ix", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 131", "location": "THE ELECTRIC CURRENT", "latex": "It would therefore seem as if a perfect vacuum would present an almost insuperable resistance to the passage of electricity. A small quantity of gas, however, introduced into the empty space renders it incapable of withstanding even a small electromotive force.", "markdown": "It would therefore seem as if a perfect vacuum would present an almost insuperable resistance to the passage of electricity. A small quantity of gas, however, introduced into the empty space renders it incapable of withstanding even a small electromotive force.", "why": "Shows the surprising result that electric strength is not simply greater in thinner gas.", "use": [ "lesson", "website" ], "concepts": [ "concept/disruptive-discharge", "quantity/electric-strength" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/x-9c4282e3ea", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-ix", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 134", "location": "THE ELECTRIC CURRENT", "latex": "The whole theory of the electric properties of gases is in a very imperfect state.", "markdown": "The whole theory of the electric properties of gases is in a very imperfect state.", "why": "Shows a great physicist plainly admitting what was not yet understood.", "use": [ "history", "website" ], "concepts": [ "concept/conductivity-of-gases" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/x-01f0144770", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-ix", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 136", "location": "THE ELECTRIC CURRENT", "latex": "Thus there is continually kept up an influx of uncharged air to the point, a luminous discharge of electricity from the point, called the Electric Glow, and a stream of charged air in the direction of the prolongation of the axis of the cone called the Electric Wind. By checking the influx of air behind the point we may weaken the glow and by increasing the current of air by blowing we may make the glow stronger.", "markdown": "Thus there is continually kept up an influx of uncharged air to the point, a luminous discharge of electricity from the point, called the Electric Glow, and a stream of charged air in the direction of the prolongation of the axis of the cone called the Electric Wind. By checking the influx of air behind the point we may weaken the glow and by increasing the current of air by blowing we may make the glow stronger.", "why": "Names the glow and the wind and shows how they are linked and can be changed by controlling the air supply.", "use": [ "lesson", "website" ], "concepts": [ "concept/electric-glow", "concept/electric-wind" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/x-d53ae7e1a4", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-ix", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 139", "location": "THE ELECTRIC CURRENT", "latex": "We may compare this breaking down of the dielectric to what occurs when we make a little rent perpendicular to the edge of a piece of paper and then apply tension to the paper in the direction of the edge. The paper is torn through, the disruption beginning at the little rent, but diverging occasionally so as to take in weak places in the paper.", "markdown": "We may compare this breaking down of the dielectric to what occurs when we make a little rent perpendicular to the edge of a piece of paper and then apply tension to the paper in the direction of the edge. The paper is torn through, the disruption beginning at the little rent, but diverging occasionally so as to take in weak places in the paper.", "why": "A vivid everyday analogy for how a spark starts at one point and runs through weak spots.", "use": [ "lesson", "website" ], "concepts": [ "concept/disruptive-discharge", "concept/electric-spark", "quantity/electric-strength" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/x-2b6bdabfc4", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-ix", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 140", "location": "THE ELECTRIC CURRENT", "latex": "It follows from this that neither the electric fluid, if there be such a substance, nor any ethereal medium such as is supposed to pervade all ordinary matter, is rendered luminous during the discharge, for if it were so its spectrum would be visible in all discharges.", "markdown": "It follows from this that neither the electric fluid, if there be such a substance, nor any ethereal medium such as is supposed to pervade all ordinary matter, is rendered luminous during the discharge, for if it were so its spectrum would be visible in all discharges.", "why": "A historical example of reasoning from spectra to rule out a hypothesized electric fluid or ether as the source of the light.", "use": [ "history", "lesson" ], "concepts": [ "concept/disruptive-discharge", "concept/spectrum", "instrument/spectroscope" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/x-01a1737dc7", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-ix", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 114", "location": "THE ELECTRIC CURRENT", "latex": "Hence the ball is acted on by the electric force always in the direction in which it is moving at the time, so that if it is properly suspended the electric force will not only keep up the backward and forward motion, but will communicate to the moving ball an amount of energy which it will expend in a series of rattling blows against the balls \\(A\\) and \\(B\\).", "markdown": "Hence the ball is acted on by the electric force always in the direction in which it is moving at the time, so that if it is properly suspended the electric force will not only keep up the backward and forward motion, but will communicate to the moving ball an amount of energy which it will expend in a series of rattling blows against the balls A and B.", "why": "A vivid picture of a convection current in which the swinging pith ball is kept moving by the electric force.", "use": [ "lesson", "website" ], "concepts": [ "concept/convection-current", "concept/electric-current", "quantity/electromotive-force" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/x-19dff27e54", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-ix", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 116", "location": "THE ELECTRIC CURRENT", "latex": "It is therefore quite possible that the velocity of electricity in a telegraph wire may be exceedingly small, less, say, than the hundredth of an inch in an hour, though signals, that is to say, changes in the state of the current, may be propagated along the wire many thousands of miles in a second.", "markdown": "It is therefore quite possible that the velocity of electricity in a telegraph wire may be exceedingly small, less, say, than the hundredth of an inch in an hour, though signals, that is to say, changes in the state of the current, may be propagated along the wire many thousands of miles in a second.", "why": "Separates how fast electricity itself moves from how fast signals travel, a common confusion.", "use": [ "lesson", "website", "history" ], "concepts": [ "concept/conduction-current", "concept/electric-current" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/x-727f22574b", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-ix", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 116", "location": "THE ELECTRIC CURRENT", "latex": "Since, therefore, we are ignorant of the true linear velocity of an electric current, we must measure the \\textit{strength} of the current by the quantity of electricity discharged through any section of the conductor in the unit of time, just as engineers measure the discharge of water and gas through pipes, not by the velocity of the water or gas, but by the quantity which passes in a minute.", "markdown": "Since, therefore, we are ignorant of the true linear velocity of an electric current, we must measure the *strength* of the current by the quantity of electricity discharged through any section of the conductor in the unit of time, just as engineers measure the discharge of water and gas through pipes, not by the velocity of the water or gas, but by the quantity which passes in a minute.", "why": "Explains how current strength is defined, using the analogy of water and gas in pipes.", "use": [ "lesson", "website" ], "concepts": [ "concept/electric-current", "concept/electric-discharge" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/x-ac0f7fad20", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-ix", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 116", "location": "THE ELECTRIC CURRENT", "latex": "In these cases it is convenient to speak of the total current as the Electric Displacement, the word displacement indicating the final result of a motion without reference to the rate at which it takes place.", "markdown": "In these cases it is convenient to speak of the total current as the Electric Displacement, the word displacement indicating the final result of a motion without reference to the rate at which it takes place.", "why": "Gives the book's definition of electric displacement as a total quantity rather than a rate.", "use": [ "lesson" ], "concepts": [ "concept/electric-displacement" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/x-f4ae0d887c", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-ix", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 123", "location": "THE ELECTRIC CURRENT", "latex": "The electromotive force, therefore, does not produce the disruptions and reunions of the molecules, but finding these disruptions and reunions already going on, it influences the motion of the constituents during their intervals of freedom.", "markdown": "The electromotive force, therefore, does not produce the disruptions and reunions of the molecules, but finding these disruptions and reunions already going on, it influences the motion of the constituents during their intervals of freedom.", "why": "Shows Clausius's picture of why any electromotive force, however small, produces electrolytic conduction.", "use": [ "lesson", "history" ], "concepts": [ "concept/electrolysis", "concept/molecular-agitation", "person/rudolf-clausius", "quantity/electromotive-force" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/x-db66f774a6", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-ix", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 123", "location": "THE ELECTRIC CURRENT", "latex": "The best test, however, is the existence of polarization, for even when the quantity of the free ions is too small to be observed or measured, their presence may be indicated by the electromotive force which they excite.", "markdown": "The best test, however, is the existence of polarization, for even when the quantity of the free ions is too small to be observed or measured, their presence may be indicated by the electromotive force which they excite.", "why": "Tells a learner how to tell electrolytic conductors from metallic ones.", "use": [ "lesson" ], "concepts": [ "concept/electrolyte", "concept/ion", "concept/polarization" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/x-e822105e35", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-ix", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 126", "location": "THE ELECTRIC CURRENT", "latex": "When the electromotive force is increasing, the increase of electric displacement is equivalent to an electric current in the same direction as the electromotive force. When the electromotive force is constant there is still displacement, but no current. When the electromotive force is diminishing, the diminution of the electric displacement is equivalent to a current in the opposite direction.", "markdown": "When the electromotive force is increasing, the increase of electric displacement is equivalent to an electric current in the same direction as the electromotive force. When the electromotive force is constant there is still displacement, but no current. When the electromotive force is diminishing, the diminution of the electric displacement is equivalent to a current in the opposite direction.", "why": "Shows in three cases how a changing displacement in a dielectric acts as a current.", "use": [ "lesson" ], "concepts": [ "concept/dielectric", "concept/electric-current", "concept/electric-displacement" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/x-30e1952f50", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-ix", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 121", "location": "THE ELECTRIC CURRENT", "latex": "In this way a constant circulation is kept up, each of the constituents travelling in one direction by electrolysis, and back again by diffusion, so that a permanent current may exist without any visible accumulation of the products of decomposition.", "markdown": "In this way a constant circulation is kept up, each of the constituents travelling in one direction by electrolysis, and back again by diffusion, so that a permanent current may exist without any visible accumulation of the products of decomposition.", "why": "Explains how a small steady current can flow in an electrolyte without visible decomposition, which defends Faraday's law.", "use": [ "lesson", "history" ], "concepts": [ "concept/electrolysis", "concept/electrolytic-convection", "law/faraday-s-laws-of-electrolysis" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/x-aa6ba317fd", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-ix", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 140", "location": "THE ELECTRIC CURRENT", "latex": "A solution of sulphate of zinc is placed in a cell of porous earthenware, and this cell is placed in a vessel containing a saturated solution of sulphate of copper. A piece of zinc is dipped into the sulphate of zinc, and a piece of copper is dipped into the sulphate of copper. Wires are soldered to the zinc and to the copper above the surface of the liquid. This combination is called a cell or element of Daniell's battery.", "markdown": "A solution of sulphate of zinc is placed in a cell of porous earthenware, and this cell is placed in a vessel containing a saturated solution of sulphate of copper. A piece of zinc is dipped into the sulphate of zinc, and a piece of copper is dipped into the sulphate of copper. Wires are soldered to the zinc and to the copper above the surface of the liquid. This combination is called a cell or element of Daniell’s battery.", "why": "Gives a concrete, physical picture of a working cell before any theory of the steady current is built on it.", "use": [ "lesson", "website" ], "concepts": [ "instrument/daniell-s-cell", "instrument/voltaic-battery" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/x-97ceed394c", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-ix", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 142", "location": "THE ELECTRIC CURRENT", "latex": "If a man were to place his body in the line of the current so that the current from copper through the wire to zinc should flow from his head to his feet, and if he were to direct his face towards the centre of the magnet, then that end of the magnet which tends to point to the north would, when the current flows, tend to point towards the man's right hand.", "markdown": "If a man were to place his body in the line of the current so that the current from copper through the wire to zinc should flow from his head to his feet, and if he were to direct his face towards the centre of the magnet, then that end of the magnet which tends to point to the north would, when the current flows, tend to point towards the man’s right hand.", "why": "Turns the direction rule for a current's effect on a magnet into a vivid image a learner can act out.", "use": [ "lesson", "website", "history" ], "concepts": [ "concept/magnetic-action-of-an-electric-current", "person/hans-christian-oersted" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/x-141cd554c9", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-ix", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 144", "location": "THE ELECTRIC CURRENT", "latex": "Or, \\textit{the resistance of a series of conductors is the sum of the resistances of the conductors taken separately}.", "markdown": "Or, *the resistance of a series of conductors is the sum of the resistances of the conductors taken separately*.", "why": "States the series rule plainly after deriving it from Ohm's law.", "use": [ "lesson" ], "concepts": [ "theorem/resistance-of-conductors-in-series" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/x-b5971c646d", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-ix", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 145", "location": "THE ELECTRIC CURRENT", "latex": "Or, \\textit{the reciprocal of the resistance of a multiple conductor is the sum of the reciprocals of the component conductors}.", "markdown": "Or, *the reciprocal of the resistance of a multiple conductor is the sum of the reciprocals of the component conductors*.", "why": "States the parallel rule that conductors side by side add their reciprocals of resistance.", "use": [ "lesson" ], "concepts": [ "theorem/resistance-of-conductors-in-multiple-arc" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/x-511d649c00", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-ix", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 146", "location": "THE ELECTRIC CURRENT", "latex": "Consider next a prismatic conductor of the same material whose length is \\(l\\), and whose section is unity. This is equivalent to \\(l\\) cubes arranged in series. The resistance of the conductor is therefore \\(l \\rho\\).", "markdown": "Consider next a prismatic conductor of the same material whose length is l, and whose section is unity. This is equivalent to l cubes arranged in series. The resistance of the conductor is therefore l .", "why": "Shows how the series rule builds up the resistance of a wire from unit cubes.", "use": [ "lesson" ], "concepts": [ "quantity/specific-resistance", "theorem/resistance-of-a-uniform-wire", "theorem/resistance-of-conductors-in-series" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/x-1005974b5c", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-x", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 149", "location": "PHENOMENA OF AN ELECTRIC CURRENT WHICH FLOWS THROUGH HETEROGENEOUS MEDIA", "latex": "Any ordinate such as \\( 0°P\\), \\(1°Q\\), \\&c., is called the Thermoelectric Power of iron with respect to lead at \\(0°\\), \\(1°\\), \\&c., and is reckoned positive when, for a small difference of temperature, the current is from lead to iron through the hot junction.", "markdown": "Any ordinate such as 0°P, 1°Q, &c., is called the Thermoelectric Power of iron with respect to lead at 0°, 1°, &c., and is reckoned positive when, for a small difference of temperature, the current is from lead to iron through the hot junction.", "why": "It gives the sign convention and meaning of thermo-electric power, which the diagram method depends on.", "use": [ "lesson" ], "concepts": [ "concept/thermo-electric-diagram", "quantity/thermo-electric-power" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/x-3d54dc9631", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-x", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 148", "location": "PHENOMENA OF AN ELECTRIC CURRENT WHICH FLOWS THROUGH HETEROGENEOUS MEDIA", "latex": "The electromotive force from one point of a conductor of homogeneous metal to another depends only on the temperature of these points unless at any part of the conductor a sensible variation of temperature occurs between points whose distance is within the limits of molecular action.", "markdown": "The electromotive force from one point of a conductor of homogeneous metal to another depends only on the temperature of these points unless at any part of the conductor a sensible variation of temperature occurs between points whose distance is within the limits of molecular action.", "why": "It states the law of Magnus with its exception, so a learner sees exactly when a single-metal circuit can carry current.", "use": [ "lesson" ], "concepts": [ "law/law-of-magnus" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/x-0663c7e389", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-x", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 153", "location": "PHENOMENA OF AN ELECTRIC CURRENT WHICH FLOWS THROUGH HETEROGENEOUS MEDIA", "latex": "We may express both the Peltier and the Thomson effects by stating that when an electric current is flowing from places of smaller to places of greater thermo-electric power, heat is absorbed, and when it is flowing in the reverse direction heat is generated, and this, whether the difference of thermo-electric power in the two places arises from a difference in the nature of the metal or from a difference of temperature in the same metal.", "markdown": "We may express both the Peltier and the Thomson effects by stating that when an electric current is flowing from places of smaller to places of greater thermo-electric power, heat is absorbed, and when it is flowing in the reverse direction heat is generated, and this, whether the difference of thermo-electric power in the two places arises from a difference in the nature of the metal or from a difference of temperature in the same metal.", "why": "It unifies two reversible heat effects into one rule about the direction of current and thermo-electric power.", "use": [ "lesson" ], "concepts": [ "concept/peltier-effect", "concept/thomson-effect", "quantity/thermo-electric-power" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/x-f349248a81", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-x", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 160", "location": "PHENOMENA OF AN ELECTRIC CURRENT WHICH FLOWS THROUGH HETEROGENEOUS MEDIA", "latex": "It is manifest that in a heterogeneous circuit we cannot determine the electromotive force acting from the point \\(A\\) to the point \\(B\\) by simply connecting these points by wires to the electrodes of a galvanometer or electrometer, for we are ignorant of the electromotive forces acting at the junctions of these wires with the matter of the circuit at \\(A\\) and \\(B\\).", "markdown": "It is manifest that in a heterogeneous circuit we cannot determine the electromotive force acting from the point A to the point B by simply connecting these points by wires to the electrodes of a galvanometer or electrometer, for we are ignorant of the electromotive forces acting at the junctions of these wires with the matter of the circuit at A and B.", "why": "It explains why electromotive force across a heterogeneous junction cannot be read off directly, which motivates the heat-based method.", "use": [ "lesson" ], "concepts": [ "quantity/electromotive-force" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/x-c68116957a", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-x", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 155", "location": "PHENOMENA OF AN ELECTRIC CURRENT WHICH FLOWS THROUGH HETEROGENEOUS MEDIA", "latex": "In this treatise we have avoided making any assumption that electricity is a body or that it is not a body, and we must also avoid any statement which might suggest that, like a body, electricity may receive or emit heat.", "markdown": "In this treatise we have avoided making any assumption that electricity is a body or that it is not a body, and we must also avoid any statement which might suggest that, like a body, electricity may receive or emit heat.", "why": "It warns the reader against treating electricity as a material fluid, a common misconception the chapter works to avoid.", "use": [ "lesson", "history" ], "concepts": [ "quantity/electric-entropy", "quantity/entropy" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/x-649b610895", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-x", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 164", "location": "PHENOMENA OF AN ELECTRIC CURRENT WHICH FLOWS THROUGH HETEROGENEOUS MEDIA", "latex": "During the passage of one unit of electricity through any section of the circuit one electrochemical equivalent of each of the electrolytes is electrolysed. There is therefore a definite amount of chemical action corresponding to a definite quantity of electricity passed through the circuit.", "markdown": "During the passage of one unit of electricity through any section of the circuit one electrochemical equivalent of each of the electrolytes is electrolysed. There is therefore a definite amount of chemical action corresponding to a definite quantity of electricity passed through the circuit.", "why": "It states the core rule of electrolysis: a fixed quantity of electricity produces a fixed chemical change.", "use": [ "lesson" ], "concepts": [ "concept/electrolysis", "quantity/electric-charge", "quantity/electrochemical-equivalent" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/x-447ba6a8fb", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-x", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 166", "location": "PHENOMENA OF AN ELECTRIC CURRENT WHICH FLOWS THROUGH HETEROGENEOUS MEDIA", "latex": "The electromotive force of an electrochemical apparatus is in absolute measure equal to the mechanical equivalent of the chemical action on one electrochemical equivalent of the substance.", "markdown": "The electromotive force of an electrochemical apparatus is in absolute measure equal to the mechanical equivalent of the chemical action on one electrochemical equivalent of the substance.", "why": "It gives Thomson's chemical method for finding an electromotive force, a result a learner can check against the definition of EMF.", "use": [ "lesson", "history" ], "concepts": [ "quantity/electrochemical-equivalent", "quantity/electromotive-force", "theorem/thomson-s-theorem" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/x-4d4e11145a", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-x", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 168", "location": "PHENOMENA OF AN ELECTRIC CURRENT WHICH FLOWS THROUGH HETEROGENEOUS MEDIA", "latex": "It does not appear that there is much polarization at the surface of the zinc plate when immersed in a solution of sulphate of zinc or in dilute sulphuric acid. The principal seat of polarization is at the surface of the negative metal.", "markdown": "It does not appear that there is much polarization at the surface of the zinc plate when immersed in a solution of sulphate of zinc or in dilute sulphuric acid. The principal seat of polarization is at the surface of the negative metal.", "why": "It locates where polarization occurs in a cell, which explains why the negative plate needs treatment.", "use": [ "lesson" ], "concepts": [ "concept/electrode", "concept/polarization", "instrument/voltaic-battery" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/x-b572a26865", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-x", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 169", "location": "PHENOMENA OF AN ELECTRIC CURRENT WHICH FLOWS THROUGH HETEROGENEOUS MEDIA", "latex": "When the current flows through the solution from the zinc to the copper no hydrogen appears on the copper plate, but copper is deposited on it.", "markdown": "When the current flows through the solution from the zinc to the copper no hydrogen appears on the copper plate, but copper is deposited on it.", "why": "It contrasts Daniell's cell with hydrogen-evolving cells, showing why it stays constant.", "use": [ "lesson", "website" ], "concepts": [ "concept/cathode", "concept/polarization", "instrument/daniell-s-cell" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/x-5f4e034fac", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-x", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 147", "location": "PHENOMENA OF AN ELECTRIC CURRENT WHICH FLOWS THROUGH HETEROGENEOUS MEDIA", "latex": "Seebeck, in 1822, discovered that if a circuit is formed of two different metals, and if the two junctions of the metals are kept at different temperatures, an electric current tends to flow round the circuit.", "markdown": "Seebeck, in 1822, discovered that if a circuit is formed of two different metals, and if the two junctions of the metals are kept at different temperatures, an electric current tends to flow round the circuit.", "why": "States the founding discovery of thermo-electricity in one sentence.", "use": [ "lesson", "website", "history" ], "concepts": [ "concept/thermo-electric-effect", "person/thomas-johann-seebeck" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/x-baec63c4d2", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-x", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 147", "location": "PHENOMENA OF AN ELECTRIC CURRENT WHICH FLOWS THROUGH HETEROGENEOUS MEDIA", "latex": "In a circuit formed of any number of metals all at the same temperature, there can be no current, for if there were a current it might be constantly employed to work a machine or to generate heat in a conductor, and this without any energy being supplied to the system from without, for in order to keep the circuit at a constant temperature nothing is required except to prevent heat from entering or leaving it.", "markdown": "In a circuit formed of any number of metals all at the same temperature, there can be no current, for if there were a current it might be constantly employed to work a machine or to generate heat in a conductor, and this without any energy being supplied to the system from without, for in order to keep the circuit at a constant temperature nothing is required except to prevent heat from entering or leaving it.", "why": "Shows how conservation of energy rules out a perpetual current, a model of physical argument.", "use": [ "lesson" ], "concepts": [ "concept/thermo-electric-effect", "law/conservation-of-energy" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/x-5de365d398", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-x", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 148", "location": "PHENOMENA OF AN ELECTRIC CURRENT WHICH FLOWS THROUGH HETEROGENEOUS MEDIA", "latex": "In fact the experiments of Le Roux and others have shewn that the law of Magnus is no longer applicable in a circuit in which there is a very abrupt variation of temperature, as at the instant when the circuit is closed by a hot wire coming in contact with a cold wire of the same metal.", "markdown": "In fact the experiments of Le Roux and others have shewn that the law of Magnus is no longer applicable in a circuit in which there is a very abrupt variation of temperature, as at the instant when the circuit is closed by a hot wire coming in contact with a cold wire of the same metal.", "why": "Shows a law's limits being found by experiment, and the law then restated more carefully.", "use": [ "lesson", "history" ], "concepts": [ "law/law-of-magnus", "person/le-roux" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/x-1400d132ea", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-x", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 151", "location": "PHENOMENA OF AN ELECTRIC CURRENT WHICH FLOWS THROUGH HETEROGENEOUS MEDIA", "latex": "The latter, which we may call with Thomson the \\textit{frictional} generation of heat, is the same when the direction of the current is reversed, and varies as the square of the strength of the current. The former which we shall call the Peltier effect, is reversed when the current is reversed, and depends simply on the strength of the current.", "markdown": "The latter, which we may call with Thomson the *frictional* generation of heat, is the same when the direction of the current is reversed, and varies as the square of the strength of the current. The former which we shall call the Peltier effect, is reversed when the current is reversed, and depends simply on the strength of the current.", "why": "Separates reversible junction heating from ordinary resistive heating, a distinction learners often miss.", "use": [ "lesson", "website" ], "concepts": [ "concept/joule-heating", "concept/peltier-effect" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/x-804b3bb422", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-x", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 152", "location": "PHENOMENA OF AN ELECTRIC CURRENT WHICH FLOWS THROUGH HETEROGENEOUS MEDIA", "latex": "Thomson has shewn that a very close analogy subsists between these thermo-electric phenomena and those of a fluid circulating in a tube consisting of two vertical branches connected by two horizontal branches.", "markdown": "Thomson has shewn that a very close analogy subsists between these thermo-electric phenomena and those of a fluid circulating in a tube consisting of two vertical branches connected by two horizontal branches.", "why": "Introduces the fluid analogy that gives the odd idea of a specific heat of electricity.", "use": [ "lesson", "history" ], "concepts": [ "concept/physical-analogy", "quantity/specific-heat-of-electricity" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/x-0a92ea887b", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-x", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 155", "location": "PHENOMENA OF AN ELECTRIC CURRENT WHICH FLOWS THROUGH HETEROGENEOUS MEDIA", "latex": "We may, however, without any such assumption, make use of the idea of entropy, introduced by Clausius and Rankine into the theory of heat, and extend it to certain thermo-electric phenomena, always remembering that entropy is not a thing but a mere instrument of scientific thought, by which we are enabled to express in a compact and convenient manner the conditions under which heat is emitted or absorbed.", "markdown": "We may, however, without any such assumption, make use of the idea of entropy, introduced by Clausius and Rankine into the theory of heat, and extend it to certain thermo-electric phenomena, always remembering that entropy is not a thing but a mere instrument of scientific thought, by which we are enabled to express in a compact and convenient manner the conditions under which heat is emitted or absorbed.", "why": "A warning that entropy is a tool of thought, not a substance.", "use": [ "lesson", "website" ], "concepts": [ "quantity/electric-entropy", "quantity/entropy" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/x-0b7c39f281", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-x", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 159", "location": "PHENOMENA OF AN ELECTRIC CURRENT WHICH FLOWS THROUGH HETEROGENEOUS MEDIA", "latex": "The obvious fact that no real fluid can have a negative specific heat need not disturb us, for we do not assert that electricity is a real fluid.", "markdown": "The obvious fact that no real fluid can have a negative specific heat need not disturb us, for we do not assert that electricity is a real fluid.", "why": "Models honest use of an analogy while saying where it stops.", "use": [ "lesson", "website" ], "concepts": [ "concept/physical-analogy", "quantity/specific-heat-of-electricity" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/x-303b0a33e2", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-x", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 161", "location": "PHENOMENA OF AN ELECTRIC CURRENT WHICH FLOWS THROUGH HETEROGENEOUS MEDIA", "latex": "The only method by which we can determine where the electromotive force acts is that of measuring the heats generated or absorbed during the transmission of a unit of electricity from \\(A\\) to \\(B\\).", "markdown": "The only method by which we can determine where the electromotive force acts is that of measuring the heats generated or absorbed during the transmission of a unit of electricity from A to B.", "why": "Explains why heat measurements are needed to find where in a circuit an electromotive force sits.", "use": [ "lesson" ], "concepts": [ "concept/thermo-electric-effect", "quantity/electromotive-force" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/x-0935dcb7f5", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-x", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 166", "location": "PHENOMENA OF AN ELECTRIC CURRENT WHICH FLOWS THROUGH HETEROGENEOUS MEDIA", "latex": "Let \\(E\\) be the electromotive force of the circuit; then the work done in driving one unit of electricity through the circuit is numerically equal to \\(E\\).", "markdown": "Let E be the electromotive force of the circuit; then the work done in driving one unit of electricity through the circuit is numerically equal to E.", "why": "Gives a plain working definition of electromotive force as work per unit of electricity, which is the first step in Thomson's argument.", "use": [ "lesson" ], "concepts": [ "quantity/electromotive-force" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/x-6d3f001e0a", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-x", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 166", "location": "PHENOMENA OF AN ELECTRIC CURRENT WHICH FLOWS THROUGH HETEROGENEOUS MEDIA", "latex": "`The electromotive force of an electrochemical apparatus is in absolute measure equal to the mechanical equivalent of the chemical action on one electrochemical equivalent of the substance.'", "markdown": "‘The electromotive force of an electrochemical apparatus is in absolute measure equal to the mechanical equivalent of the chemical action on one electrochemical equivalent of the substance.’", "why": "Thomson's statement ties electrical push to chemical energy in a single sentence.", "use": [ "lesson", "website", "history" ], "concepts": [ "quantity/electrochemical-equivalent", "quantity/electromotive-force", "theorem/thomson-s-rule-for-electromotive-force-and-chemical-action" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/x-54cff3e837", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-x", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 165", "location": "PHENOMENA OF AN ELECTRIC CURRENT WHICH FLOWS THROUGH HETEROGENEOUS MEDIA", "latex": "Thus in a battery the electrodes of which are connected by a short thick wire the current is very strong and the heat is generated principally in the cells of the battery and to a much smaller extent in the wire; but if the wire is long and thin, the heat generated in the wire is far greater than that generated in the cells, but if we take into account the heat generated in the wire as well as that generated in the cells, we find that the whole heat generated for each grain of zinc dissolved is the same in both cases.", "markdown": "Thus in a battery the electrodes of which are connected by a short thick wire the current is very strong and the heat is generated principally in the cells of the battery and to a much smaller extent in the wire; but if the wire is long and thin, the heat generated in the wire is far greater than that generated in the cells, but if we take into account the heat generated in the wire as well as that generated in the cells, we find that the whole heat generated for each grain of zinc dissolved is the same in both cases.", "why": "A concrete example of Joule's result: the heat moves between wire and cells, but the total for each grain of zinc stays the same.", "use": [ "lesson", "history" ], "concepts": [ "concept/electric-circuit", "concept/thermal-effect-of-an-electric-current", "experiment/joule-s-experiments", "instrument/voltaic-battery", "law/conservation-of-energy" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/x-52d79efe8b", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-x", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 166", "location": "PHENOMENA OF AN ELECTRIC CURRENT WHICH FLOWS THROUGH HETEROGENEOUS MEDIA", "latex": "Or if the circuit includes an electromagnetic engine which is employed to do work, the heat generated in the circuit is less than that corresponding to the zinc consumed by an amount equal to the heat which would be generated if the work done by the engine were entirely expended in friction.", "markdown": "Or if the circuit includes an electromagnetic engine which is employed to do work, the heat generated in the circuit is less than that corresponding to the zinc consumed by an amount equal to the heat which would be generated if the work done by the engine were entirely expended in friction.", "why": "Shows that when a circuit does mechanical work, the heat in the wire falls by exactly the energy that left as work.", "use": [ "lesson" ], "concepts": [ "law/conservation-of-energy", "quantity/electromotive-force" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/x-fbfa7ca40d", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-x", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 167", "location": "PHENOMENA OF AN ELECTRIC CURRENT WHICH FLOWS THROUGH HETEROGENEOUS MEDIA", "latex": "It is only the strictly reversible processes that must be taken into account in calculating the electromotive force of the circuit.", "markdown": "It is only the strictly reversible processes that must be taken into account in calculating the electromotive force of the circuit.", "why": "Warns learners that irreversible losses do not count towards the electromotive force.", "use": [ "lesson" ], "concepts": [ "concept/reversible-process", "quantity/electromotive-force" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/x-87d9fa7e2c", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-x", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 168", "location": "PHENOMENA OF AN ELECTRIC CURRENT WHICH FLOWS THROUGH HETEROGENEOUS MEDIA", "latex": "The principal seat of polarization is at the surface of the negative metal. When the fluid in which the negative metal is immersed is dilute sulphuric acid, it is seen to become covered with bubbles of hydrogen gas, arising from the electrolytic decomposition of the fluid.", "markdown": "The principal seat of polarization is at the surface of the negative metal. When the fluid in which the negative metal is immersed is dilute sulphuric acid, it is seen to become covered with bubbles of hydrogen gas, arising from the electrolytic decomposition of the fluid.", "why": "Says where polarization happens and what can be seen when it does.", "use": [ "lesson" ], "concepts": [ "concept/polarization", "instrument/voltaic-battery" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/x-17ba27d8f3", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-x", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 170", "location": "PHENOMENA OF AN ELECTRIC CURRENT WHICH FLOWS THROUGH HETEROGENEOUS MEDIA", "latex": "The only difference is that diffusion is always going on, while the current flows only when the battery is in action.", "markdown": "The only difference is that diffusion is always going on, while the current flows only when the battery is in action.", "why": "Compares two processes with the same mathematical form and states the one way they differ.", "use": [ "lesson" ], "concepts": [ "concept/diffusion", "concept/electrolysis" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/x-6a7bd92141", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-x", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 172", "location": "PHENOMENA OF AN ELECTRIC CURRENT WHICH FLOWS THROUGH HETEROGENEOUS MEDIA", "latex": "These defects, however, are more than counterbalanced in all cases where exact measurements are required, by the fact that Daniell's cell exceeds every other known arrangement in constancy of electromotive force.", "markdown": "These defects, however, are more than counterbalanced in all cases where exact measurements are required, by the fact that Daniell’s cell exceeds every other known arrangement in constancy of electromotive force.", "why": "Explains why a cell with a weaker and more resistant output is still preferred for precise measurement.", "use": [ "lesson", "history" ], "concepts": [ "concept/constant-voltaic-element", "instrument/daniell-s-cell" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/x-54a75a0488", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-x", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 167", "location": "PHENOMENA OF AN ELECTRIC CURRENT WHICH FLOWS THROUGH HETEROGENEOUS MEDIA", "latex": "In a voltaic circuit the sum of the electromotive forces from zinc to the electrolyte, from the electrolyte to copper, and from copper to zinc, is not zero but is what is called the electromotive force of the circuit---a measurable quantity. Of these three electromotive forces only one can be separately measured by a legitimate process, that, namely, from copper to zinc.", "markdown": "In a voltaic circuit the sum of the electromotive forces from zinc to the electrolyte, from the electrolyte to copper, and from copper to zinc, is not zero but is what is called the electromotive force of the circuit---a measurable quantity. Of these three electromotive forces only one can be separately measured by a legitimate process, that, namely, from copper to zinc.", "why": "Maxwell's own note on a limit of measurement: the whole circuit's electromotive force is known, but most of its parts are not.", "use": [ "history", "website" ], "concepts": [ "concept/electrolyte", "instrument/voltaic-battery", "person/james-clerk-maxwell", "quantity/electromotive-force" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/x-bbe6c7add1", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-xi", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 173", "location": "METHODS OF MAINTAINING AN ELECTRIC CURRENT", "latex": "The electrification is here produced between the surfaces of two different substances, such as glass and amalgam or ebonite and fur.", "markdown": "The electrification is here produced between the surfaces of two different substances, such as glass and amalgam or ebonite and fur.", "why": "It states plainly where the charge in a frictional machine comes from, before any mechanism is described.", "use": [ "lesson" ], "concepts": [ "concept/electrification", "instrument/frictional-electric-machine" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/x-5d18e17163", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-xi", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 174", "location": "METHODS OF MAINTAINING AN ELECTRIC CURRENT", "latex": "The electromotive force of the machine is the excess of the potential of the comb above that of the rubber. The most convenient test of the electromotive force of an electrical machine is the length of the sparks which it will give.", "markdown": "The electromotive force of the machine is the excess of the potential of the comb above that of the rubber. The most convenient test of the electromotive force of an electrical machine is the length of the sparks which it will give.", "why": "It defines electromotive force as a potential difference and shows a practical way to test it.", "use": [ "lesson" ], "concepts": [ "concept/electric-spark", "quantity/electric-potential", "quantity/electromotive-force" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/x-ffee7d32a9", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-xi", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 180", "location": "METHODS OF MAINTAINING AN ELECTRIC CURRENT", "latex": "I do not propose it as a useful form of machine, but as an example of the method by which the contrivance called in heat-engines a regenerator may be applied to an electrical machine to prevent loss of work.", "markdown": "I do not propose it as a useful form of machine, but as an example of the method by which the contrivance called in heat-engines a regenerator may be applied to an electrical machine to prevent loss of work.", "why": "It shows how an engineering idea from heat-engines carries over to electricity, which helps a learner see the analogy.", "use": [ "history", "lesson" ], "concepts": [ "concept/physical-analogy", "instrument/regenerator" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/x-c4f2368c14", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-xi", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 183", "location": "METHODS OF MAINTAINING AN ELECTRIC CURRENT", "latex": "A great number of the experiments by which Coulomb established the fundamental laws of electricity were made by measuring the force between two small spheres charged with electricity, one of which was fixed while the other was held in equilibrium by two forces, the electrical action between the spheres, and the torsional elasticity of a glass fibre or metal wire.", "markdown": "A great number of the experiments by which Coulomb established the fundamental laws of electricity were made by measuring the force between two small spheres charged with electricity, one of which was fixed while the other was held in equilibrium by two forces, the electrical action between the spheres, and the torsional elasticity of a glass fibre or metal wire.", "why": "It explains how a torsion balance turns an invisible electric force into a measurable twist.", "use": [ "history", "lesson" ], "concepts": [ "instrument/coulomb-s-torsion-balance", "person/charles-augustin-de-coulomb" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/x-808eebec61", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-xi", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 186", "location": "METHODS OF MAINTAINING AN ELECTRIC CURRENT", "latex": "Besides this, by connecting the guard-ring with a metal case surrounding the back of the attracted disk and all its suspending apparatus, the electrification of the back of the disk is rendered impossible, for it is part of the inner surface of a closed hollow conductor all at the same potential.", "markdown": "Besides this, by connecting the guard-ring with a metal case surrounding the back of the attracted disk and all its suspending apparatus, the electrification of the back of the disk is rendered impossible, for it is part of the inner surface of a closed hollow conductor all at the same potential.", "why": "It gives the reason a guarded disk measures only the force it should, a useful lesson in controlling stray effects.", "use": [ "lesson" ], "concepts": [ "concept/closed-conducting-surface", "concept/guard-ring", "instrument/attracted-disk-electrometer" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/x-407d2d5dbf", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-xi", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 176", "location": "METHODS OF MAINTAINING AN ELECTRIC CURRENT", "latex": "In the ordinary frictional electrical machine the work done in overcoming friction is far greater than that done in increasing the electrification. Hence any arrangement by which the electrification may be produced entirely by mechanical work against the electrical forces is of scientific importance if not of practical value.", "markdown": "In the ordinary frictional electrical machine the work done in overcoming friction is far greater than that done in increasing the electrification. Hence any arrangement by which the electrification may be produced entirely by mechanical work against the electrical forces is of scientific importance if not of practical value.", "why": "It frames why machines that avoid friction matter, in Maxwell's own dry, measured tone.", "use": [ "history", "website" ], "concepts": [ "concept/work", "instrument/frictional-electric-machine", "instrument/revolving-doubler" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/x-2504f2dea7", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-xi", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 191", "location": "METHODS OF MAINTAINING AN ELECTRIC CURRENT", "latex": "In order to determine large differences of potential in absolute measure we may employ the attracted disk electrometer, and compare the attraction with the effect of a weight.", "markdown": "In order to determine large differences of potential in absolute measure we may employ the attracted disk electrometer, and compare the attraction with the effect of a weight.", "why": "It introduces how an absolute measure of potential can be made by balancing an electrical attraction against a weight.", "use": [ "lesson", "history" ], "concepts": [ "instrument/attracted-disk-electrometer", "quantity/electric-potential" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/x-14c680b43f", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-xi", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 191", "location": "METHODS OF MAINTAINING AN ELECTRIC CURRENT", "latex": "If the conductor is not large compared with the electrometer, \\(K'\\) will be comparable with \\(K\\), and unless we can ascertain the values of \\(K\\) and \\(K'\\) the second term of the expression will have a doubtful value.", "markdown": "If the conductor is not large compared with the electrometer, K’ will be comparable with K, and unless we can ascertain the values of K and K’ the second term of the expression will have a doubtful value.", "why": "It warns learners that sharing charge with a large or comparable instrument spoils a potential reading unless the capacities are known.", "use": [ "lesson" ], "concepts": [ "instrument/electrometer", "method/measuring-electric-potential", "quantity/capacity" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/x-922f36ed8a", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-xi", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 192", "location": "METHODS OF MAINTAINING AN ELECTRIC CURRENT", "latex": "Since the sphere is not electrified it will be at the potential of the air at the place.", "markdown": "Since the sphere is not electrified it will be at the potential of the air at the place.", "why": "It gives the clear reason why an uncharged sphere can serve as a probe of the air's potential.", "use": [ "lesson" ], "concepts": [ "concept/sphere", "method/measuring-the-potential-at-a-point-in-air", "quantity/electric-charge" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/x-293ae86c2c", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-xi", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 190", "location": "METHODS OF MAINTAINING AN ELECTRIC CURRENT", "latex": "This method of using an auxiliary electrification besides the electrification to be measured is called the Heterostatic method of electrometry, in opposition to the Idiostatic method in which the whole effect is produced by the electrification to be measured.", "markdown": "This method of using an auxiliary electrification besides the electrification to be measured is called the Heterostatic method of electrometry, in opposition to the Idiostatic method in which the whole effect is produced by the electrification to be measured.", "why": "A clear pair of definitions that separates two ways of designing an electrometer.", "use": [ "lesson" ], "concepts": [ "concept/heterostatic-instrument", "concept/idiostatic-instrument" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/x-10ac65d8a8", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-xi", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 193", "location": "METHODS OF MAINTAINING AN ELECTRIC CURRENT", "latex": "If there be a hollow nearly surrounded by the conductor, then the potential at any point of the air in this hollow will be very nearly that of the conductor.", "markdown": "If there be a hollow nearly surrounded by the conductor, then the potential at any point of the air in this hollow will be very nearly that of the conductor.", "why": "It explains how a conductor's potential can be read without touching it, by sampling the air inside a nearly closed hollow.", "use": [ "lesson", "website" ], "concepts": [ "concept/closed-conducting-surface", "method/measuring-potential-without-touching-the-conductor" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/x-64fc2c6286", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-xi", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 193", "location": "METHODS OF MAINTAINING AN ELECTRIC CURRENT", "latex": "If by any means we can cause a succession of small bodies to detach themselves from the end of the electrode, the potential of the electrode will approximate to that of the surrounding air. This may be done by causing shot, filings, sand, or water to drop out of a funnel or pipe connected with the electrode. The point at which the potential is measured is that at which the stream ceases to be continuous and breaks into separate parts or drops.", "markdown": "If by any means we can cause a succession of small bodies to detach themselves from the end of the electrode, the potential of the electrode will approximate to that of the surrounding air. This may be done by causing shot, filings, sand, or water to drop out of a funnel or pipe connected with the electrode. The point at which the potential is measured is that at which the stream ceases to be continuous and breaks into separate parts or drops.", "why": "It gives a vivid, concrete way to equalise an electrode's potential with the air using falling drops.", "use": [ "lesson", "website" ], "concepts": [ "concept/electrode", "method/measuring-potential-by-a-stream-of-falling-drops" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/x-1c734f3b86", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-xi", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 191", "location": "METHODS OF MAINTAINING AN ELECTRIC CURRENT", "latex": "To ascertain the potential of a charged conductor of finite size we may connect the conductor with one electrode of the electrometer, while the other is connected to earth or to a body of constant potential. The electrometer reading will give the potential of the conductor after the division of its electricity between it and the part of the electrometer with which it is put in contact.", "markdown": "To ascertain the potential of a charged conductor of finite size we may connect the conductor with one electrode of the electrometer, while the other is connected to earth or to a body of constant potential. The electrometer reading will give the potential of the conductor after the division of its electricity between it and the part of the electrometer with which it is put in contact.", "why": "It states the basic way to measure a conductor's potential and why the reading is a shared, post-contact value.", "use": [ "lesson", "website" ], "concepts": [ "concept/electrode", "instrument/electrometer", "method/measuring-the-potential-of-a-charged-conductor-of-finite-size" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/x-a453ad3e17", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-xi", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 191", "location": "METHODS OF MAINTAINING AN ELECTRIC CURRENT", "latex": "But if we can make the potential of the electrode of the electrometer very nearly equal to that of the body before making contact, then the uncertainty of the values of \\(K\\) and \\(K'\\) will be of little consequence.", "markdown": "But if we can make the potential of the electrode of the electrometer very nearly equal to that of the body before making contact, then the uncertainty of the values of K and K’ will be of little consequence.", "why": "It shows how a clever setup removes the need to know the capacities.", "use": [ "lesson" ], "concepts": [ "quantity/capacity", "theorem/common-potential-after-contact" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/x-a12903328e", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-xi", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 192", "location": "METHODS OF MAINTAINING AN ELECTRIC CURRENT", "latex": "Now let the sphere thus discharged be carried to the end of the wire and made to touch it. Since the sphere is not electrified it will be at the potential of the air at the place. If the electrode wire is at the same potential it will not be affected by the contact, but if the electrode is at a different potential it will by contact with the sphere be made nearer to that of the air than it was before. By a succession of such operations, the sphere being alternately discharged and made to touch the electrode, the potential of the electrode of the electrometer will continually approach that of the air at the given point.", "markdown": "Now let the sphere thus discharged be carried to the end of the wire and made to touch it. Since the sphere is not electrified it will be at the potential of the air at the place. If the electrode wire is at the same potential it will not be affected by the contact, but if the electrode is at a different potential it will by contact with the sphere be made nearer to that of the air than it was before. By a succession of such operations, the sphere being alternately discharged and made to touch the electrode, the potential of the electrode of the electrometer will continually approach that of the air at the given point.", "why": "It explains step by step how repeated contacts bring the electrode closer to the air's potential.", "use": [ "lesson", "website" ], "concepts": [ "method/approximating-air-potential-by-repeated-contact-with-a-discharged-sphere", "method/discharging-a-conductor", "quantity/electric-potential" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/x-5dc967468a", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-xi", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 193", "location": "METHODS OF MAINTAINING AN ELECTRIC CURRENT", "latex": "To measure the potential of a conductor without touching it, we may measure the potential of the air at any point in the neighbourhood of the conductor, and calculate that of the conductor from the result. If there be a hollow nearly surrounded by the conductor, then the potential at any point of the air in this hollow will be very nearly that of the conductor.", "markdown": "To measure the potential of a conductor without touching it, we may measure the potential of the air at any point in the neighbourhood of the conductor, and calculate that of the conductor from the result. If there be a hollow nearly surrounded by the conductor, then the potential at any point of the air in this hollow will be very nearly that of the conductor.", "why": "It shows that a potential can be inferred from the surrounding air without touching the conductor.", "use": [ "lesson" ], "concepts": [ "concept/conductor", "method/measuring-potential-without-touching-the-conductor" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/x-67146d2af8", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-xi", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 193", "location": "METHODS OF MAINTAINING AN ELECTRIC CURRENT", "latex": "In this way it has been ascertained by Sir W. Thomson that if two hollow conductors, one of copper and the other of zinc, are in metallic contact, then the potential of the air in the hollow surrounded by zinc is positive with reference to that of the air in the hollow surrounded by copper.", "markdown": "In this way it has been ascertained by Sir W. Thomson that if two hollow conductors, one of copper and the other of zinc, are in metallic contact, then the potential of the air in the hollow surrounded by zinc is positive with reference to that of the air in the hollow surrounded by copper.", "why": "A historical result showing the method applied to a real experimental question.", "use": [ "history", "website" ], "concepts": [ "concept/closed-conducting-surface", "method/measuring-potential-without-touching-the-conductor", "person/william-thomson", "quantity/electric-potential" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/x-c5712abe54", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-xi", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 174", "location": "METHODS OF MAINTAINING AN ELECTRIC CURRENT", "latex": "Thus the rotation of the machine carries the positive electrification of the surface of the glass from the rubber to the comb, and the negative electric wind of the comb either neutralizes the positively electrified surface, or is carried round with it to the rubber, so that there is a continual current of positive electricity kept up from the rubber to the comb, or, what is the same thing, of negative electricity from the comb to the rubber, or, since the mode of expressing the fact is indifferent, we may, if we please, describe it as consisting of a positive current in the one direction combined with a negative current in the other the arithmetical sum of these two imaginary currents being the actual current observed.", "markdown": "Thus the rotation of the machine carries the positive electrification of the surface of the glass from the rubber to the comb, and the negative electric wind of the comb either neutralizes the positively electrified surface, or is carried round with it to the rubber, so that there is a continual current of positive electricity kept up from the rubber to the comb, or, what is the same thing, of negative electricity from the comb to the rubber, or, since the mode of expressing the fact is indifferent, we may, if we please, describe it as consisting of a positive current in the one direction combined with a negative current in the other the arithmetical sum of these two imaginary currents being the actual current observed.", "why": "Shows that a current can be described as positive charge one way or negative charge the other, and that the choice of description is a convention.", "use": [ "lesson" ], "concepts": [ "concept/electric-current", "instrument/frictional-electric-machine" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/x-089a98bfe5", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-xi", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 175", "location": "METHODS OF MAINTAINING AN ELECTRIC CURRENT", "latex": "In order that the machine may work to the best advantage this slipping back of the electricity must be prevented.", "markdown": "In order that the machine may work to the best advantage this slipping back of the electricity must be prevented.", "why": "Names the practical limit on a frictional machine and leads into the idea of an even potential slope.", "use": [ "lesson" ], "concepts": [ "concept/potential-gradient", "concept/silk-flap", "instrument/frictional-electric-machine" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/x-bd48ac009a", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-xi", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 176", "location": "METHODS OF MAINTAINING AN ELECTRIC CURRENT", "latex": "It was by means of the revolving doubler that Volta succeeded in developing from the electrification of the pile an electrification capable of affecting his electrometer.", "markdown": "It was by means of the revolving doubler that Volta succeeded in developing from the electrification of the pile an electrification capable of affecting his electrometer.", "why": "A historical remark showing why the doubler mattered: it let Volta detect a very small electrification.", "use": [ "history", "website" ], "concepts": [ "instrument/revolving-doubler", "person/alessandro-volta" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/x-62d7728e7b", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-xi", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 178", "location": "METHODS OF MAINTAINING AN ELECTRIC CURRENT", "latex": "On the other hand, the quantity \\(pU - qV\\) continually increases, so that, however little \\(pU\\) may exceed or fall short of \\(qV\\) at first, the difference will be increased in a geometrical ratio in each revolution till the electromotive forces become so great that the insulation of the apparatus is overcome.", "markdown": "On the other hand, the quantity pU - qV continually increases, so that, however little pU may exceed or fall short of qV at first, the difference will be increased in a geometrical ratio in each revolution till the electromotive forces become so great that the insulation of the apparatus is overcome.", "why": "Shows geometrical growth at work: any tiny initial imbalance in a doubler is multiplied every turn until insulation fails.", "use": [ "lesson" ], "concepts": [ "concept/geometrical-progression", "instrument/revolving-doubler" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/x-58b8417eea", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-xi", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 181", "location": "METHODS OF MAINTAINING AN ELECTRIC CURRENT", "latex": "This conductor \\(C'\\), by which the carrier is enabled to be connected to earth without a spark, answers to the contrivance called a regenerator in heat-engines. We shall therefore call it a Regenerator.", "markdown": "This conductor C’, by which the carrier is enabled to be connected to earth without a spark, answers to the contrivance called a regenerator in heat-engines. We shall therefore call it a Regenerator.", "why": "An analogy across fields: a heat-engine device is borrowed to explain how a machine avoids the energy lost in sparks.", "use": [ "lesson", "history" ], "concepts": [ "instrument/carrier", "instrument/regenerator" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/x-690a9082ee", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-xi", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 184", "location": "METHODS OF MAINTAINING AN ELECTRIC CURRENT", "latex": "In all electrometers it is of the greatest importance to know what force we are measuring. The force acting on the suspended sphere is due partly to the direct action of the fixed sphere, but partly also to the electrification, if any, of the sides of the case.", "markdown": "In all electrometers it is of the greatest importance to know what force we are measuring. The force acting on the suspended sphere is due partly to the direct action of the fixed sphere, but partly also to the electrification, if any, of the sides of the case.", "why": "A warning about measurement: stray electrification of the apparatus itself can corrupt a reading.", "use": [ "lesson", "website" ], "concepts": [ "instrument/coulomb-s-torsion-balance", "instrument/electrometer" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/x-a36a008a14", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-xi", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 189", "location": "METHODS OF MAINTAINING AN ELECTRIC CURRENT", "latex": "When the distance is too small a small change of absolute distance makes a great change in the force, since the force varies inversely as the square of the distance, so that any error in the absolute distance introduces a large error in the result unless the distance is large compared with the limits of error of the micrometer screw.", "markdown": "When the distance is too small a small change of absolute distance makes a great change in the force, since the force varies inversely as the square of the distance, so that any error in the absolute distance introduces a large error in the result unless the distance is large compared with the limits of error of the micrometer screw.", "why": "Explains with an inverse-square law why experimenters measure differences at convenient distances instead of trusting small absolute distances.", "use": [ "lesson" ], "concepts": [ "instrument/attracted-disk-electrometer", "method/measuring-a-small-electromotive-force" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/x-c6819dbe56", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-xii", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 208", "location": "THE MEASUREMENT OF ELECTRIC RESISTANCE", "latex": "The comparison which can be effected with the greatest exactness is that of two equal resistances.", "markdown": "The comparison which can be effected with the greatest exactness is that of two equal resistances.", "why": "States why the bridge is best used for matching equal resistances, which sets up the whole section.", "use": [ "lesson", "website" ], "concepts": [ "instrument/wheatstone-s-bridge", "method/comparing-equal-resistances-with-wheatstone-s-bridge", "method/comparing-two-equal-resistances-with-wheatstone-s-bridge", "quantity/resistance" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/x-8d29231383", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-xii", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 209", "location": "THE MEASUREMENT OF ELECTRIC RESISTANCE", "latex": "The remaining difference between \\(\\beta\\) and \\(\\gamma\\) will now produce a ten times greater difference in the position of \\(Q\\) than with the original coils \\(b\\) and \\(c\\), and in this way we can continually increase the accuracy of the comparison.", "markdown": "The remaining difference between and will now produce a ten times greater difference in the position of Q than with the original coils b and c, and in this way we can continually increase the accuracy of the comparison.", "why": "It shows learners how replacing the arm coils with ones ten times larger magnifies the scale shift, so that accuracy can be raised step by step.", "use": [ "lesson" ], "concepts": [ "instrument/resistance-coil", "method/comparing-two-equal-resistances-with-wheatstone-s-bridge" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/x-a83384a938", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-xii", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 210", "location": "THE MEASUREMENT OF ELECTRIC RESISTANCE", "latex": "The battery must never be introduced instead of the galvanometer into the wire with a sliding contact, for the passage of a powerful current at the point of contact would injure the surface of the wire.", "markdown": "The battery must never be introduced instead of the galvanometer into the wire with a sliding contact, for the passage of a powerful current at the point of contact would injure the surface of the wire.", "why": "Gives a practical warning about which instrument goes where, with the reason.", "use": [ "lesson", "website" ], "concepts": [ "concept/battery", "instrument/galvanometer", "instrument/slide-wire", "instrument/voltaic-battery", "instrument/wheatstone-s-bridge" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/x-69b3d6ba0c", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-xii", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 211", "location": "THE MEASUREMENT OF ELECTRIC RESISTANCE", "latex": "It will be observed that though this is not a null method, in the sense of there being no current in the galvanometer, it is so in the sense of the fact observed being the negative one, that the deflexion of the galvanometer is not changed when a certain contact is made. An observation of this kind is of greater value than an observation of the equality of two different deflexions of the same galvanometer, for in the latter case there is time for alteration in the strength of the battery or the sensitiveness of the galvanometer, whereas when the deflexion remains constant, in spite of certain changes which we can repeat at pleasure, we are sure that the current is quite independent of these changes.", "markdown": "It will be observed that though this is not a null method, in the sense of there being no current in the galvanometer, it is so in the sense of the fact observed being the negative one, that the deflexion of the galvanometer is not changed when a certain contact is made. An observation of this kind is of greater value than an observation of the equality of two different deflexions of the same galvanometer, for in the latter case there is time for alteration in the strength of the battery or the sensitiveness of the galvanometer, whereas when the deflexion remains constant, in spite of certain changes which we can repeat at pleasure, we are sure that the current is quite independent of these changes.", "why": "Explains why seeing no change is a stronger observation than comparing two readings.", "use": [ "lesson", "website" ], "concepts": [ "instrument/galvanometer", "method/determining-galvanometer-resistance-by-thomson-s-method", "method/null-method", "method/thomson-s-method-of-determining-galvanometer-resistance" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/x-c40af54fd8", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-xii", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 212", "location": "THE MEASUREMENT OF ELECTRIC RESISTANCE", "latex": "In this method of measuring the resistance of the battery, the current in the battery is not in any way interfered with during the operation, so that we may ascertain its resistance for any given strength of current, so as to determine how the strength of current affects the resistance.", "markdown": "In this method of measuring the resistance of the battery, the current in the battery is not in any way interfered with during the operation, so that we may ascertain its resistance for any given strength of current, so as to determine how the strength of current affects the resistance.", "why": "It explains why a measurement that leaves the current undisturbed can reveal how battery resistance depends on current strength.", "use": [ "lesson", "history" ], "concepts": [ "instrument/voltaic-battery", "method/determining-battery-resistance-by-mance-s-method", "quantity/resistance" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/x-5b4c48bbab", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-xii", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 214", "location": "THE MEASUREMENT OF ELECTRIC RESISTANCE", "latex": "This method, in which, at the time of the comparison, there is no current through either of the electromotors, is a modification of Poggendorff's method, and is due to Mr.\\ Latimer Clark, who has deduced the following values of electromotive forces:", "markdown": "This method, in which, at the time of the comparison, there is no current through either of the electromotors, is a modification of Poggendorff’s method, and is due to Mr. Latimer Clark, who has deduced the following values of electromotive forces:", "why": "It credits a named modification to its author and introduces the table of cell EMFs in volts that follows it.", "use": [ "history" ], "concepts": [ "method/comparing-electromotive-forces-by-poggendorff-s-compensation-method", "person/latimer-clark", "unit/volt" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/x-7736342d61", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-xii", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 195", "location": "THE MEASUREMENT OF ELECTRIC RESISTANCE", "latex": "In the electromagnetic system a resistance is a quantity homogeneous with a velocity, and may therefore be expressed as a velocity.", "markdown": "In the electromagnetic system a resistance is a quantity homogeneous with a velocity, and may therefore be expressed as a velocity.", "why": "It gives the learner a striking way to see what a resistance is in the electromagnetic system, as a velocity rather than a fixed property of a wire.", "use": [ "lesson" ], "concepts": [ "quantity/resistance" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/x-ebcf565c74", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-xii", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 202", "location": "THE MEASUREMENT OF ELECTRIC RESISTANCE", "latex": "The merit of the method consists in the fact that the thing observed is the absence of any deflexion, or in other words, the method is a Null method, one in which the non-existence of a force is asserted from an observation in which the force, if it had been different from zero by more than a certain small amount, would have produced an observable effect.", "markdown": "The merit of the method consists in the fact that the thing observed is the absence of any deflexion, or in other words, the method is a Null method, one in which the non-existence of a force is asserted from an observation in which the force, if it had been different from zero by more than a certain small amount, would have produced an observable effect.", "why": "It explains in one sentence why measuring zero is more reliable than measuring a small nonzero reading.", "use": [ "lesson" ], "concepts": [ "instrument/differential-galvanometer", "method/null-method" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/x-4fda1f8c87", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-xii", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 204", "location": "THE MEASUREMENT OF ELECTRIC RESISTANCE", "latex": "The conductors \\(BC\\) and \\(OA\\) are then said to be \\textit{conjugate} to each other, which implies a certain relation between the resistances of the other four conductors, and this relation is made use of in measuring resistances.", "markdown": "The conductors BC and OA are then said to be *conjugate* to each other, which implies a certain relation between the resistances of the other four conductors, and this relation is made use of in measuring resistances.", "why": "It shows the learner the idea behind the bridge: a balanced arrangement fixes a relation among four resistances, which is then used to find one of them.", "use": [ "lesson" ], "concepts": [ "concept/conjugate-conductors", "instrument/wheatstone-s-bridge" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/x-fd3639a2ff", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-xii", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 199", "location": "THE MEASUREMENT OF ELECTRIC RESISTANCE", "latex": "This method, founded on the binary scale, is that in which the smallest number of separate coils is needed, and it is also that which can be most readily tested.", "markdown": "This method, founded on the binary scale, is that in which the smallest number of separate coils is needed, and it is also that which can be most readily tested.", "why": "It shows a practical use of the binary scale, where fewer coils make a resistance box both smaller and easier to check.", "use": [ "lesson", "website" ], "concepts": [ "concept/binary-scale", "instrument/resistance-box" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/x-da0427caf6", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-xii", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 206", "location": "THE MEASUREMENT OF ELECTRIC RESISTANCE", "latex": "Of the two resistances, that of the battery and that of the galvanometer, connect the greater resistance so as to join the two greatest to the two least of the four other resistances.", "markdown": "Of the two resistances, that of the battery and that of the galvanometer, connect the greater resistance so as to join the two greatest to the two least of the four other resistances.", "why": "It gives the learner a clear rule for arranging a bridge to get the largest galvanometer deflexion.", "use": [ "lesson" ], "concepts": [ "instrument/galvanometer", "instrument/wheatstone-s-bridge" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/x-5e90638488", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-xii", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 195", "location": "THE MEASUREMENT OF ELECTRIC RESISTANCE", "latex": "It is sometimes referred to as the B.A. unit, but in order to connect it with the name of the discoverer of the laws of resistance, it is called the Ohm.", "markdown": "It is sometimes referred to as the B.A. unit, but in order to connect it with the name of the discoverer of the laws of resistance, it is called the Ohm.", "why": "It tells the story behind the name of the ohm, linking a unit to the physicist who discovered the laws of resistance.", "use": [ "history", "website" ], "concepts": [ "person/georg-simon-ohm" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/x-89fbdc0215", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-xii", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 209", "location": "THE MEASUREMENT OF ELECTRIC RESISTANCE", "latex": "The coils \\(\\beta\\) and \\(\\gamma\\) are then made to change places, and a new position is found for \\(Q\\). If this new position is the same as the old one, then we know that the exchange of \\(\\beta\\) and \\(\\gamma\\) has produced no change in the proportions of the resistances, and therefore \\(\\gamma\\) is rightly adjusted.", "markdown": "The coils and are then made to change places, and a new position is found for Q. If this new position is the same as the old one, then we know that the exchange of and has produced no change in the proportions of the resistances, and therefore is rightly adjusted.", "why": "Shows the swap trick that turns a balance into a check for equality.", "use": [ "lesson" ], "concepts": [ "method/comparing-equal-resistances-with-wheatstone-s-bridge" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/x-1890dd46d6", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-xii", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 211", "location": "THE MEASUREMENT OF ELECTRIC RESISTANCE", "latex": "By the method now described the galvanometer itself is employed to measure its own resistance.", "markdown": "By the method now described the galvanometer itself is employed to measure its own resistance.", "why": "A short, memorable summary of the idea behind Thomson's method.", "use": [ "website", "lesson" ], "concepts": [ "instrument/galvanometer", "method/thomson-s-method-of-determining-galvanometer-resistance" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/x-13f15d9736", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-xii", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 211", "location": "THE MEASUREMENT OF ELECTRIC RESISTANCE", "latex": "The measurement of the resistance of a battery when in action is of a much higher order of difficulty, since the resistance of the battery is found to change considerably for some time after the strength of the current through it is changed.", "markdown": "The measurement of the resistance of a battery when in action is of a much higher order of difficulty, since the resistance of the battery is found to change considerably for some time after the strength of the current through it is changed.", "why": "Explains why measuring battery resistance is hard and why Mance's method was needed.", "use": [ "lesson", "history" ], "concepts": [ "concept/battery", "method/determining-battery-resistance-by-mance-s-method", "quantity/resistance" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/x-fafd00188e", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-xii", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 213", "location": "THE MEASUREMENT OF ELECTRIC RESISTANCE", "latex": "This method, as has been pointed out by Professor Oliver Lodge, is not free from error on account of the variation of the E.M.F. of the battery, as the current through it is diminished or increased by raising or depressing the key.", "markdown": "This method, as has been pointed out by Professor Oliver Lodge, is not free from error on account of the variation of the E.M.F. of the battery, as the current through it is diminished or increased by raising or depressing the key.", "why": "The editor's footnote records a known flaw in the method, showing that methods carry their own limitations.", "use": [ "history", "lesson" ], "concepts": [ "method/determining-battery-resistance-by-mance-s-method", "person/oliver-lodge", "quantity/electromotive-force" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/x-957cb978cf", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-xii", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 213", "location": "THE MEASUREMENT OF ELECTRIC RESISTANCE", "latex": "Let the electromotive force \\(E\\) of the battery be greater than that of either of the electromotors to be compared, then, if a sufficient resistance, \\(R_1\\), be interposed between the points \\(A_1\\), \\(B_1\\) of the primary circuit \\(EB_1A_1E\\), the electromotive force from \\(B_1\\) to \\(A_1\\) may be made equal to that of the electromotor \\(E_1\\). If the electrodes of this electromotor are now connected with the points \\(A_1\\), \\(B_1\\) no current will flow through the electromotor.", "markdown": "Let the electromotive force E of the battery be greater than that of either of the electromotors to be compared, then, if a sufficient resistance, R_1, be interposed between the points A_1, B_1 of the primary circuit EB_1A_1E, the electromotive force from B_1 to A_1 may be made equal to that of the electromotor E_1. If the electrodes of this electromotor are now connected with the points A_1, B_1 no current will flow through the electromotor.", "why": "Describes the core of the compensation method: balance an unknown electromotive force against a known fall of potential so that it draws no current.", "use": [ "lesson" ], "concepts": [ "method/comparing-electromotive-forces-by-poggendorff-s-compensation-method", "quantity/electromotive-force", "quantity/resistance" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/x-c45fd744be", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-xii", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 194", "location": "THE MEASUREMENT OF ELECTRIC RESISTANCE", "latex": "\\textsc{In} the present state of electrical science, the determination of the electric resistance of a conductor may be considered as the cardinal operation in electricity, in the same sense that the determination of weight is the cardinal operation in chemistry.", "markdown": "In the present state of electrical science, the determination of the electric resistance of a conductor may be considered as the cardinal operation in electricity, in the same sense that the determination of weight is the cardinal operation in chemistry.", "why": "It explains why resistance is the central measurement in electricity, using the chemist's balance as a comparison.", "use": [ "lesson", "website" ], "concepts": [ "concept/standard-of-resistance", "quantity/resistance" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/x-19bf434cbf", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-xii", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 195", "location": "THE MEASUREMENT OF ELECTRIC RESISTANCE", "latex": "To recollect its value in absolute measure it is useful to know that ten millions of metres is professedly the distance from the pole to the equator, measured along the meridian of Paris. A body, therefore, which in one second travels along a meridian from the pole to the equator would have a velocity which, on the electromagnetic system, is professedly represented by an Ohm.", "markdown": "To recollect its value in absolute measure it is useful to know that ten millions of metres is professedly the distance from the pole to the equator, measured along the meridian of Paris. A body, therefore, which in one second travels along a meridian from the pole to the equator would have a velocity which, on the electromagnetic system, is professedly represented by an Ohm.", "why": "It gives a memorable picture of the size of an ohm by tying it to a velocity across the Earth.", "use": [ "lesson", "website" ], "concepts": [ "concept/electromagnetic-system-of-units", "person/georg-simon-ohm", "quantity/resistance" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/x-3553f8c73f", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-xii", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 195", "location": "THE MEASUREMENT OF ELECTRIC RESISTANCE", "latex": "In the same way the metre is professedly one ten-millionth of a certain quadrantal arc, but though this is found not to be exactly true, the length of the metre has not been altered, but the dimensions of the earth are expressed by a less simple number.", "markdown": "In the same way the metre is professedly one ten-millionth of a certain quadrantal arc, but though this is found not to be exactly true, the length of the metre has not been altered, but the dimensions of the earth are expressed by a less simple number.", "why": "It shows that a standard is kept fixed and the measurements are corrected, using the metre as the example.", "use": [ "history", "lesson" ], "concepts": [ "concept/standard-of-resistance", "person/georg-simon-ohm" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/x-0a3956c65a", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-xii", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 199", "location": "THE MEASUREMENT OF ELECTRIC RESISTANCE", "latex": "Each interval between the electrodes is marked with the resistance of the corresponding coil, so that if we wish to make the resistance box equal to 107 we express 107 in the binary scale as \\(64 + 32 + 8 + 2 + 1\\) or \\(1101011\\). We then take the plugs out of the holes corresponding to 64, 32, 8, 2 and 1, and leave the plugs in 16 and 4.", "markdown": "Each interval between the electrodes is marked with the resistance of the corresponding coil, so that if we wish to make the resistance box equal to 107 we express 107 in the binary scale as 64 + 32 + 8 + 2 + 1 or 1101011. We then take the plugs out of the holes corresponding to 64, 32, 8, 2 and 1, and leave the plugs in 16 and 4.", "why": "A worked example showing how binary numbers set a resistance box to a chosen value.", "use": [ "lesson", "website" ], "concepts": [ "concept/binary-scale", "instrument/resistance-box" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/x-7442fda949", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-xii", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 202", "location": "THE MEASUREMENT OF ELECTRIC RESISTANCE", "latex": "Null methods are of great value where they can be employed, but they can only be employed where we can cause two equal and opposite quantities of the same kind to enter into the experiment together.", "markdown": "Null methods are of great value where they can be employed, but they can only be employed where we can cause two equal and opposite quantities of the same kind to enter into the experiment together.", "why": "It states both the strength and the limit of null methods in one sentence.", "use": [ "lesson" ], "concepts": [ "method/null-method" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/x-0104d48317", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-xii", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 200", "location": "THE MEASUREMENT OF ELECTRIC RESISTANCE", "latex": "But this is rather to be taken as an example of a faulty method than as a practical method of determining resistance. The electromotive force \\(E\\) cannot be maintained rigorously constant, and the internal resistance of the battery is also exceedingly variable, so that any methods in which these are assumed to be even for a short time constant are not to be depended on.", "markdown": "But this is rather to be taken as an example of a faulty method than as a practical method of determining resistance. The electromotive force E cannot be maintained rigorously constant, and the internal resistance of the battery is also exceedingly variable, so that any methods in which these are assumed to be even for a short time constant are not to be depended on.", "why": "A warning that a method is unsound if it assumes quantities stay constant that really drift.", "use": [ "lesson", "website" ], "concepts": [ "concept/comparison-of-resistances", "quantity/electromotive-force", "theorem/ohm-s-formula" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/x-2ab2efb45a", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-xii", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 204", "location": "THE MEASUREMENT OF ELECTRIC RESISTANCE", "latex": "The galvanometer is only required to be sensitive enough to detect the existence and direction of a current, without in any way determining its value or comparing its value with that of another current.", "markdown": "The galvanometer is only required to be sensitive enough to detect the existence and direction of a current, without in any way determining its value or comparing its value with that of another current.", "why": "It shows why the bridge method is robust: it needs only a yes/no signal of current, not a calibrated reading.", "use": [ "lesson" ], "concepts": [ "instrument/galvanometer", "instrument/wheatstone-s-bridge", "method/null-method" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/x-9f3ec35fcd", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-xiii", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 215", "location": "ON THE ELECTRIC RESISTANCE OF SUBSTANCES", "latex": "The resistance of this class of bodies is enormous compared with that of the metals. It diminishes as the temperature rises.", "markdown": "The resistance of this class of bodies is enormous compared with that of the metals. It diminishes as the temperature rises.", "why": "It gives a learner the contrast that dielectrics resist far more than metals, yet their resistance falls as they warm.", "use": [ "lesson" ], "concepts": [ "concept/dielectric", "quantity/resistance" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/x-68a8313e38", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-xiii", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 218", "location": "ON THE ELECTRIC RESISTANCE OF SUBSTANCES", "latex": "The measurement of the electric resistance of electrolytes is rendered difficult on account of the polarization of the electrodes, which causes the observed difference of potentials of the metallic electrodes to be greater than the electromotive force which actually produces the current.", "markdown": "The measurement of the electric resistance of electrolytes is rendered difficult on account of the polarization of the electrodes, which causes the observed difference of potentials of the metallic electrodes to be greater than the electromotive force which actually produces the current.", "why": "It explains the practical obstacle that polarization poses when measuring an electrolyte's resistance.", "use": [ "lesson", "website" ], "concepts": [ "concept/electrolyte", "concept/polarization" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/x-ad7bee4e88", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-xiii", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 215", "location": "ON THE ELECTRIC RESISTANCE OF SUBSTANCES", "latex": "In all these substances conduction takes place without any decomposition, or alteration of the chemical nature of the substance, either in its interior or where the current enters and leaves the body. In all of them the resistance increases as the temperature rises.", "markdown": "In all these substances conduction takes place without any decomposition, or alteration of the chemical nature of the substance, either in its interior or where the current enters and leaves the body. In all of them the resistance increases as the temperature rises.", "why": "It shows that metals conduct without changing their chemistry, and that their resistance grows with temperature, which sets them apart from electrolytes.", "use": [ "lesson" ], "concepts": [ "concept/conductor", "quantity/resistance", "quantity/temperature-coefficient-of-resistance" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/x-961c9e9dca", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-xiii", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 221", "location": "ON THE ELECTRIC RESISTANCE OF SUBSTANCES", "latex": "These phenomena seem to be due to a condition of the gutta-percha, which, for want of a better name, we may call polarization, and which we may compare on the one hand with that of a series of Leyden jars charged by cascade, and, on the other, with Ritter's secondary pile.", "markdown": "These phenomena seem to be due to a condition of the gutta-percha, which, for want of a better name, we may call polarization, and which we may compare on the one hand with that of a series of Leyden jars charged by cascade, and, on the other, with Ritter’s secondary pile.", "why": "It gives the author's own analogy for polarization in a dielectric, linking it to charged Leyden jars.", "use": [ "history", "website" ], "concepts": [ "concept/dielectric", "concept/polarization", "concept/residual-discharge" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/x-b51d67aae3", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-xiii", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 217", "location": "ON THE ELECTRIC RESISTANCE OF SUBSTANCES", "latex": "Hence ordinary resistance coils are made of German silver, on account of its great resistance, and its small variation with temperature.", "markdown": "Hence ordinary resistance coils are made of German silver, on account of its great resistance, and its small variation with temperature.", "why": "It shows how an alloy's properties are chosen for a practical instrument, giving learners a concrete reason to care about temperature dependence.", "use": [ "lesson" ], "concepts": [ "concept/alloy", "quantity/resistance", "quantity/temperature-coefficient-of-resistance" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/x-4696da793a", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-xiii", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 216", "location": "ON THE ELECTRIC RESISTANCE OF SUBSTANCES", "latex": "It is of the utmost importance in the electric telegraph that the metal of which the wires are made should have the smallest attainable resistance. Measurements of resistance must therefore be made before selecting the materials.", "markdown": "It is of the utmost importance in the electric telegraph that the metal of which the wires are made should have the smallest attainable resistance. Measurements of resistance must therefore be made before selecting the materials.", "why": "Shows a learner why measuring resistance mattered in practical telegraph engineering.", "use": [ "lesson", "history" ], "concepts": [ "concept/conductor", "instrument/resistance-coil", "quantity/resistance" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/x-a101d83262", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-xiii", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 215", "location": "ON THE ELECTRIC RESISTANCE OF SUBSTANCES", "latex": "\\textsc{There} are three classes in which we may place different substances in relation to the passage of electricity through them.", "markdown": "There are three classes in which we may place different substances in relation to the passage of electricity through them.", "why": "Opens the chapter with the organising idea that substances divide into conductors, electrolytes and dielectrics.", "use": [ "lesson", "website" ], "concepts": [ "concept/conductor", "concept/dielectric", "concept/electrolyte" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/x-39bffe1e9e", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-xiii", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 218", "location": "ON THE ELECTRIC RESISTANCE OF SUBSTANCES", "latex": "Finally, by making two different experiments, in one of which the path of the current through the electrolyte is much longer than in the other, and so adjusting the electromotive force that the actual current, and the time during which it flows, are nearly the same in each case, we can eliminate the effect of polarization altogether.", "markdown": "Finally, by making two different experiments, in one of which the path of the current through the electrolyte is much longer than in the other, and so adjusting the electromotive force that the actual current, and the time during which it flows, are nearly the same in each case, we can eliminate the effect of polarization altogether.", "why": "Shows how a clever experimental design cancels a systematic error instead of correcting for it.", "use": [ "lesson" ], "concepts": [ "concept/electrolyte", "concept/polarization", "method/paalzow-s-siphon-method" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/x-cb854a1911", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-xiii", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 220", "location": "ON THE ELECTRIC RESISTANCE OF SUBSTANCES", "latex": "But even after this current has been allowed to subside the residual current is not constant, and does not indicate the true conductivity of the substance. It is found that the current continues to decrease for at least half an hour, so that a determination of the resistance deduced from the current will give a greater value if a certain time is allowed to elapse than if taken immediately after applying the battery.", "markdown": "But even after this current has been allowed to subside the residual current is not constant, and does not indicate the true conductivity of the substance. It is found that the current continues to decrease for at least half an hour, so that a determination of the resistance deduced from the current will give a greater value if a certain time is allowed to elapse than if taken immediately after applying the battery.", "why": "Warns that a measured resistance can depend on how long one waits, so the timing of a reading matters.", "use": [ "lesson", "website" ], "concepts": [ "concept/dielectric", "concept/residual-discharge", "quantity/resistance" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/x-58c84fe670", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-xiii", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 221", "location": "ON THE ELECTRIC RESISTANCE OF SUBSTANCES", "latex": "Thus, with Hooper's insulating material the apparent resistance at the end of ten minutes was four times, and at the end of nineteen hours twenty-three times that observed at the end of one minute.", "markdown": "Thus, with Hooper’s insulating material the apparent resistance at the end of ten minutes was four times, and at the end of nineteen hours twenty-three times that observed at the end of one minute.", "why": "Gives concrete numbers showing how strongly the apparent resistance of an insulator drifts over time.", "use": [ "lesson", "history" ], "concepts": [ "concept/dielectric", "concept/polarization", "quantity/resistance" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/x-31d0c395dd", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-xiii", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 223", "location": "ON THE ELECTRIC RESISTANCE OF SUBSTANCES", "latex": "When the maximum polarization is established, the excess of electromotive force above that of 304 cells is devoted to maintaining the current according to Ohm's Law.", "markdown": "When the maximum polarization is established, the excess of electromotive force above that of 304 cells is devoted to maintaining the current according to Ohm’s Law.", "why": "Explains how Varley's gas-tube results combine a fixed threshold with an Ohm's-law part.", "use": [ "lesson", "history" ], "concepts": [ "concept/current-through-a-rarefied-gas", "concept/polarization", "law/ohm-s-law" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/x-53180185a2", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-xiii", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 222", "location": "ON THE ELECTRIC RESISTANCE OF SUBSTANCES", "latex": "The whole theory of what has been called residual discharge, absorption of electricity, electrification, or polarization, deserves a careful investigation, and will probably lead to important discoveries relating to the internal structure of bodies.", "markdown": "The whole theory of what has been called residual discharge, absorption of electricity, electrification, or polarization, deserves a careful investigation, and will probably lead to important discoveries relating to the internal structure of bodies.", "why": "Shows the author's sense of an open problem and his forecast that it would reveal the structure of matter.", "use": [ "history", "website" ], "concepts": [ "concept/polarization", "concept/residual-discharge" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/x-6465b38914", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-xiii", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 226", "location": "ON THE ELECTRIC RESISTANCE OF SUBSTANCES", "latex": "`Multiply each cycle sign (i.e.\\ current) by the sum of all the resistances which bound that cycle, and subtract from it the sign of each neighbouring cycle multiplied by the resistance separating the cycles, and equate the result to the E. M. F. in the cycle.'", "markdown": "‘Multiply each cycle sign (i.e. current) by the sum of all the resistances which bound that cycle, and subtract from it the sign of each neighbouring cycle multiplied by the resistance separating the cycles, and equate the result to the E. M. F. in the cycle.’", "why": "Gives a compact working procedure for writing the equations of a multi-loop circuit such as the bridge.", "use": [ "lesson" ], "concepts": [ "instrument/wheatstone-s-bridge", "law/kirchhoff-s-second-law", "method/cycle-rule-for-linear-circuits" ] } ], "equations": [ { "id": "maxwell-elementary-treatise-electricity-1888/eq-9b98794d09", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-iii", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 44", "location": "ON ELECTRICAL WORK AND ENERGY", "latex": "Q = \\tfrac{1}{2}\\sum(EP)", "name": null, "statement": "The electrical energy of a system of conductors is half the sum of the products of each conductor's charge and potential.", "kind": "result", "symbols": [ { "unit": null, "symbol": "Q", "meaning": "electric energy of the system" }, { "unit": null, "symbol": "E", "meaning": "charge of a conductor" }, { "unit": null, "symbol": "P", "meaning": "potential of a conductor" } ], "sympy": null, "physics": true, "states": [], "concepts": [ "concept/conductor", "concept/sum", "quantity/electric-charge", "quantity/electric-energy", "quantity/electric-potential" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/eq-aa3a898705", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-iii", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 45", "location": "ON ELECTRICAL WORK AND ENERGY", "latex": "Q' = Q + \\tfrac{1}{2}\\sum\\{(E' - E)(P' + P)\\}", "name": null, "statement": "After the charges change, the energy equals the original energy plus half the sum of each charge increment times the sum of its initial and final potentials.", "kind": "result", "symbols": [ { "unit": null, "symbol": "Q", "meaning": "electric energy before the change" }, { "unit": null, "symbol": "Q'", "meaning": "electric energy after the change" }, { "unit": null, "symbol": "E", "meaning": "initial charge of a conductor" }, { "unit": null, "symbol": "E'", "meaning": "final charge of a conductor" }, { "unit": null, "symbol": "P", "meaning": "initial potential of a conductor" }, { "unit": null, "symbol": "P'", "meaning": "final potential of a conductor" } ], "sympy": null, "physics": true, "states": [], "concepts": [ "concept/conductor", "concept/increment", "concept/sum", "quantity/electric-charge", "quantity/electric-energy", "quantity/electric-potential" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/eq-0a7bb14a6a", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-iii", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 46", "location": "ON ELECTRICAL WORK AND ENERGY", "latex": "\\frac{Q' - Q}{E' - E} = \\tfrac{1}{2}(P' + P)", "name": null, "statement": "When all charges but one are held constant, the rate of increase of energy with that charge equals half the sum of the initial and final potentials.", "kind": "result", "symbols": [ { "unit": null, "symbol": "Q", "meaning": "electric energy before the change" }, { "unit": null, "symbol": "Q'", "meaning": "electric energy after the change" }, { "unit": null, "symbol": "E", "meaning": "initial charge of the conductor" }, { "unit": null, "symbol": "E'", "meaning": "final charge of the conductor" }, { "unit": null, "symbol": "P", "meaning": "initial potential of the conductor" }, { "unit": null, "symbol": "P'", "meaning": "final potential of the conductor" } ], "sympy": "Eq((Qp - Q)/(Ep - E), (Pp + P)/2)", "physics": true, "states": [], "concepts": [ "concept/conductor", "concept/rate-of-change", "quantity/electric-charge", "quantity/electric-energy", "quantity/electric-potential" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/eq-db4bfe1cc4", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-iii", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 46", "location": "ON ELECTRICAL WORK AND ENERGY", "latex": "\\frac{dQ_e}{dE} = P", "name": null, "statement": "The rate at which the electric energy grows with the charge of one conductor, the others held constant, equals that conductor's potential.", "kind": "result", "symbols": [ { "unit": null, "symbol": "Q_e", "meaning": "electric energy of the system" }, { "unit": null, "symbol": "E", "meaning": "charge of the conductor" }, { "unit": null, "symbol": "P", "meaning": "potential of the conductor" } ], "sympy": "Eq(Derivative(Q_e, E), P)", "physics": true, "states": [], "concepts": [ "concept/derivative", "concept/partial-derivative", "quantity/electric-charge", "quantity/electric-energy", "quantity/electric-potential" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/eq-32ac0e2a8f", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-iii", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 46", "location": "ON ELECTRICAL WORK AND ENERGY", "latex": "\\sum(EP') = \\sum(E'P)", "name": "Theorem III", "statement": "In a fixed system of conductors, the sum of original charge times final potential equals the sum of final charge times original potential.", "kind": "result", "symbols": [ { "unit": null, "symbol": "E", "meaning": "original charge of a conductor" }, { "unit": null, "symbol": "E'", "meaning": "final charge of a conductor" }, { "unit": null, "symbol": "P", "meaning": "original potential of a conductor" }, { "unit": null, "symbol": "P'", "meaning": "final potential of a conductor" } ], "sympy": null, "physics": true, "states": [ "theorem/line-perpendicular-to-two-intersecting-lines-is-perpendicular-to-their-plane" ], "concepts": [ "concept/conductor", "concept/sum", "quantity/electric-charge", "quantity/electric-potential", "theorem/green-s-theorem" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/eq-8845502cd2", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-iii", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 46", "location": "ON ELECTRICAL WORK AND ENERGY", "latex": "\\tfrac{1}{2}\\sum\\{(E' - E)(P' + P)\\} = Q' - Q = \\tfrac{1}{2}\\sum\\{(E' + E)(P' - P)\\}", "name": null, "statement": "The increment of energy of a fixed system equals half the sum of charge increments times summed potentials, and equally half the sum of potential increments times summed charges.", "kind": "result", "symbols": [ { "unit": null, "symbol": "Q", "meaning": "electric energy before the change" }, { "unit": null, "symbol": "Q'", "meaning": "electric energy after the change" }, { "unit": null, "symbol": "E", "meaning": "initial charge of a conductor" }, { "unit": null, "symbol": "E'", "meaning": "final charge of a conductor" }, { "unit": null, "symbol": "P", "meaning": "initial potential of a conductor" }, { "unit": null, "symbol": "P'", "meaning": "final potential of a conductor" } ], "sympy": null, "physics": true, "states": [], "concepts": [ "concept/conductor", "concept/increment", "concept/sum", "quantity/electric-charge", "quantity/electric-energy", "quantity/electric-potential" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/eq-dcf42f1f70", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-iii", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 47", "location": "ON ELECTRICAL WORK AND ENERGY", "latex": "\\frac{Q' - Q}{P' - P} = \\tfrac{1}{2}(E' + E)", "name": null, "statement": "When all potentials but one are held constant, the rate of increase of energy with that potential equals half the sum of the initial and final charges.", "kind": "result", "symbols": [ { "unit": null, "symbol": "Q", "meaning": "electric energy before the change" }, { "unit": null, "symbol": "Q'", "meaning": "electric energy after the change" }, { "unit": null, "symbol": "P", "meaning": "initial potential of the conductor" }, { "unit": null, "symbol": "P'", "meaning": "final potential of the conductor" }, { "unit": null, "symbol": "E", "meaning": "initial charge of the conductor" }, { "unit": null, "symbol": "E'", "meaning": "final charge of the conductor" } ], "sympy": "Eq((Qp - Q)/(Pp - P), (Ep + E)/2)", "physics": true, "states": [], "concepts": [ "concept/conductor", "concept/rate-of-change", "quantity/electric-charge", "quantity/electric-energy", "quantity/electric-potential" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/eq-ca9420bca2", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-iii", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 47", "location": "ON ELECTRICAL WORK AND ENERGY", "latex": "\\frac{dQ_p}{dP} = E", "name": null, "statement": "The rate at which the electric energy grows with the potential of one conductor, the others held constant, equals that conductor's charge.", "kind": "result", "symbols": [ { "unit": null, "symbol": "Q_p", "meaning": "electric energy when potentials are varied" }, { "unit": null, "symbol": "P", "meaning": "potential of the conductor" }, { "unit": null, "symbol": "E", "meaning": "charge of the conductor" } ], "sympy": "Eq(Derivative(Q_p, P), E)", "physics": true, "states": [], "concepts": [ "concept/derivative", "concept/partial-derivative", "quantity/electric-charge", "quantity/electric-energy", "quantity/electric-potential" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/eq-f4d3757be2", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-iii", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 47", "location": "ON ELECTRICAL WORK AND ENERGY", "latex": "E_t{P_t}' = 0\\quad\\text{and}\\quad {E_t}'P_t = 0", "name": null, "statement": "If a conductor is insulated and uncharged in both the initial and final states, the terms involving it vanish from the reciprocal relation.", "kind": "result", "symbols": [ { "unit": null, "symbol": "E_t", "meaning": "initial charge of conductor A_t" }, { "unit": null, "symbol": "E_t'", "meaning": "final charge of conductor A_t" }, { "unit": null, "symbol": "P_t", "meaning": "initial potential of conductor A_t" }, { "unit": null, "symbol": "P_t'", "meaning": "final potential of conductor A_t" } ], "sympy": "Eq(Et*Ptp, 0)", "physics": true, "states": [], "concepts": [ "concept/conductor", "concept/insulator", "quantity/electric-charge", "quantity/electric-potential" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/eq-291bb8887a", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-iii", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 47", "location": "ON ELECTRICAL WORK AND ENERGY", "latex": "E_r{P_r}' + E_s{P_s}' = {E_r}'P_r + {E_s}'P_s", "name": null, "statement": "With all but two conductors insulated and uncharged or earthed, the reciprocal relation holds between the two remaining conductors.", "kind": "result", "symbols": [ { "unit": null, "symbol": "E_r", "meaning": "initial charge of conductor A_r" }, { "unit": null, "symbol": "E_r'", "meaning": "final charge of conductor A_r" }, { "unit": null, "symbol": "E_s", "meaning": "initial charge of conductor A_s" }, { "unit": null, "symbol": "E_s'", "meaning": "final charge of conductor A_s" }, { "unit": null, "symbol": "P_r", "meaning": "initial potential of conductor A_r" }, { "unit": null, "symbol": "P_r'", "meaning": "final potential of conductor A_r" }, { "unit": null, "symbol": "P_s", "meaning": "initial potential of conductor A_s" }, { "unit": null, "symbol": "P_s'", "meaning": "final potential of conductor A_s" } ], "sympy": "Eq(Er*Prp + Eslp*Psp, Erp*Pr + Esp*Ps)", "physics": true, "states": [], "concepts": [ "concept/conductor", "concept/sum", "quantity/electric-charge", "quantity/electric-potential", "theorem/reciprocity-of-potentials" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/eq-278c574939", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-iii", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 48", "location": "ON ELECTRICAL WORK AND ENERGY", "latex": "E_r{P_r}' = {E_s}'P_s", "name": "Reciprocity of potentials", "statement": "Charge on A_r times its final potential equals the final charge on A_s times the potential of A_s, in the two-conductor case.", "kind": "result", "symbols": [ { "unit": null, "symbol": "E_r", "meaning": "initial charge of conductor A_r" }, { "unit": null, "symbol": "P_r'", "meaning": "final potential of conductor A_r" }, { "unit": null, "symbol": "E_s'", "meaning": "final charge of conductor A_s" }, { "unit": null, "symbol": "P_s", "meaning": "potential of conductor A_s" } ], "sympy": "Eq(Er*Prp, Esp*Ps)", "physics": true, "states": [ "theorem/reciprocity-of-potentials" ], "concepts": [ "concept/conductor", "quantity/electric-charge", "quantity/electric-potential" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/eq-33d5ed2a1e", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-iii", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 48", "location": "ON ELECTRICAL WORK AND ENERGY", "latex": "\\frac{P_s}{E_r} = \\frac{{P_r}'}{{E_s}'}", "name": null, "statement": "The ratio of the potential of A_s to the charge on A_r equals the ratio of the potential of A_r to the charge on A_s.", "kind": "result", "symbols": [ { "unit": null, "symbol": "P_s", "meaning": "potential of conductor A_s" }, { "unit": null, "symbol": "E_r", "meaning": "charge on conductor A_r" }, { "unit": null, "symbol": "P_r'", "meaning": "potential of conductor A_r" }, { "unit": null, "symbol": "E_s'", "meaning": "charge on conductor A_s" } ], "sympy": "Eq(Ps/Er, Prp/Esp)", "physics": true, "states": [], "concepts": [ "concept/conductor", "quantity/electric-charge", "quantity/electric-potential", "theorem/reciprocity-of-potentials" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/eq-3e510e32cf", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-iii", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 48", "location": "ON ELECTRICAL WORK AND ENERGY", "latex": "E_r = {E_s}'", "name": "Reciprocity of potentials", "statement": "The charge on A_r equals the final charge on A_s, in the reciprocity case of Theorem V.", "kind": "result", "symbols": [ { "unit": null, "symbol": "E_r", "meaning": "charge on conductor A_r" }, { "unit": null, "symbol": "E_s'", "meaning": "charge on conductor A_s" } ], "sympy": "Eq(Er, Esp)", "physics": true, "states": [ "theorem/reciprocity-of-potentials" ], "concepts": [ "concept/conductor", "quantity/electric-charge" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/eq-dee94845a8", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-iii", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 48", "location": "ON ELECTRICAL WORK AND ENERGY", "latex": "P_s = {P_r}'", "name": "Reciprocity of potentials", "statement": "The potential of A_s produced by a charge on A_r equals the potential of A_r produced by an equal charge on A_s.", "kind": "result", "symbols": [ { "unit": null, "symbol": "P_s", "meaning": "potential of conductor A_s" }, { "unit": null, "symbol": "P_r'", "meaning": "potential of conductor A_r" } ], "sympy": "Eq(Ps, Prp)", "physics": true, "states": [ "theorem/reciprocity-of-potentials" ], "concepts": [ "concept/conductor", "quantity/electric-potential" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/eq-cff7c360f7", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-iii", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 49", "location": "ON ELECTRICAL WORK AND ENERGY", "latex": "0 = {E_r}'P_r + {E_s}'P_s", "name": null, "statement": "With A_r charged and A_s earthed, the final charges and original potentials of the two conductors sum to zero.", "kind": "result", "symbols": [ { "unit": null, "symbol": "E_r'", "meaning": "final charge of conductor A_r" }, { "unit": null, "symbol": "P_r", "meaning": "potential of conductor A_r" }, { "unit": null, "symbol": "E_s'", "meaning": "final charge of conductor A_s" }, { "unit": null, "symbol": "P_s", "meaning": "potential of conductor A_s" } ], "sympy": "Eq(0, Erp*Pr + Esp*Ps)", "physics": true, "states": [], "concepts": [ "concept/conductor", "concept/induced-electrification", "concept/sum", "quantity/electric-charge", "quantity/electric-potential" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/eq-37d36fae7f", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-iii", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 49", "location": "ON ELECTRICAL WORK AND ENERGY", "latex": "\\frac{P_s}{P_r} = -\\frac{{E_r}'}{{E_s}'}", "name": null, "statement": "The ratio of the two potentials equals minus the ratio of the induced final charges.", "kind": "result", "symbols": [ { "unit": null, "symbol": "P_s", "meaning": "potential of conductor A_s" }, { "unit": null, "symbol": "P_r", "meaning": "potential of conductor A_r" }, { "unit": null, "symbol": "E_r'", "meaning": "final charge of conductor A_r" }, { "unit": null, "symbol": "E_s'", "meaning": "final charge of conductor A_s" } ], "sympy": "Eq(Ps/Pr, -Erp/Esp)", "physics": true, "states": [], "concepts": [ "concept/conductor", "concept/induced-electrification", "quantity/electric-charge", "quantity/electric-potential" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/eq-f82769f0de", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-iii", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 49", "location": "ON ELECTRICAL WORK AND ENERGY", "latex": "P_s = nP_r", "name": null, "statement": "The potential of A_s is n times the potential of A_r in the induction case.", "kind": "result", "symbols": [ { "unit": null, "symbol": "P_s", "meaning": "potential of conductor A_s" }, { "unit": null, "symbol": "P_r", "meaning": "potential of conductor A_r" }, { "unit": null, "symbol": "n", "meaning": "ratio of the two potentials" } ], "sympy": "Eq(Ps, n*Pr)", "physics": true, "states": [], "concepts": [ "concept/common-ratio", "concept/conductor", "quantity/electric-potential" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/eq-eb1c306935", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-iii", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 49", "location": "ON ELECTRICAL WORK AND ENERGY", "latex": "{E_r}' = -n{E_s}'", "name": null, "statement": "The charge induced on A_r is minus n times the charge induced on A_s, where n is the potential ratio.", "kind": "result", "symbols": [ { "unit": null, "symbol": "E_r'", "meaning": "final charge induced on conductor A_r" }, { "unit": null, "symbol": "E_s'", "meaning": "final charge induced on conductor A_s" }, { "unit": null, "symbol": "n", "meaning": "ratio of the two potentials" } ], "sympy": "Eq(Erp, -n*Esp)", "physics": true, "states": [], "concepts": [ "concept/conductor", "concept/induced-electrification", "quantity/electric-charge" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/eq-1d080cba6f", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-iii", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 50", "location": "ON ELECTRICAL WORK AND ENERGY", "latex": "Q = W + Q'", "name": "Conservation of energy", "statement": "The original energy of an insulated system equals the work done by the electric forces plus the final energy, by conservation of energy.", "kind": "law", "symbols": [ { "unit": null, "symbol": "Q", "meaning": "electric energy before the displacement" }, { "unit": null, "symbol": "W", "meaning": "work done by the electric forces during the displacement" }, { "unit": null, "symbol": "Q'", "meaning": "electric energy after the displacement" } ], "sympy": "Eq(Q, W + Qp)", "physics": true, "states": [ "law/conservation-of-energy" ], "concepts": [ "concept/conservative-system", "concept/work", "quantity/electric-energy" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/eq-43842d678c", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-iii", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 50", "location": "ON ELECTRICAL WORK AND ENERGY", "latex": "W = \\tfrac{1}{2}\\sum[E(P - P')]", "name": null, "statement": "The work done during a displacement of an insulated system is half the sum of each charge times the potential drop of its conductor.", "kind": "formula", "symbols": [ { "unit": null, "symbol": "W", "meaning": "work done by the electric forces during the displacement" }, { "unit": null, "symbol": "E", "meaning": "charge of a conductor, constant during displacement" }, { "unit": null, "symbol": "P", "meaning": "initial potential of a conductor" }, { "unit": null, "symbol": "P'", "meaning": "final potential of a conductor" } ], "sympy": null, "physics": true, "states": [], "concepts": [ "concept/conductor", "concept/sum", "concept/work", "quantity/electric-charge", "quantity/electric-potential" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/eq-d87d9dd652", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-iii", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 50", "location": "ON ELECTRICAL WORK AND ENERGY", "latex": "Q' = \\tfrac{1}{2}\\sum(EP')", "name": null, "statement": "The energy remaining in the system after a displacement is half the sum of charge times final potential.", "kind": "formula", "symbols": [ { "unit": null, "symbol": "Q'", "meaning": "electric energy after the displacement" }, { "unit": null, "symbol": "E", "meaning": "charge of a conductor" }, { "unit": null, "symbol": "P'", "meaning": "final potential of a conductor" } ], "sympy": null, "physics": true, "states": [], "concepts": [ "concept/conductor", "concept/sum", "quantity/electric-charge", "quantity/electric-energy", "quantity/electric-potential" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/eq-3f2c192701", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-iii", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 50", "location": "ON ELECTRICAL WORK AND ENERGY", "latex": "W = \\tfrac{1}{2}\\sum[E(P - P_1)]", "name": null, "statement": "For a small displacement of an insulated system, the work is half the sum of charge times the potential change.", "kind": "formula", "symbols": [ { "unit": null, "symbol": "W", "meaning": "work done by the electric forces during the displacement" }, { "unit": null, "symbol": "E", "meaning": "charge of a conductor" }, { "unit": null, "symbol": "P", "meaning": "potential of a conductor before the displacement" }, { "unit": null, "symbol": "P_1", "meaning": "potential of a conductor after the small displacement" } ], "sympy": null, "physics": true, "states": [], "concepts": [ "concept/conductor", "concept/sum", "concept/work", "quantity/electric-charge", "quantity/electric-potential" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/eq-08ba10e986", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-iii", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 50", "location": "ON ELECTRICAL WORK AND ENERGY", "latex": "\\sum(EP - E_1P_1) = 0", "name": null, "statement": "Restoring the original potentials by changing charges leaves the sum of charge times potential unchanged.", "kind": "result", "symbols": [ { "unit": null, "symbol": "E", "meaning": "charge of a conductor before the operation" }, { "unit": null, "symbol": "P", "meaning": "potential of a conductor before the operation" }, { "unit": null, "symbol": "E_1", "meaning": "charge of a conductor after restoring the potential" }, { "unit": null, "symbol": "P_1", "meaning": "potential of a conductor after the displacement" } ], "sympy": null, "physics": true, "states": [], "concepts": [ "concept/conductor", "concept/sum", "quantity/electric-charge", "quantity/electric-potential" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/eq-f9851eafd3", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-iii", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 50", "location": "ON ELECTRICAL WORK AND ENERGY", "latex": "W = \\tfrac{1}{2}\\sum[(E_1 - E)P_1]", "name": null, "statement": "The work of an alternating displacement and charge adjustment is half the sum of the charge change times the potential.", "kind": "formula", "symbols": [ { "unit": null, "symbol": "W", "meaning": "work done by the electric forces" }, { "unit": null, "symbol": "E", "meaning": "charge before the operation" }, { "unit": null, "symbol": "E_1", "meaning": "charge after the operation" }, { "unit": null, "symbol": "P_1", "meaning": "potential after the displacement" } ], "sympy": null, "physics": true, "states": [], "concepts": [ "concept/conductor", "concept/sum", "concept/work", "quantity/electric-charge", "quantity/electric-potential" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/eq-1a80a70e12", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-iii", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 51", "location": "ON ELECTRICAL WORK AND ENERGY", "latex": "W = \\tfrac{1}{2}\\sum[(E' - E)P]", "name": null, "statement": "For a displacement with each conductor's potential held constant, the work is half the sum of the charge increment times the constant potential.", "kind": "result", "symbols": [ { "unit": null, "symbol": "W", "meaning": "work done by the electric forces during the displacement" }, { "unit": null, "symbol": "E", "meaning": "initial charge of a conductor" }, { "unit": null, "symbol": "E'", "meaning": "final charge of a conductor" }, { "unit": null, "symbol": "P", "meaning": "constant potential of a conductor" } ], "sympy": null, "physics": true, "states": [], "concepts": [ "concept/conductor", "concept/sum", "concept/work", "quantity/electric-charge", "quantity/electric-potential" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/eq-283d361b8f", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-iii", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 51", "location": "ON ELECTRICAL WORK AND ENERGY", "latex": "W = \\tfrac{1}{2}\\sum(E'P) - \\tfrac{1}{2}\\sum(EP)", "name": null, "statement": "The work done with constant potentials equals the final electric energy minus the initial electric energy.", "kind": "formula", "symbols": [ { "unit": null, "symbol": "W", "meaning": "work done by the electric forces during the displacement" }, { "unit": null, "symbol": "E", "meaning": "initial charge of a conductor" }, { "unit": null, "symbol": "E'", "meaning": "final charge of a conductor" }, { "unit": null, "symbol": "P", "meaning": "potential of a conductor" } ], "sympy": null, "physics": true, "states": [], "concepts": [ "concept/sum", "concept/work", "quantity/electric-charge", "quantity/electric-energy", "quantity/electric-potential" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/eq-96c158bdfd", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-iii", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 51", "location": "ON ELECTRICAL WORK AND ENERGY", "latex": "W = Q' - Q", "name": null, "statement": "With each conductor's potential held constant, the work done by the electric forces equals the increase of electric energy.", "kind": "result", "symbols": [ { "unit": null, "symbol": "W", "meaning": "work done by the electric forces during the displacement" }, { "unit": null, "symbol": "Q", "meaning": "electric energy before the displacement" }, { "unit": null, "symbol": "Q'", "meaning": "electric energy after the displacement" } ], "sympy": "Eq(W, Qp - Q)", "physics": true, "states": [], "concepts": [ "concept/work", "law/conservation-of-energy", "quantity/electric-energy" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/eq-7d40d4d662", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-iv", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 56", "location": "THE ELECTRIC FIELD", "latex": "\\tfrac{1}{4}(1 - n)e + (-ne) &= 0\\text{,}", "name": null, "statement": "The charge left on the first sphere after the second sphere has been discharged and the charge shared, plus the charge on the neutralised vessel, sums to zero, so the segment's removed charge is exactly balanced by the sphere's remaining charge.", "kind": "formula", "symbols": [ { "unit": null, "symbol": "e", "meaning": "electrification of the first sphere" }, { "unit": null, "symbol": "n", "meaning": "fraction of the sphere's charge removed by the segment" } ], "sympy": "Eq(Rational(1, 4)*(1 - n)*e + (-n*e), 0)", "physics": true, "states": [], "concepts": [ "concept/electrification", "instrument/coulomb-s-proof-plane", "law/conservation-of-electric-charge", "quantity/electric-charge" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/eq-2cb1b759fe", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-iv", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 56", "location": "THE ELECTRIC FIELD", "latex": "n &= \\tfrac{1}{5}\\text{,}", "name": null, "statement": "Solving the charge balance gives n = 1/5, so the segment covering one-fifth of the sphere's surface removes one-fifth of its total charge.", "kind": "result", "symbols": [ { "unit": null, "symbol": "n", "meaning": "fraction of the sphere's charge removed by the segment" } ], "sympy": "Eq(n, Rational(1, 5))", "physics": true, "states": [], "concepts": [ "instrument/coulomb-s-proof-plane", "quantity/electric-charge", "quantity/surface-charge-density" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/eq-9eb4fc0872", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-v", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 63", "location": "FARADAY'S LAW OF LINES OF INDUCTION", "latex": "e(p - P)\\text{,}", "name": null, "statement": "For a single positively electrified body inside a closed conducting vessel, the whole number of cells the tubes of induction are cut into equals the body's charge times the difference between its potential and the vessel's potential.", "kind": "result", "symbols": [ { "unit": null, "symbol": "e", "meaning": "charge of the electrified body" }, { "unit": null, "symbol": "p", "meaning": "potential of the electrified body" }, { "unit": null, "symbol": "P", "meaning": "potential of the vessel" }, { "unit": null, "symbol": "N", "meaning": "whole number of cells (the number of cells the tubes of induction are cut into)" } ], "sympy": "Eq(N, e*(p - P))", "physics": true, "states": [], "concepts": [ "concept/closed-conducting-surface", "concept/electric-induction", "concept/tube-of-induction", "concept/unit-cell", "quantity/electric-charge", "quantity/electric-potential" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/eq-95c044a5d5", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-v", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 63", "location": "FARADAY'S LAW OF LINES OF INDUCTION", "latex": "ep + EP\\text{.}", "name": null, "statement": "Using E = -e, the cell count e(p - P) can be written as ep + EP, which the book notes is double the electrical energy of the system.", "kind": "result", "symbols": [ { "unit": null, "symbol": "e", "meaning": "charge of the electrified body" }, { "unit": null, "symbol": "p", "meaning": "potential of the electrified body" }, { "unit": null, "symbol": "E", "meaning": "charge of the vessel" }, { "unit": null, "symbol": "P", "meaning": "potential of the vessel" }, { "unit": null, "symbol": "N", "meaning": "whole number of cells" } ], "sympy": "Eq(N, e*p + E*P)", "physics": true, "states": [], "concepts": [ "concept/closed-conducting-surface", "concept/unit-cell", "quantity/electric-charge", "quantity/electric-energy", "quantity/electric-potential" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/eq-89e6314fac", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-v", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 64", "location": "FARADAY'S LAW OF LINES OF INDUCTION", "latex": "E_{BA} = -E_{AB}\\text{,}", "name": null, "statement": "The number of tubes passing from B to A is the negative of the number passing from A to B, so the count is signed by direction.", "kind": "definition", "symbols": [ { "unit": null, "symbol": "E_{AB}", "meaning": "number of tubes of induction passing from A to B" }, { "unit": null, "symbol": "E_{BA}", "meaning": "number of tubes of induction passing from B to A" } ], "sympy": "Eq(E_BA, -E_AB)", "physics": false, "states": [], "concepts": [ "concept/electric-induction", "concept/tube-of-induction", "concept/unit-tube-of-induction" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/eq-e32b66fdcd", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-v", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 64", "location": "FARADAY'S LAW OF LINES OF INDUCTION", "latex": "P_0E_0 + P_1E_1 + P_2E_2 + P_3E_3\\text{,}", "name": null, "statement": "For several electrified bodies A, B, C inside a vessel, the total number of cells equals the sum of each conductor's potential times its charge, which is double the electrical energy of the system.", "kind": "result", "symbols": [ { "unit": null, "symbol": "P_0", "meaning": "potential of the vessel" }, { "unit": null, "symbol": "E_0", "meaning": "charge of the vessel" }, { "unit": null, "symbol": "P_1", "meaning": "potential of body A" }, { "unit": null, "symbol": "E_1", "meaning": "charge of body A" }, { "unit": null, "symbol": "P_2", "meaning": "potential of body B" }, { "unit": null, "symbol": "E_2", "meaning": "charge of body B" }, { "unit": null, "symbol": "P_3", "meaning": "potential of body C" }, { "unit": null, "symbol": "E_3", "meaning": "charge of body C" }, { "unit": null, "symbol": "N", "meaning": "whole number of cells" } ], "sympy": "Eq(N, P_0*E_0 + P_1*E_1 + P_2*E_2 + P_3*E_3)", "physics": true, "states": [], "concepts": [ "concept/tube-of-induction", "concept/unit-cell", "quantity/electric-charge", "quantity/electric-energy", "quantity/electric-potential" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/eq-193f340c7a", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-v", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 63", "location": "FARADAY'S LAW OF LINES OF INDUCTION", "latex": "E = -e", "name": null, "statement": "The charge of the enclosing vessel's inner surface is equal and opposite to the charge of the body inside it.", "kind": "rule", "symbols": [ { "unit": null, "symbol": "E", "meaning": "charge of the vessel (inner surface)" }, { "unit": null, "symbol": "e", "meaning": "charge of the electrified body" } ], "sympy": "Eq(E, -e)", "physics": true, "states": [], "concepts": [ "concept/closed-conducting-surface", "concept/electric-induction", "concept/electrification", "quantity/electric-charge" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/eq-2d9aa78fe6", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-v", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 77", "location": "FARADAY'S LAW OF LINES OF INDUCTION", "latex": "\\sigma = P_A \\sigma _2 - P_B \\sigma _1", "name": null, "statement": "The surface density at a point P on body A equals the potential of A times the surface density from the unit-potential case, minus the potential of B times the surface density from the other unit case.", "kind": "formula", "symbols": [ { "unit": null, "symbol": "\\sigma", "meaning": "surface-density at the point P on the surface of A, with potentials P_A and P_B" }, { "unit": null, "symbol": "P_A", "meaning": "potential of body A" }, { "unit": null, "symbol": "P_B", "meaning": "potential of body B (the inductor)" }, { "unit": null, "symbol": "\\sigma_2", "meaning": "surface-density at P when the potential of A is unity and that of B is zero" }, { "unit": null, "symbol": "\\sigma_1", "meaning": "surface-density at P when the potential of A is zero and that of B is unity (with the sign taken as -\\sigma_1)" } ], "sympy": "Eq(sigma, P_A*sigma_2 - P_B*sigma_1)", "physics": true, "states": [], "concepts": [ "concept/coefficients-of-capacity", "law/superposition-of-electric-effects", "quantity/electric-potential", "quantity/surface-charge-density" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/eq-f13d74eff3", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-v", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 77", "location": "FARADAY'S LAW OF LINES OF INDUCTION", "latex": "E_A = P_A q_A - P_B q_{AB}", "name": null, "statement": "The total charge of body A is its potential times its capacity coefficient, minus the potential of B times the mutual coefficient of induction.", "kind": "formula", "symbols": [ { "unit": null, "symbol": "E_A", "meaning": "total charge of body A" }, { "unit": null, "symbol": "P_A", "meaning": "potential of body A" }, { "unit": null, "symbol": "q_A", "meaning": "capacity of A: the whole charge on A when the potential of A is unity and that of B is zero" }, { "unit": null, "symbol": "P_B", "meaning": "potential of body B" }, { "unit": null, "symbol": "q_{AB}", "meaning": "the whole charge of A when the potential of A is zero and that of B is unity (a negative quantity, written -q_{AB})" } ], "sympy": "Eq(E_A, P_A*q_A - P_B*q_AB)", "physics": true, "states": [], "concepts": [ "quantity/capacity", "quantity/coefficient-of-induction", "quantity/electric-charge", "quantity/electric-potential" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/eq-aaf3e9d4dd", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-v", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 77", "location": "FARADAY'S LAW OF LINES OF INDUCTION", "latex": "E_B = P_Bq_B - P_A q_{AB}", "name": null, "statement": "The total charge of body B is its potential times its own coefficient, minus the potential of A times the mutual coefficient of induction.", "kind": "formula", "symbols": [ { "unit": null, "symbol": "E_B", "meaning": "total charge of body B" }, { "unit": null, "symbol": "P_B", "meaning": "potential of body B" }, { "unit": null, "symbol": "q_B", "meaning": "charge of B when the potential of A is zero and that of B is unity" }, { "unit": null, "symbol": "P_A", "meaning": "potential of body A" }, { "unit": null, "symbol": "q_{AB}", "meaning": "the whole charge of A when the potential of A is zero and that of B is unity (a negative quantity)" } ], "sympy": "Eq(E_B, P_B*q_B - P_A*q_AB)", "physics": true, "states": [], "concepts": [ "quantity/capacity", "quantity/coefficient-of-induction", "quantity/electric-charge", "quantity/electric-potential" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/eq-bab8621675", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-v", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 77", "location": "FARADAY'S LAW OF LINES OF INDUCTION", "latex": "P_A = P_B \\frac{q_{AB}}{q_A}", "name": null, "statement": "When the insulated body A carries no charge, its potential equals the potential of B times the ratio of the mutual coefficient of induction to the capacity of A.", "kind": "result", "symbols": [ { "unit": null, "symbol": "P_A", "meaning": "potential of body A when A is insulated and uncharged" }, { "unit": null, "symbol": "P_B", "meaning": "potential of body B" }, { "unit": null, "symbol": "q_{AB}", "meaning": "the whole charge of A when the potential of A is zero and that of B is unity (a negative quantity)" }, { "unit": null, "symbol": "q_A", "meaning": "capacity of A" } ], "sympy": "Eq(P_A, P_B*q_AB/q_A)", "physics": true, "states": [], "concepts": [ "concept/electrification", "quantity/capacity", "quantity/coefficient-of-induction", "quantity/electric-potential" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/eq-d554a63ec1", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-v", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 77", "location": "FARADAY'S LAW OF LINES OF INDUCTION", "latex": "\\sigma = \\frac{P_B}{q_A}(q_{AB} \\sigma _2 - q_A \\sigma _1)", "name": null, "statement": "For insulated uncharged body A, the surface density at P is the potential of B divided by the capacity of A, times the difference of the two unit-case surface densities weighted by the coefficients.", "kind": "result", "symbols": [ { "unit": null, "symbol": "\\sigma", "meaning": "surface-density at the point P on the surface of A when A is insulated and uncharged" }, { "unit": null, "symbol": "P_B", "meaning": "potential of body B" }, { "unit": null, "symbol": "q_A", "meaning": "capacity of A" }, { "unit": null, "symbol": "q_{AB}", "meaning": "the whole charge of A when the potential of A is zero and that of B is unity (a negative quantity)" }, { "unit": null, "symbol": "\\sigma_2", "meaning": "surface-density at P when the potential of A is unity and that of B is zero" }, { "unit": null, "symbol": "\\sigma_1", "meaning": "surface-density at P when the potential of A is zero and that of B is unity" } ], "sympy": "Eq(sigma, P_B/q_A*(q_AB*sigma_2 - q_A*sigma_1))", "physics": true, "states": [], "concepts": [ "concept/neutral-line", "quantity/capacity", "quantity/electric-potential", "quantity/surface-charge-density" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/eq-662129152a", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-vi", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 78", "location": "PARTICULAR CASES OF ELECTRIFICATION", "latex": "E = -e\\text{.}", "name": null, "statement": "The charge on the internal surface of the outer sphere is equal and opposite to the charge on the inner sphere.", "kind": "result", "symbols": [ { "unit": null, "symbol": "E", "meaning": "quantity of electricity on the internal surface of the outer sphere" }, { "unit": null, "symbol": "e", "meaning": "quantity of electricity on the inner sphere" } ], "sympy": "Eq(E, -e)", "physics": true, "states": [], "concepts": [ "concept/closed-conducting-surface", "concept/conductor", "law/conservation-of-electric-charge", "quantity/electric-charge" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/eq-06590c4a9c", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-vi", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 78", "location": "PARTICULAR CASES OF ELECTRIFICATION", "latex": "s = 4 \\pi r^2", "name": null, "statement": "The surface of a sphere of radius r is 4 pi r squared.", "kind": "formula", "symbols": [ { "unit": null, "symbol": "s", "meaning": "surface of the inner sphere" }, { "unit": null, "symbol": "r", "meaning": "radius of the inner sphere" }, { "unit": null, "symbol": "\\pi", "meaning": "ratio of the circumference of a circle to its diameter" } ], "sympy": "Eq(s, 4*pi*r**2)", "physics": false, "states": [], "concepts": [ "concept/sphere", "quantity/pi", "quantity/radius", "theorem/area-of-a-sphere" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/eq-2a30ac1e48", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-vi", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 78", "location": "PARTICULAR CASES OF ELECTRIFICATION", "latex": "S = 4 \\pi R^2", "name": null, "statement": "The surface of a sphere of radius R is 4 pi R squared.", "kind": "formula", "symbols": [ { "unit": null, "symbol": "S", "meaning": "surface of the internal surface of the outer sphere" }, { "unit": null, "symbol": "R", "meaning": "radius of the outer sphere" }, { "unit": null, "symbol": "\\pi", "meaning": "ratio of the circumference of a circle to its diameter" } ], "sympy": "Eq(S, 4*pi*R**2)", "physics": false, "states": [], "concepts": [ "concept/sphere", "quantity/pi", "quantity/radius", "theorem/area-of-a-sphere" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/eq-c341cd67eb", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-vi", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 78", "location": "PARTICULAR CASES OF ELECTRIFICATION", "latex": "e = s \\sigma", "name": null, "statement": "The whole charge on a surface is its area multiplied by its surface density.", "kind": "formula", "symbols": [ { "unit": null, "symbol": "e", "meaning": "quantity of electricity on the inner sphere" }, { "unit": null, "symbol": "s", "meaning": "surface of the inner sphere" }, { "unit": null, "symbol": "\\sigma", "meaning": "surface density of electricity on the inner sphere" } ], "sympy": "Eq(e, s*sigma)", "physics": true, "states": [], "concepts": [ "quantity/area", "quantity/electric-charge", "quantity/surface-charge-density" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/eq-286b6f320f", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-vi", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 78", "location": "PARTICULAR CASES OF ELECTRIFICATION", "latex": "E = S \\Sigma", "name": null, "statement": "The whole charge on the internal surface of the outer sphere is its area multiplied by its surface density.", "kind": "formula", "symbols": [ { "unit": null, "symbol": "E", "meaning": "quantity of electricity on the internal surface of the outer sphere" }, { "unit": null, "symbol": "S", "meaning": "surface of the internal surface of the outer sphere" }, { "unit": null, "symbol": "\\Sigma", "meaning": "surface density of electricity on the internal surface of the outer sphere" } ], "sympy": "Eq(E, S*Sigma)", "physics": true, "states": [], "concepts": [ "quantity/area", "quantity/electric-charge", "quantity/surface-charge-density" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/eq-911964209f", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-vi", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 78", "location": "PARTICULAR CASES OF ELECTRIFICATION", "latex": "\\sigma = \\frac{e}{4 \\pi r^2}", "name": null, "statement": "The surface density on the inner sphere equals its charge divided by its area.", "kind": "formula", "symbols": [ { "unit": null, "symbol": "\\sigma", "meaning": "surface density of electricity on the inner sphere" }, { "unit": null, "symbol": "e", "meaning": "quantity of electricity on the inner sphere" }, { "unit": null, "symbol": "r", "meaning": "radius of the inner sphere" } ], "sympy": "Eq(sigma, e/(4*pi*r**2))", "physics": true, "states": [], "concepts": [ "concept/sphere", "quantity/electric-charge", "quantity/surface-charge-density" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/eq-c90f189e3d", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-vi", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 78", "location": "PARTICULAR CASES OF ELECTRIFICATION", "latex": "\\Sigma = \\frac{E}{4 \\pi R^2}", "name": null, "statement": "The surface density on the internal surface of the outer sphere equals its charge divided by its area.", "kind": "formula", "symbols": [ { "unit": null, "symbol": "\\Sigma", "meaning": "surface density of electricity on the internal surface of the outer sphere" }, { "unit": null, "symbol": "E", "meaning": "quantity of electricity on the internal surface of the outer sphere" }, { "unit": null, "symbol": "R", "meaning": "radius of the outer sphere" } ], "sympy": "Eq(Sigma, E/(4*pi*R**2))", "physics": true, "states": [], "concepts": [ "concept/sphere", "quantity/electric-charge", "quantity/surface-charge-density" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/eq-0756bd782f", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-vi", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 78", "location": "PARTICULAR CASES OF ELECTRIFICATION", "latex": "\\Sigma = \\frac{-e}{4 \\pi R^2}", "name": null, "statement": "Substituting E = -e, the surface density on the internal surface of the outer sphere is minus e divided by its area.", "kind": "result", "symbols": [ { "unit": null, "symbol": "\\Sigma", "meaning": "surface density of electricity on the internal surface of the outer sphere" }, { "unit": null, "symbol": "e", "meaning": "quantity of electricity on the inner sphere" }, { "unit": null, "symbol": "R", "meaning": "radius of the outer sphere" } ], "sympy": "Eq(Sigma, -e/(4*pi*R**2))", "physics": true, "states": [], "concepts": [ "concept/sphere", "quantity/electric-charge", "quantity/surface-charge-density" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/eq-60050a18a6", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-vi", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 80", "location": "PARTICULAR CASES OF ELECTRIFICATION", "latex": "f = \\frac{ee'}{r^2}", "name": "Coulomb's law", "statement": "The force between two small charged bodies is the product of their charges divided by the square of their distance; it is a repulsion for like charges and an attraction for unlike charges.", "kind": "law", "symbols": [ { "unit": null, "symbol": "f", "meaning": "whole repulsion between the two charged bodies (negative means attraction)" }, { "unit": "electrostatic unit", "symbol": "e", "meaning": "charge of the first body" }, { "unit": "electrostatic unit", "symbol": "e'", "meaning": "charge of the second body" }, { "unit": null, "symbol": "r", "meaning": "distance between the bodies" } ], "sympy": "Eq(f, e*ep/r**2)", "physics": true, "states": [ "law/coulomb-s-law" ], "concepts": [ "law/electrostatic-attraction-and-repulsion", "quantity/distance", "quantity/electric-charge" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/eq-ac67f5c38b", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-vi", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 80", "location": "PARTICULAR CASES OF ELECTRIFICATION", "latex": "\\mathfrak{E} = \\frac{e}{r'^2}", "name": null, "statement": "At a point outside a uniformly electrified sphere at distance r' from its centre, the electric force is the sphere's charge divided by r' squared, directed from the centre.", "kind": "law", "symbols": [ { "unit": null, "symbol": "\\mathfrak{E}", "meaning": "electric force (electromotive force) at the point" }, { "unit": null, "symbol": "e", "meaning": "total charge of the sphere" }, { "unit": null, "symbol": "r'", "meaning": "distance of the point from the centre of the sphere" } ], "sympy": "Eq(Ef, e/rp**2)", "physics": true, "states": [], "concepts": [ "concept/sphere", "law/coulomb-s-law", "quantity/electric-charge", "quantity/electromotive-force" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/eq-d6bcec4059", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-vi", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 80", "location": "PARTICULAR CASES OF ELECTRIFICATION", "latex": "\\mathfrak{E} = \\frac{e}{r^2} = 4 \\pi \\sigma", "name": null, "statement": "Close to the surface of an electrified sphere, the electric force equals the surface density multiplied by 4 pi.", "kind": "result", "symbols": [ { "unit": null, "symbol": "\\mathfrak{E}", "meaning": "electric force close to the surface" }, { "unit": null, "symbol": "e", "meaning": "total charge of the sphere" }, { "unit": null, "symbol": "r", "meaning": "radius of the sphere" }, { "unit": null, "symbol": "\\sigma", "meaning": "surface density of the electrification" } ], "sympy": "Eq(Ef, 4*pi*sigma)", "physics": true, "states": [], "concepts": [ "concept/sphere", "quantity/electromotive-force", "quantity/pi", "quantity/surface-charge-density" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/eq-7d07c3e678", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-vi", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 81", "location": "PARTICULAR CASES OF ELECTRIFICATION", "latex": "\\mathfrak{E} = 4 \\pi \\sigma", "name": "Coulomb's law", "statement": "The electric force at a conductor's surface is at right angles to the surface and equals 4 pi times the surface density; this is Coulomb's law in complete form.", "kind": "law", "symbols": [ { "unit": null, "symbol": "\\mathfrak{E}", "meaning": "electric force at the surface" }, { "unit": null, "symbol": "\\sigma", "meaning": "surface density of the electrification" } ], "sympy": "Eq(Ef, 4*pi*sigma)", "physics": true, "states": [ "law/coulomb-s-law" ], "concepts": [ "quantity/electromotive-force", "quantity/pi", "quantity/surface-charge-density" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/eq-08b79ca622", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-vi", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 80", "location": "PARTICULAR CASES OF ELECTRIFICATION", "latex": "e = 4 \\pi r^2 \\sigma", "name": null, "statement": "The total charge of a uniformly electrified sphere is 4 pi r squared times its surface density.", "kind": "formula", "symbols": [ { "unit": null, "symbol": "e", "meaning": "total charge of the sphere" }, { "unit": null, "symbol": "r", "meaning": "radius of the sphere" }, { "unit": null, "symbol": "\\sigma", "meaning": "surface density of the electrification" } ], "sympy": "Eq(e, 4*pi*r**2*sigma)", "physics": true, "states": [], "concepts": [ "concept/sphere", "quantity/electric-charge", "quantity/pi", "quantity/surface-charge-density" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/eq-7a66f57d23", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-vi", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 81", "location": "PARTICULAR CASES OF ELECTRIFICATION", "latex": "\\psi' - \\psi = \\overline{BA} \\ldot \\mathfrak{E}", "name": null, "statement": "If the electric force is constant and equal to E along BA, the work done per unit charge from B to A equals the distance BA times E.", "kind": "formula", "symbols": [ { "unit": null, "symbol": "\\psi", "meaning": "electric potential at A" }, { "unit": null, "symbol": "\\psi'", "meaning": "electric potential at B" }, { "unit": null, "symbol": "\\overline{BA}", "meaning": "distance from B to A" }, { "unit": null, "symbol": "\\mathfrak{E}", "meaning": "constant electric force from B to A" } ], "sympy": null, "physics": true, "states": [], "concepts": [ "concept/work", "quantity/distance", "quantity/electric-potential", "quantity/electromotive-force" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/eq-f0a0f9c92e", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-vi", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 82", "location": "PARTICULAR CASES OF ELECTRIFICATION", "latex": "\\left(\\frac{1}{b} - \\frac{1}{a}\\right)\\frac{a}{b} < B - A < \\left(\\frac{1}{b} - \\frac{1}{a}\\right) \\frac{a}{b}", "name": null, "statement": "Bounds on the potential difference B - A between points at distances a and b from a unit charge. FLAG: the printed lower bound reads a/b, but the derivation just above gives (1/b - 1/a) times b/a as the lower bound; the printed left-hand bound looks like a printing slip in the book.", "kind": "result", "symbols": [ { "unit": null, "symbol": "A", "meaning": "electric potential at the point A" }, { "unit": null, "symbol": "B", "meaning": "electric potential at the point B" }, { "unit": null, "symbol": "a", "meaning": "distance of point A from the unit charge at O" }, { "unit": null, "symbol": "b", "meaning": "distance of point B from the unit charge at O" } ], "sympy": null, "physics": true, "states": [], "concepts": [ "concept/inequality", "quantity/electric-charge", "quantity/electric-potential" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/eq-ad365b9501", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-vi", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 82", "location": "PARTICULAR CASES OF ELECTRIFICATION", "latex": "\\left(\\frac{1}{z} - \\frac{1}{a}\\right) \\frac{1}{p} < Z - A < \\left(\\frac{1}{z} - \\frac{1}{y}\\right) p", "name": null, "statement": "Summed bounds on Z - A obtained by adding the stepwise inequalities, with p the greatest ratio of successive distances. FLAG: the upper bound is printed as (1/z - 1/y) p; adding the steps gives (1/z - 1/a) p, so the y appears to be a printing slip in the book.", "kind": "result", "symbols": [ { "unit": null, "symbol": "A", "meaning": "electric potential at the point A" }, { "unit": null, "symbol": "Z", "meaning": "electric potential at the point Z" }, { "unit": null, "symbol": "p", "meaning": "greatest ratio of successive distances along the path" }, { "unit": null, "symbol": "z", "meaning": "distance of point Z from the unit charge" }, { "unit": null, "symbol": "a", "meaning": "distance of point A from the unit charge" } ], "sympy": null, "physics": false, "states": [], "concepts": [ "concept/inequality", "concept/limit", "quantity/electric-potential" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/eq-c1feeb7495", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-vi", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 83", "location": "PARTICULAR CASES OF ELECTRIFICATION", "latex": "Z - A = \\frac{1}{z} - \\frac{1}{a}", "name": null, "statement": "In the limit of an infinitely fine subdivision, the potential difference between two points is the difference of the reciprocals of their distances from a unit charge.", "kind": "result", "symbols": [ { "unit": null, "symbol": "Z", "meaning": "electric potential at the point Z" }, { "unit": null, "symbol": "A", "meaning": "electric potential at the point A" }, { "unit": null, "symbol": "z", "meaning": "distance of point Z from the unit charge" }, { "unit": null, "symbol": "a", "meaning": "distance of point A from the unit charge" } ], "sympy": "Eq(Z - A, 1/z - 1/a)", "physics": true, "states": [], "concepts": [ "concept/limit", "quantity/electric-charge", "quantity/electric-potential" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/eq-c1a6d6af48", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-vi", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 83", "location": "PARTICULAR CASES OF ELECTRIFICATION", "latex": "Z = \\frac{1}{z}", "name": null, "statement": "With the potential at infinity taken as zero, the potential at a point due to unit charge at distance z is the reciprocal of z.", "kind": "result", "symbols": [ { "unit": null, "symbol": "Z", "meaning": "electric potential at the point Z" }, { "unit": null, "symbol": "z", "meaning": "distance of the point from the unit charge" } ], "sympy": "Eq(Z, 1/z)", "physics": true, "states": [], "concepts": [ "quantity/electric-charge", "quantity/electric-potential" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/eq-ea99e458f0", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-vi", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 83", "location": "PARTICULAR CASES OF ELECTRIFICATION", "latex": "\\psi = \\frac{e}{r}", "name": null, "statement": "For points outside a uniformly electrified spherical surface, the potential equals the total charge divided by the distance from the centre.", "kind": "result", "symbols": [ { "unit": null, "symbol": "\\psi", "meaning": "electric potential at the point" }, { "unit": null, "symbol": "e", "meaning": "whole charge of the spherical surface" }, { "unit": null, "symbol": "r", "meaning": "distance of the point from the centre" } ], "sympy": "Eq(psi, e/r)", "physics": true, "states": [], "concepts": [ "concept/sphere", "quantity/electric-charge", "quantity/electric-potential" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/eq-e8a4624014", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-vi", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 84", "location": "PARTICULAR CASES OF ELECTRIFICATION", "latex": "\\psi_a = \\frac{e}{a}", "name": null, "statement": "The potential at the surface of a sphere of radius a due to its own charge is the charge divided by the radius.", "kind": "result", "symbols": [ { "unit": null, "symbol": "\\psi_a", "meaning": "electric potential at the surface of the sphere" }, { "unit": null, "symbol": "e", "meaning": "whole charge of the surface" }, { "unit": null, "symbol": "a", "meaning": "radius of the spherical surface" } ], "sympy": "Eq(psi_a, e/a)", "physics": true, "states": [], "concepts": [ "concept/sphere", "quantity/electric-potential", "quantity/radius" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/eq-794cf9f594", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-vi", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 84", "location": "PARTICULAR CASES OF ELECTRIFICATION", "latex": "e = a", "name": null, "statement": "When the potential of a sphere is unity its charge is numerically equal to its radius, which gives the capacity of an isolated sphere.", "kind": "result", "symbols": [ { "unit": null, "symbol": "e", "meaning": "whole charge of the sphere" }, { "unit": null, "symbol": "a", "meaning": "radius of the sphere" } ], "sympy": "Eq(e, a)", "physics": true, "states": [], "concepts": [ "concept/sphere", "quantity/capacity", "quantity/electric-potential", "quantity/radius" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/eq-87a2d55b0f", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-vi", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 85", "location": "PARTICULAR CASES OF ELECTRIFICATION", "latex": "e\\xp\\left(\\dfrac{1}{r} - \\dfrac{1}{b} \\right)", "name": null, "statement": "The potential at a point between the two concentric spherical surfaces, at distance r from the centre, is e times (1/r minus 1/b).", "kind": "result", "symbols": [ { "unit": null, "symbol": "e", "meaning": "charge on the inner sphere" }, { "unit": null, "symbol": "r", "meaning": "distance from the centre" }, { "unit": null, "symbol": "b", "meaning": "radius of the internal surface of the vessel" } ], "sympy": null, "physics": true, "states": [], "concepts": [ "concept/closed-conducting-surface", "concept/sphere", "quantity/electric-potential" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/eq-85396a49df", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-vi", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 85", "location": "PARTICULAR CASES OF ELECTRIFICATION", "latex": "e\\xp\\left(\\dfrac{1}{a} - \\dfrac{1}{b} \\right)", "name": null, "statement": "The potential of the inner sphere, which is uniform throughout it, is e times (1/a minus 1/b).", "kind": "result", "symbols": [ { "unit": null, "symbol": "e", "meaning": "charge on the inner sphere" }, { "unit": null, "symbol": "a", "meaning": "radius of the inner sphere" }, { "unit": null, "symbol": "b", "meaning": "radius of the internal surface of the vessel" } ], "sympy": null, "physics": true, "states": [], "concepts": [ "concept/closed-conducting-surface", "concept/sphere", "quantity/electric-potential" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/eq-f383bf7dda", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-vi", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 85", "location": "PARTICULAR CASES OF ELECTRIFICATION", "latex": "e = \\frac{1}{\\dfrac{1}{a} - \\dfrac{1}{b}} = \\frac{ab}{b - a}", "name": null, "statement": "The capacity of the inner sphere, the charge needed to raise its potential to unity, equals ab divided by (b - a).", "kind": "result", "symbols": [ { "unit": null, "symbol": "e", "meaning": "charge on the inner sphere when its potential is unity (its capacity)" }, { "unit": null, "symbol": "a", "meaning": "radius of the inner sphere" }, { "unit": null, "symbol": "b", "meaning": "radius of the internal surface of the vessel" } ], "sympy": "Eq(e, a*b/(b - a))", "physics": true, "states": [], "concepts": [ "concept/closed-conducting-surface", "concept/sphere", "quantity/capacity" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/eq-8b0ab4820e", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-vi", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 86", "location": "PARTICULAR CASES OF ELECTRIFICATION", "latex": "\\sigma = \\frac{A - B}{4 \\pi c}", "name": null, "statement": "For two parallel plane electrodes at distance c with potentials A and B, the surface density on the upper plane is the potential difference divided by 4 pi c.", "kind": "formula", "symbols": [ { "unit": null, "symbol": "\\sigma", "meaning": "surface density on the upper plane" }, { "unit": null, "symbol": "A", "meaning": "potential of the upper plane" }, { "unit": null, "symbol": "B", "meaning": "potential of the lower plane" }, { "unit": null, "symbol": "c", "meaning": "distance between the planes" } ], "sympy": "Eq(sigma, (A - B)/(4*pi*c))", "physics": true, "states": [], "concepts": [ "concept/parallel-planes", "quantity/electric-potential", "quantity/pi", "quantity/surface-charge-density" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/eq-06a2f54410", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-vi", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 86", "location": "PARTICULAR CASES OF ELECTRIFICATION", "latex": "\\xp\\dfrac{A-B}{c}", "name": null, "statement": "The electric force between two parallel planes, away from their edges, has magnitude (A - B) divided by c and acts from A to B.", "kind": "result", "symbols": [ { "unit": null, "symbol": "A", "meaning": "potential of the upper plane" }, { "unit": null, "symbol": "B", "meaning": "potential of the lower plane" }, { "unit": null, "symbol": "c", "meaning": "distance between the planes" } ], "sympy": null, "physics": true, "states": [], "concepts": [ "concept/parallel-planes", "quantity/electric-potential", "quantity/electromotive-force" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/eq-f45c5c252d", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-vi", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 86", "location": "PARTICULAR CASES OF ELECTRIFICATION", "latex": "e = \\frac{A - B}{4 \\pi c} S", "name": null, "statement": "The charge on an area S cut from the upper plane is the surface density times S.", "kind": "formula", "symbols": [ { "unit": null, "symbol": "e", "meaning": "charge on the area S of the upper plane" }, { "unit": null, "symbol": "A", "meaning": "potential of the upper plane" }, { "unit": null, "symbol": "B", "meaning": "potential of the lower plane" }, { "unit": null, "symbol": "c", "meaning": "distance between the planes" }, { "unit": null, "symbol": "S", "meaning": "area cut out from the upper plane" } ], "sympy": "Eq(e, (A - B)*S/(4*pi*c))", "physics": true, "states": [], "concepts": [ "concept/parallel-planes", "quantity/area", "quantity/electric-charge", "quantity/surface-charge-density" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/eq-e9bdb6770a", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-vi", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 86", "location": "PARTICULAR CASES OF ELECTRIFICATION", "latex": "Q = \\tfrac{1}{2}\\{Ae + B(-e)\\} = \\tfrac{1}{2} (A - B)e", "name": null, "statement": "The electrical energy of the two equal and opposite charges on the parallel planes is half the potential difference times the charge.", "kind": "formula", "symbols": [ { "unit": null, "symbol": "Q", "meaning": "electrical energy of the two charged portions" }, { "unit": null, "symbol": "A", "meaning": "potential of the upper plane" }, { "unit": null, "symbol": "B", "meaning": "potential of the lower plane" }, { "unit": null, "symbol": "e", "meaning": "charge on the area S of the upper plane" } ], "sympy": "Eq(Q, (A - B)*e/2)", "physics": true, "states": [], "concepts": [ "concept/parallel-planes", "quantity/electric-charge", "quantity/electric-energy", "quantity/electric-potential" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/eq-57a933fd37", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-vi", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 86", "location": "PARTICULAR CASES OF ELECTRIFICATION", "latex": "Q = \\frac{2 \\pi}{S} e^2c", "name": null, "statement": "The electrical energy of the parallel-plane pair, written in terms of the charge e and the separation c.", "kind": "formula", "symbols": [ { "unit": null, "symbol": "Q", "meaning": "electrical energy of the system" }, { "unit": null, "symbol": "e", "meaning": "charge on the area S" }, { "unit": null, "symbol": "S", "meaning": "area of the plates" }, { "unit": null, "symbol": "c", "meaning": "distance between the planes" } ], "sympy": "Eq(Q, 2*pi*e**2*c/S)", "physics": true, "states": [], "concepts": [ "concept/parallel-planes", "quantity/electric-energy", "quantity/pi" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/eq-aa849ed6ef", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-vi", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 86", "location": "PARTICULAR CASES OF ELECTRIFICATION", "latex": "Q' = \\frac{2 \\pi}{S} e^2c'", "name": null, "statement": "With the charges kept fixed and the separation increased to c', the electrical energy becomes this value.", "kind": "formula", "symbols": [ { "unit": null, "symbol": "Q'", "meaning": "electrical energy after separation to c'" }, { "unit": null, "symbol": "e", "meaning": "charge on the area S" }, { "unit": null, "symbol": "S", "meaning": "area of the plates" }, { "unit": null, "symbol": "c'", "meaning": "increased distance between the planes" } ], "sympy": "Eq(Q_p, 2*pi*e**2*cp/S)", "physics": true, "states": [], "concepts": [ "concept/parallel-planes", "quantity/electric-energy", "quantity/pi" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/eq-aef7651eb9", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-vi", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 87", "location": "PARTICULAR CASES OF ELECTRIFICATION", "latex": "Q' - Q = \\frac{2 \\pi}{S} e^2(c' - c)", "name": null, "statement": "The increase in electrical energy when the planes are pulled apart is 2 pi e squared over S times the increase in separation.", "kind": "result", "symbols": [ { "unit": null, "symbol": "Q'", "meaning": "electrical energy after separation" }, { "unit": null, "symbol": "Q", "meaning": "electrical energy before separation" }, { "unit": null, "symbol": "e", "meaning": "charge on the area S" }, { "unit": null, "symbol": "S", "meaning": "area of the plates" }, { "unit": null, "symbol": "c", "meaning": "original distance between the planes" }, { "unit": null, "symbol": "c'", "meaning": "increased distance between the planes" } ], "sympy": "Eq(Q_p - Q, 2*pi*e**2*(cp - c)/S)", "physics": true, "states": [], "concepts": [ "concept/parallel-planes", "concept/work", "quantity/electric-energy", "quantity/pi" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/eq-35173f0ee6", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-vi", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 87", "location": "PARTICULAR CASES OF ELECTRIFICATION", "latex": "F(c' - c) = \\frac{2 \\pi}{S} e^2(c' - c)", "name": null, "statement": "The work done by external agency in pulling the planes apart equals the attraction F times the increase in separation, which equals the increase in electrical energy.", "kind": "result", "symbols": [ { "unit": null, "symbol": "F", "meaning": "electric attraction between the two areas S" }, { "unit": null, "symbol": "c", "meaning": "original distance between the planes" }, { "unit": null, "symbol": "c'", "meaning": "increased distance between the planes" }, { "unit": null, "symbol": "e", "meaning": "charge on the area S" }, { "unit": null, "symbol": "S", "meaning": "area of the plates" } ], "sympy": "Eq(F*(cp - c), 2*pi*e**2*(cp - c)/S)", "physics": true, "states": [], "concepts": [ "concept/parallel-planes", "concept/work", "quantity/electric-energy" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/eq-8c05557d70", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-vi", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 87", "location": "PARTICULAR CASES OF ELECTRIFICATION", "latex": "F = \\frac{2 \\pi}{S} e^2", "name": null, "statement": "The electric attraction between two parallel plane areas S carrying equal and opposite charge e is 2 pi e squared divided by S.", "kind": "law", "symbols": [ { "unit": null, "symbol": "F", "meaning": "electric attraction between the two areas S" }, { "unit": null, "symbol": "e", "meaning": "charge on the area S" }, { "unit": null, "symbol": "S", "meaning": "area of the plates" } ], "sympy": "Eq(F, 2*pi*e**2/S)", "physics": true, "states": [], "concepts": [ "concept/parallel-planes", "law/electrostatic-attraction-and-repulsion", "quantity/electric-charge", "quantity/pi" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/eq-dee5661bb7", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-vi", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 87", "location": "PARTICULAR CASES OF ELECTRIFICATION", "latex": "e = \\sqrt\\frac{FS}{2 \\pi}", "name": null, "statement": "The charge on an area S can be measured from the dynamically measured attraction F between the planes.", "kind": "formula", "symbols": [ { "unit": null, "symbol": "e", "meaning": "charge on the area S" }, { "unit": null, "symbol": "F", "meaning": "force of attraction on the area S, in dynamical measure" }, { "unit": null, "symbol": "S", "meaning": "area of the surface" } ], "sympy": "Eq(e, sqrt(F*S/(2*pi)))", "physics": true, "states": [], "concepts": [ "concept/parallel-planes", "quantity/electric-charge", "quantity/pi" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/eq-4297ebe920", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-vi", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 87", "location": "PARTICULAR CASES OF ELECTRIFICATION", "latex": "A - B = 4 \\pi c \\frac{e}{S} = c \\sqrt{\\frac{8 \\pi F}{S}}", "name": null, "statement": "The potential difference between the two planes equals 4 pi c times the surface density, and also c times the square root of 8 pi F over S.", "kind": "formula", "symbols": [ { "unit": null, "symbol": "A", "meaning": "potential of the upper plane" }, { "unit": null, "symbol": "B", "meaning": "potential of the lower plane" }, { "unit": null, "symbol": "c", "meaning": "distance between the planes" }, { "unit": null, "symbol": "e", "meaning": "charge on the area S" }, { "unit": null, "symbol": "S", "meaning": "area of the plates" }, { "unit": null, "symbol": "F", "meaning": "electric attraction between the areas S" } ], "sympy": "Eq(A - B, 4*pi*c*e/S)", "physics": true, "states": [], "concepts": [ "concept/parallel-planes", "quantity/electric-potential", "quantity/pi" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/eq-7a89f1df38", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-vi", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 93", "location": "PARTICULAR CASES OF ELECTRIFICATION", "latex": "V = \\xp\\dfrac{E}{r}", "name": null, "statement": "The potential at distance r from a single small electrified body with charge E.", "kind": "formula", "symbols": [ { "unit": null, "symbol": "V", "meaning": "electric potential at distance r" }, { "unit": null, "symbol": "E", "meaning": "charge of the centre of force" }, { "unit": null, "symbol": "r", "meaning": "distance from the centre of force" } ], "sympy": "Eq(V, E/r)", "physics": true, "states": [], "concepts": [ "quantity/electric-charge", "quantity/electric-potential" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/eq-58e4dde4eb", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-vi", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 93", "location": "PARTICULAR CASES OF ELECTRIFICATION", "latex": "r = \\xp\\dfrac{E}{V}", "name": null, "statement": "The radius of the equipotential sphere of potential V around a single charge E.", "kind": "formula", "symbols": [ { "unit": null, "symbol": "r", "meaning": "radius of the equipotential sphere" }, { "unit": null, "symbol": "E", "meaning": "charge of the centre of force" }, { "unit": null, "symbol": "V", "meaning": "electric potential of the sphere" } ], "sympy": "Eq(r, E/V)", "physics": true, "states": [], "concepts": [ "concept/equipotential-surface", "quantity/electric-potential", "quantity/radius" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/eq-5c7555095c", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-vi", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 94", "location": "PARTICULAR CASES OF ELECTRIFICATION", "latex": "V_1 + V_2 = V", "name": "superposition of potentials", "statement": "The potential due to two centres of force is the sum of the potentials due to each.", "kind": "law", "symbols": [ { "unit": null, "symbol": "V_1", "meaning": "potential due to one centre of force" }, { "unit": null, "symbol": "V_2", "meaning": "potential due to the other centre of force" }, { "unit": null, "symbol": "V", "meaning": "potential due to both centres together" } ], "sympy": "Eq(V_1 + V_2, V)", "physics": true, "states": [ "law/superposition-of-potentials" ], "concepts": [ "concept/equipotential-surface", "law/superposition-of-electric-effects", "quantity/electric-potential" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/eq-199251558f", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-vi", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 94", "location": "PARTICULAR CASES OF ELECTRIFICATION", "latex": "2 \\pi E(1 - cos \\theta)", "name": null, "statement": "The surface-integral of induction through the part of a surface cut off by a cone of half-angle theta from a centre of charge E is 2 pi E times (1 minus cos theta).", "kind": "result", "symbols": [ { "unit": null, "symbol": "E", "meaning": "charge of the centre of force" }, { "unit": null, "symbol": "\\theta", "meaning": "angle between the radiating line and the axis" } ], "sympy": null, "physics": true, "states": [], "concepts": [ "concept/electric-displacement", "concept/tube-of-induction", "quantity/angle", "quantity/pi" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/eq-8ea65b18a6", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-vi", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 94", "location": "PARTICULAR CASES OF ELECTRIFICATION", "latex": "E(1 - cos \\theta) = 2 \\Psi", "name": null, "statement": "Defines Psi as half the induction through the bounded surface, so that the induction equals E times (1 minus cos theta) over 2.", "kind": "definition", "symbols": [ { "unit": null, "symbol": "E", "meaning": "charge of the centre of force" }, { "unit": null, "symbol": "\\theta", "meaning": "angle between the radiating line and the axis" }, { "unit": null, "symbol": "\\Psi", "meaning": "half the induction through the bounded surface (index number of the line of force)" } ], "sympy": "Eq(E*(1 - cos(theta)), 2*Psi)", "physics": true, "states": [], "concepts": [ "concept/electric-displacement", "concept/line-of-electric-force" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/eq-c240aeff26", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-vi", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 94", "location": "PARTICULAR CASES OF ELECTRIFICATION", "latex": "\\theta = cos^{-1}\\left(1 - 2 \\frac{\\Psi}{E}\\right)", "name": null, "statement": "The angle of a line of force with the axis is the inverse cosine of 1 minus 2 Psi over E.", "kind": "formula", "symbols": [ { "unit": null, "symbol": "\\theta", "meaning": "angle between the line of force and the axis" }, { "unit": null, "symbol": "\\Psi", "meaning": "index number of the line of force" }, { "unit": null, "symbol": "E", "meaning": "charge of the centre of force" } ], "sympy": "Eq(theta, acos(1 - 2*Psi/E))", "physics": true, "states": [], "concepts": [ "concept/line-of-electric-force", "quantity/angle" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/eq-25d677701f", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-vi", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 97", "location": "PARTICULAR CASES OF ELECTRIFICATION", "latex": "1 - 2 \\xp\\dfrac{\\Psi}{E}", "name": null, "statement": "The cosine of the angle between the asymptote of a line of force and the axis of a finite system, where E is the total electrification.", "kind": "result", "symbols": [ { "unit": null, "symbol": "\\Psi", "meaning": "index number of the line of force" }, { "unit": null, "symbol": "E", "meaning": "total electrification of the system" } ], "sympy": null, "physics": true, "states": [], "concepts": [ "concept/line-of-electric-force", "quantity/angle", "quantity/electric-charge" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/eq-4848cfcebd", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-vii", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 101", "location": "THEORY OF ELECTRICAL IMAGES", "latex": "\\overline{CA} = ma", "name": null, "statement": "The point A is placed at distance ma from the centre C, where m is the ratio of CA to the sphere's radius a.", "kind": "definition", "symbols": [ { "unit": null, "symbol": "CA", "meaning": "distance from the centre of the sphere to the electrified point A" }, { "unit": null, "symbol": "m", "meaning": "ratio of CA to the radius a" }, { "unit": null, "symbol": "a", "meaning": "radius of the sphere" } ], "sympy": "Eq(CA, m*a)", "physics": false, "states": [], "concepts": [ "concept/electrical-image", "concept/inverse-points-with-respect-to-a-sphere", "concept/sphere" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/eq-861bb630c8", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-vii", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 101", "location": "THEORY OF ELECTRICAL IMAGES", "latex": "\\overline{AP} : \\overline{PB} : : \\overline{AC} : \\overline{PC}", "name": null, "statement": "Triangles APC and PCB are similar, so AP is to PB as AC is to PC.", "kind": "result", "symbols": [ { "unit": null, "symbol": "AP", "meaning": "distance from A to the point P on the sphere" }, { "unit": null, "symbol": "PB", "meaning": "distance from B to the point P on the sphere" }, { "unit": null, "symbol": "AC", "meaning": "distance from A to the centre C" }, { "unit": null, "symbol": "PC", "meaning": "radius of the sphere" } ], "sympy": null, "physics": false, "states": [], "concepts": [ "concept/inverse-points-with-respect-to-a-sphere", "concept/proportion" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/eq-6aa66a3f46", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-vii", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 101", "location": "THEORY OF ELECTRICAL IMAGES", "latex": "\\overline{AP} = m \\overline{BP}", "name": null, "statement": "The distance from A to any point P of the sphere is m times the distance from B to P.", "kind": "result", "symbols": [ { "unit": null, "symbol": "AP", "meaning": "distance from A to P" }, { "unit": null, "symbol": "BP", "meaning": "distance from B to P" }, { "unit": null, "symbol": "m", "meaning": "ratio of CA to the radius a" } ], "sympy": "Eq(AP, m*BP)", "physics": false, "states": [], "concepts": [ "concept/electrical-image", "concept/inverse-points-with-respect-to-a-sphere" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/eq-c0cf6a49d4", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-vii", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 101", "location": "THEORY OF ELECTRICAL IMAGES", "latex": "V &= \\frac{e}{\\overline{AP}} + \\frac{e'}{\\overline{BP}}", "name": null, "statement": "The potential at P due to the charge e at A and the image charge e' at B is the sum of the two charges divided by their distances from P.", "kind": "formula", "symbols": [ { "unit": null, "symbol": "V", "meaning": "electric potential at the point P" }, { "unit": null, "symbol": "e", "meaning": "electric charge of the point A" }, { "unit": null, "symbol": "e'", "meaning": "imaginary charge at the image point B" }, { "unit": null, "symbol": "AP", "meaning": "distance from A to P" }, { "unit": null, "symbol": "BP", "meaning": "distance from B to P" } ], "sympy": "Eq(V, e/AP + e_prime/BP)", "physics": true, "states": [], "concepts": [ "concept/electrical-image", "law/superposition-of-potentials", "quantity/electric-potential" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/eq-14fc81cfad", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-vii", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 102", "location": "THEORY OF ELECTRICAL IMAGES", "latex": "AD = \\frac{a^2}{c}", "name": null, "statement": "The image of B in the sphere a lies at D, at distance a^2/c from A.", "kind": "result", "symbols": [ { "unit": null, "symbol": "AD", "meaning": "distance from the centre A of sphere a to the image D" }, { "unit": null, "symbol": "a", "meaning": "radius of sphere a" }, { "unit": null, "symbol": "c", "meaning": "distance between the centres of the two spheres" } ], "sympy": "Eq(AD, a**2/c)", "physics": false, "states": [], "concepts": [ "concept/electrical-image", "concept/inverse-points-with-respect-to-a-sphere" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/eq-2a169a5a96", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-vii", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 102", "location": "THEORY OF ELECTRICAL IMAGES", "latex": "BE = \\frac{b^2}{c}", "name": null, "statement": "The image of A in the sphere b lies at E, at distance b^2/c from B.", "kind": "result", "symbols": [ { "unit": null, "symbol": "BE", "meaning": "distance from the centre B of sphere b to the image E" }, { "unit": null, "symbol": "b", "meaning": "radius of sphere b" }, { "unit": null, "symbol": "c", "meaning": "distance between the centres of the two spheres" } ], "sympy": "Eq(BE, b**2/c)", "physics": false, "states": [], "concepts": [ "concept/electrical-image", "concept/inverse-points-with-respect-to-a-sphere" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/eq-3a3045c436", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-vii", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 103", "location": "THEORY OF ELECTRICAL IMAGES", "latex": "AF = \\frac{a^2}{AE} = \\frac{a^2 c}{c^2 - b^2}", "name": null, "statement": "The image of E in the sphere a, a third-order image, lies at F at the stated distance from A.", "kind": "result", "symbols": [ { "unit": null, "symbol": "AF", "meaning": "distance from the centre A of sphere a to the image F" }, { "unit": null, "symbol": "AE", "meaning": "distance from A to the image E" }, { "unit": null, "symbol": "a", "meaning": "radius of sphere a" }, { "unit": null, "symbol": "b", "meaning": "radius of sphere b" }, { "unit": null, "symbol": "c", "meaning": "distance between the centres" } ], "sympy": "Eq(AF, a**2*c/(c**2 - b**2))", "physics": false, "states": [], "concepts": [ "concept/electrical-image", "concept/inverse-points-with-respect-to-a-sphere" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/eq-3de372884b", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-vii", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 103", "location": "THEORY OF ELECTRICAL IMAGES", "latex": "BG = \\frac{b^2}{DB} = \\frac{b^2 c}{c^2 - a^2}", "name": null, "statement": "The image of D in the sphere b, a third-order image, lies at G at the stated distance from B.", "kind": "result", "symbols": [ { "unit": null, "symbol": "BG", "meaning": "distance from the centre B of sphere b to the image G" }, { "unit": null, "symbol": "DB", "meaning": "distance from B to the image D" }, { "unit": null, "symbol": "a", "meaning": "radius of sphere a" }, { "unit": null, "symbol": "b", "meaning": "radius of sphere b" }, { "unit": null, "symbol": "c", "meaning": "distance between the centres" } ], "sympy": "Eq(BG, b**2*c/(c**2 - a**2))", "physics": false, "states": [], "concepts": [ "concept/electrical-image", "concept/inverse-points-with-respect-to-a-sphere" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/eq-7f2cc10557", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-vii", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 103", "location": "THEORY OF ELECTRICAL IMAGES", "latex": "q_{aa} &= a + \\frac{a^2 b}{c^2 - b^2} + \\text{\\&c.,}", "name": null, "statement": "The coefficient q_aa, summing the images that contribute to the charge of sphere a, is a series whose first terms are given.", "kind": "definition", "symbols": [ { "unit": null, "symbol": "q_{aa}", "meaning": "coefficient of P_a in the charge of sphere a" }, { "unit": null, "symbol": "a", "meaning": "radius of sphere a" }, { "unit": null, "symbol": "b", "meaning": "radius of sphere b" }, { "unit": null, "symbol": "c", "meaning": "distance between the centres" } ], "sympy": null, "physics": true, "states": [], "concepts": [ "concept/electrical-image", "quantity/electric-charge", "quantity/electric-potential" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/eq-795dd232e3", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-vii", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 103", "location": "THEORY OF ELECTRICAL IMAGES", "latex": "q_{ab} &= - \\frac{ab}{c} - \\frac{a^2 b^2}{c (c^2 - a^2 - b^2)} - \\text{\\&c.,}", "name": null, "statement": "The coefficient q_ab, the cross-coefficient linking the two spheres' charges and potentials, is a series whose first terms are given.", "kind": "definition", "symbols": [ { "unit": null, "symbol": "q_{ab}", "meaning": "cross-coefficient between the two spheres" }, { "unit": null, "symbol": "a", "meaning": "radius of sphere a" }, { "unit": null, "symbol": "b", "meaning": "radius of sphere b" }, { "unit": null, "symbol": "c", "meaning": "distance between the centres" } ], "sympy": null, "physics": true, "states": [], "concepts": [ "concept/electrical-image", "quantity/electric-charge", "quantity/electric-potential" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/eq-27185acbea", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-vii", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 103", "location": "THEORY OF ELECTRICAL IMAGES", "latex": "q_{bb} &= b + \\frac{ab^2}{c^2 -a^2} + \\text{\\&c.,}", "name": null, "statement": "The coefficient q_bb, summing the images that contribute to the charge of sphere b, is a series whose first terms are given.", "kind": "definition", "symbols": [ { "unit": null, "symbol": "q_{bb}", "meaning": "coefficient of P_b in the charge of sphere b" }, { "unit": null, "symbol": "a", "meaning": "radius of sphere a" }, { "unit": null, "symbol": "b", "meaning": "radius of sphere b" }, { "unit": null, "symbol": "c", "meaning": "distance between the centres" } ], "sympy": null, "physics": true, "states": [], "concepts": [ "concept/electrical-image", "quantity/electric-charge", "quantity/electric-potential" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/eq-577e5a8e6f", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-vii", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 103", "location": "THEORY OF ELECTRICAL IMAGES", "latex": "E_a = q_{aa} P_a + q_{ab} P_b", "name": null, "statement": "The total charge of sphere a is the sum of its potential terms weighted by the coefficients q_aa and q_ab.", "kind": "result", "symbols": [ { "unit": null, "symbol": "E_a", "meaning": "total charge of sphere a" }, { "unit": null, "symbol": "P_a", "meaning": "potential of sphere a" }, { "unit": null, "symbol": "P_b", "meaning": "potential of sphere b" }, { "unit": null, "symbol": "q_{aa}", "meaning": "coefficient of P_a in the charge of sphere a" }, { "unit": null, "symbol": "q_{ab}", "meaning": "cross-coefficient between the two spheres" } ], "sympy": "Eq(E_a, q_aa*P_a + q_ab*P_b)", "physics": true, "states": [], "concepts": [ "concept/coefficients-of-capacity", "quantity/electric-charge", "quantity/electric-potential" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/eq-a3d61257ed", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-vii", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 103", "location": "THEORY OF ELECTRICAL IMAGES", "latex": "E_b = q_{ab} P_a + q_{bb} P_b", "name": null, "statement": "The total charge of sphere b is the sum of its potential terms weighted by the coefficients q_ab and q_bb.", "kind": "result", "symbols": [ { "unit": null, "symbol": "E_b", "meaning": "total charge of sphere b" }, { "unit": null, "symbol": "P_a", "meaning": "potential of sphere a" }, { "unit": null, "symbol": "P_b", "meaning": "potential of sphere b" }, { "unit": null, "symbol": "q_{ab}", "meaning": "cross-coefficient between the two spheres" }, { "unit": null, "symbol": "q_{bb}", "meaning": "coefficient of P_b in the charge of sphere b" } ], "sympy": "Eq(E_b, q_ab*P_a + q_bb*P_b)", "physics": true, "states": [], "concepts": [ "concept/coefficients-of-capacity", "quantity/electric-charge", "quantity/electric-potential" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/eq-eef64e9514", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-vii", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 103", "location": "THEORY OF ELECTRICAL IMAGES", "latex": "&P_a = \\frac{1}{a} E_a + \\frac{1}{c} E_b", "name": null, "statement": "Neglecting terms in b^3, the potential of sphere a is expressed in terms of the two charges.", "kind": "approximation", "symbols": [ { "unit": null, "symbol": "P_a", "meaning": "potential of sphere a" }, { "unit": null, "symbol": "E_a", "meaning": "total charge of sphere a" }, { "unit": null, "symbol": "E_b", "meaning": "total charge of sphere b" }, { "unit": null, "symbol": "a", "meaning": "radius of sphere a" }, { "unit": null, "symbol": "c", "meaning": "distance between the centres" } ], "sympy": "Eq(P_a, E_a/a + E_b/c)", "physics": true, "states": [], "concepts": [ "concept/electrical-image", "quantity/electric-charge", "quantity/electric-potential" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/eq-6f45be4433", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-vii", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 103", "location": "THEORY OF ELECTRICAL IMAGES", "latex": "&P_b = \\frac{1}{c} E_a + \\left\\{\\frac{1}{b} - \\frac{a^3}{c^2 (c^2 - a^2)}\\right\\} E_b", "name": null, "statement": "Neglecting terms in b^3, the potential of sphere b is expressed in terms of the two charges.", "kind": "approximation", "symbols": [ { "unit": null, "symbol": "P_b", "meaning": "potential of sphere b" }, { "unit": null, "symbol": "E_a", "meaning": "total charge of sphere a" }, { "unit": null, "symbol": "E_b", "meaning": "total charge of sphere b" }, { "unit": null, "symbol": "a", "meaning": "radius of sphere a" }, { "unit": null, "symbol": "b", "meaning": "radius of sphere b" }, { "unit": null, "symbol": "c", "meaning": "distance between the centres" } ], "sympy": "Eq(P_b, E_a/c + (1/b - a**3/(c**2*(c**2 - a**2)))*E_b)", "physics": true, "states": [], "concepts": [ "concept/electrical-image", "quantity/electric-charge", "quantity/electric-potential" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/eq-64bd1bcc1c", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-vii", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 103", "location": "THEORY OF ELECTRICAL IMAGES", "latex": "\\frac{1}{2} (E_a P_a + E_b P_b) = \\frac{1}{2} \\frac{1}{a}\\, E_a^2 + \\frac{1}{c}\\, E_a E_b + \\frac{1}{2} \\left\\{\\frac{1}{b} - \\frac{a^3}{c^2 (c^2 - a^2 )}\\right\\} E_b^2", "name": null, "statement": "The electric energy of the two-sphere system is half the sum of charge times potential for each sphere, written as a quadratic form in the charges.", "kind": "result", "symbols": [ { "unit": null, "symbol": "E_a", "meaning": "total charge of sphere a" }, { "unit": null, "symbol": "E_b", "meaning": "total charge of sphere b" }, { "unit": null, "symbol": "P_a", "meaning": "potential of sphere a" }, { "unit": null, "symbol": "P_b", "meaning": "potential of sphere b" }, { "unit": null, "symbol": "a", "meaning": "radius of sphere a" }, { "unit": null, "symbol": "b", "meaning": "radius of sphere b" }, { "unit": null, "symbol": "c", "meaning": "distance between the centres" } ], "sympy": "Eq(E_a*P_a/2 + E_b*P_b/2, E_a**2/(2*a) + E_a*E_b/c + (1/b - a**3/(c**2*(c**2 - a**2)))*E_b**2/2)", "physics": true, "states": [], "concepts": [ "quantity/electric-charge", "quantity/electric-energy", "quantity/electric-potential" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/eq-c5d1ee7bfb", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-vii", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 104", "location": "THEORY OF ELECTRICAL IMAGES", "latex": "R =\\frac{ E_b}{c^2}\\left\\{E_a - E_b\\frac{a^3 (2c^2 - a^2)}{c(c^2 - a^2)^2}\\right\\}", "name": null, "statement": "The repulsion between the two spheres is the rate at which the electric energy diminishes as the distance c increases.", "kind": "result", "symbols": [ { "unit": null, "symbol": "R", "meaning": "repulsion between the two spheres" }, { "unit": null, "symbol": "E_a", "meaning": "total charge of sphere a" }, { "unit": null, "symbol": "E_b", "meaning": "total charge of sphere b" }, { "unit": null, "symbol": "a", "meaning": "radius of sphere a" }, { "unit": null, "symbol": "c", "meaning": "distance between the centres" } ], "sympy": "Eq(R, E_b/c**2*(E_a - E_b*a**3*(2*c**2 - a**2)/(c*(c**2 - a**2)**2)))", "physics": true, "states": [], "concepts": [ "law/electrostatic-attraction-and-repulsion", "quantity/electric-charge", "quantity/electric-energy" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/eq-3bd272abd1", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-vii", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 104", "location": "THEORY OF ELECTRICAL IMAGES", "latex": "E_a \\text{ must be greater than } E_b\\frac{ a^3(2c^2 - a^2)}{c(c^2 - a^2)^2}", "name": null, "statement": "For the force to be repulsive, the charge of sphere a must exceed the stated multiple of the charge of sphere b.", "kind": "rule", "symbols": [ { "unit": null, "symbol": "E_a", "meaning": "total charge of sphere a" }, { "unit": null, "symbol": "E_b", "meaning": "total charge of sphere b" }, { "unit": null, "symbol": "a", "meaning": "radius of sphere a" }, { "unit": null, "symbol": "c", "meaning": "distance between the centres" } ], "sympy": "Gt(E_a, E_b*a**3*(2*c**2 - a**2)/(c*(c**2 - a**2)**2))", "physics": true, "states": [], "concepts": [ "law/electrostatic-attraction-and-repulsion", "quantity/electric-charge" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/eq-9048db91fa", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-vii", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 100", "location": "THEORY OF ELECTRICAL IMAGES", "latex": "\\xp", "name": null, "statement": "placeholder", "kind": "rule", "symbols": [], "sympy": null, "physics": false, "states": [], "concepts": [] }, { "id": "maxwell-elementary-treatise-electricity-1888/eq-b771914988", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-vii", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 105", "location": "THEORY OF ELECTRICAL IMAGES", "latex": "\\sigma = - \\frac{1}{4\\pi} \\frac{ea}{r^3} (m^2 - 1)", "name": null, "statement": "The surface density of the induced charge on the sphere due to a point A outside it is negative everywhere and falls off as the inverse cube of the distance from A.", "kind": "result", "symbols": [ { "unit": null, "symbol": "sigma", "meaning": "surface density of electrification on the sphere" }, { "unit": null, "symbol": "e", "meaning": "electric charge of the point A" }, { "unit": null, "symbol": "a", "meaning": "radius of the sphere" }, { "unit": null, "symbol": "r", "meaning": "distance AP from the inducing point A to the point P" }, { "unit": null, "symbol": "m", "meaning": "ratio of CA to the radius a" } ], "sympy": "Eq(sigma, -1/(4*pi)*e*a/r**3*(m**2 - 1))", "physics": true, "states": [], "concepts": [ "concept/electric-induction", "concept/electrical-image", "quantity/surface-charge-density" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/eq-641dcaed8d", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-vii", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 105", "location": "THEORY OF ELECTRICAL IMAGES", "latex": "4 \\pi \\sigma = R", "name": "Coulomb's law", "statement": "By Coulomb's law, 4π times the surface density equals the resultant force acting outwards at the surface.", "kind": "law", "symbols": [ { "unit": null, "symbol": "sigma", "meaning": "surface density of electrification" }, { "unit": null, "symbol": "R", "meaning": "resultant electric force at the surface, acting outwards" } ], "sympy": "Eq(4*pi*sigma, R)", "physics": true, "states": [ "law/coulomb-s-law" ], "concepts": [ "concept/electric-field", "quantity/surface-charge-density" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/eq-ba8287018e", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-viii", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 108", "location": "ON ELECTROSTATIC CAPACITY", "latex": "Q &= K(P-p) + HP", "name": null, "statement": "The charge of the first conductor is K times its potential difference from the second conductor plus H times its potential, where H is the part of its capacity that depends on external objects.", "kind": "formula", "symbols": [ { "unit": null, "symbol": "Q", "meaning": "charge of the first conductor" }, { "unit": null, "symbol": "K", "meaning": "capacity of the condenser so far as it depends on the mutual relation of the two conductors" }, { "unit": null, "symbol": "P", "meaning": "potential of the first conductor (walls of the room at zero)" }, { "unit": null, "symbol": "p", "meaning": "potential of the second conductor" }, { "unit": null, "symbol": "H", "meaning": "part of the capacity of the first conductor depending on its relation to external objects such as the walls of the room" } ], "sympy": "Eq(Q, K*(P-p) + H*P)", "physics": true, "states": [], "concepts": [ "instrument/condenser", "quantity/capacity", "quantity/electric-charge", "quantity/electric-potential" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/eq-b7538c7c44", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-viii", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 108", "location": "ON ELECTROSTATIC CAPACITY", "latex": "q &= K(p-P) + hp", "name": null, "statement": "The charge of the second conductor is K times its potential difference from the first conductor plus h times its potential, where h is the part of its capacity depending on external objects.", "kind": "formula", "symbols": [ { "unit": null, "symbol": "q", "meaning": "charge of the second conductor" }, { "unit": null, "symbol": "K", "meaning": "capacity of the condenser so far as it depends on the mutual relation of the two conductors" }, { "unit": null, "symbol": "P", "meaning": "potential of the first conductor" }, { "unit": null, "symbol": "p", "meaning": "potential of the second conductor" }, { "unit": null, "symbol": "h", "meaning": "part of the capacity of the second conductor depending on its relation to external objects" } ], "sympy": "Eq(q, K*(p-P) + h*p)", "physics": true, "states": [], "concepts": [ "instrument/condenser", "quantity/capacity", "quantity/electric-charge", "quantity/electric-potential" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/eq-dcedd21e9f", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-viii", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 108", "location": "ON ELECTROSTATIC CAPACITY", "latex": "P_1=P-\\frac{K}{K+H}p", "name": null, "statement": "After the second conductor is connected to earth, the potential of the first conductor falls to P_1 by the fraction K/(K+H) of the second conductor's former potential.", "kind": "result", "symbols": [ { "unit": null, "symbol": "P_1", "meaning": "potential of the first conductor after the second is connected to earth" }, { "unit": null, "symbol": "P", "meaning": "potential of the first conductor before the connection" }, { "unit": null, "symbol": "p", "meaning": "potential of the second conductor before it is earthed" }, { "unit": null, "symbol": "K", "meaning": "capacity of the condenser depending on the mutual relation of the two conductors" }, { "unit": null, "symbol": "H", "meaning": "part of the capacity of the first conductor depending on external objects" } ], "sympy": "Eq(P_1, P - K/(K+H)*p)", "physics": true, "states": [], "concepts": [ "concept/electrical-earth", "method/discharging-a-conductor", "quantity/capacity", "quantity/electric-potential" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/eq-31be88cd1e", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-viii", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 108", "location": "ON ELECTROSTATIC CAPACITY", "latex": "Q_1=(K+H)P_1", "name": null, "statement": "After the earthing, the charge of the first conductor equals its capacity K+H times its new potential P_1.", "kind": "result", "symbols": [ { "unit": null, "symbol": "Q_1", "meaning": "charge of the first conductor after the second is earthed (in Art. 108 only; Art. 109 reuses the symbol for another charge)" }, { "unit": null, "symbol": "K", "meaning": "mutual capacity of the two conductors" }, { "unit": null, "symbol": "H", "meaning": "external part of the capacity of the first conductor" }, { "unit": null, "symbol": "P_1", "meaning": "potential of the first conductor after the second is earthed" } ], "sympy": "Eq(Q_1, (K+H)*P_1)", "physics": true, "states": [], "concepts": [ "method/discharging-a-conductor", "quantity/capacity", "quantity/electric-charge" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/eq-b34956cafd", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-viii", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 108", "location": "ON ELECTROSTATIC CAPACITY", "latex": "q_1=-KP_1", "name": null, "statement": "After the earthing, the charge of the second conductor equals minus K times the first conductor's new potential.", "kind": "result", "symbols": [ { "unit": null, "symbol": "q_1", "meaning": "charge of the second conductor after it is earthed" }, { "unit": null, "symbol": "K", "meaning": "mutual capacity of the two conductors" }, { "unit": null, "symbol": "P_1", "meaning": "potential of the first conductor after the second is earthed" } ], "sympy": "Eq(q_1, -K*P_1)", "physics": true, "states": [], "concepts": [ "method/discharging-a-conductor", "quantity/capacity", "quantity/electric-charge" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/eq-bc144d0269", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-viii", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 108", "location": "ON ELECTROSTATIC CAPACITY", "latex": "p_2=-\\frac{K}{K+h}P_1", "name": null, "statement": "When the second conductor is insulated and the first is earthed, the second conductor's potential becomes minus K/(K+h) times P_1.", "kind": "result", "symbols": [ { "unit": null, "symbol": "p_2", "meaning": "potential of the second conductor after the first is earthed" }, { "unit": null, "symbol": "K", "meaning": "mutual capacity of the two conductors" }, { "unit": null, "symbol": "h", "meaning": "external part of the capacity of the second conductor" }, { "unit": null, "symbol": "P_1", "meaning": "potential of the first conductor after the previous step" } ], "sympy": "Eq(p_2, -K/(K+h)*P_1)", "physics": true, "states": [], "concepts": [ "concept/electrical-earth", "method/discharging-a-conductor", "quantity/capacity", "quantity/electric-potential" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/eq-aaf0e2683b", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-viii", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 108", "location": "ON ELECTROSTATIC CAPACITY", "latex": "Q_2=-Kp_2", "name": null, "statement": "After the first conductor is earthed, the charge of the first conductor equals minus K times the second conductor's potential p_2.", "kind": "result", "symbols": [ { "unit": null, "symbol": "Q_2", "meaning": "charge of the first conductor after the first is earthed" }, { "unit": null, "symbol": "K", "meaning": "mutual capacity of the two conductors" }, { "unit": null, "symbol": "p_2", "meaning": "potential of the second conductor after the first is earthed" } ], "sympy": "Eq(Q_2, -K*p_2)", "physics": true, "states": [], "concepts": [ "method/discharging-a-conductor", "quantity/capacity", "quantity/electric-charge" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/eq-b3a4853c56", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-viii", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 108", "location": "ON ELECTROSTATIC CAPACITY", "latex": "q_2=(K+h)p_2", "name": null, "statement": "After the first conductor is earthed, the charge of the second conductor equals its capacity K+h times its potential p_2.", "kind": "result", "symbols": [ { "unit": null, "symbol": "q_2", "meaning": "charge of the second conductor after the first is earthed" }, { "unit": null, "symbol": "K", "meaning": "mutual capacity of the two conductors" }, { "unit": null, "symbol": "h", "meaning": "external part of the capacity of the second conductor" }, { "unit": null, "symbol": "p_2", "meaning": "potential of the second conductor after the first is earthed" } ], "sympy": "Eq(q_2, (K+h)*p_2)", "physics": true, "states": [], "concepts": [ "method/discharging-a-conductor", "quantity/capacity", "quantity/electric-charge" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/eq-a111219051", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-viii", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 109", "location": "ON ELECTROSTATIC CAPACITY", "latex": "P_3=-\\frac{K}{K+H}p_2", "name": null, "statement": "When the second conductor is earthed again, the first conductor's potential becomes minus K/(K+H) times p_2.", "kind": "result", "symbols": [ { "unit": null, "symbol": "P_3", "meaning": "potential of the first conductor after the second conductor is earthed again" }, { "unit": null, "symbol": "K", "meaning": "mutual capacity of the two conductors" }, { "unit": null, "symbol": "H", "meaning": "external part of the capacity of the first conductor" }, { "unit": null, "symbol": "p_2", "meaning": "potential of the second conductor before this step" } ], "sympy": "Eq(P_3, -K/(K+H)*p_2)", "physics": true, "states": [], "concepts": [ "concept/electrical-earth", "method/discharging-a-conductor", "quantity/capacity", "quantity/electric-potential" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/eq-15f5747cb8", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-viii", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 109", "location": "ON ELECTROSTATIC CAPACITY", "latex": "Q_3=(K+H)P_3", "name": null, "statement": "After the second earthing, the charge of the first conductor equals its capacity K+H times P_3.", "kind": "result", "symbols": [ { "unit": null, "symbol": "Q_3", "meaning": "charge of the first conductor after the second earthing" }, { "unit": null, "symbol": "K", "meaning": "mutual capacity of the two conductors" }, { "unit": null, "symbol": "H", "meaning": "external part of the capacity of the first conductor" }, { "unit": null, "symbol": "P_3", "meaning": "potential of the first conductor after the second earthing" } ], "sympy": "Eq(Q_3, (K+H)*P_3)", "physics": true, "states": [], "concepts": [ "method/discharging-a-conductor", "quantity/capacity", "quantity/electric-charge" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/eq-3b38c6e471", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-viii", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 109", "location": "ON ELECTROSTATIC CAPACITY", "latex": "q_3=-KP_3", "name": null, "statement": "After the second earthing, the charge of the second conductor equals minus K times the first conductor's potential P_3.", "kind": "result", "symbols": [ { "unit": null, "symbol": "q_3", "meaning": "charge of the second conductor after the second earthing" }, { "unit": null, "symbol": "K", "meaning": "mutual capacity of the two conductors" }, { "unit": null, "symbol": "P_3", "meaning": "potential of the first conductor after the second earthing" } ], "sympy": "Eq(q_3, -K*P_3)", "physics": true, "states": [], "concepts": [ "method/discharging-a-conductor", "quantity/capacity", "quantity/electric-charge" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/eq-ee099e4ac7", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-viii", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 109", "location": "ON ELECTROSTATIC CAPACITY", "latex": "Q_1=(K_1+H_1)P", "name": null, "statement": "The inner coating of the first jar, held at potential P, carries charge (K_1+H_1) times P when its outer coating is at earth.", "kind": "formula", "symbols": [ { "unit": null, "symbol": "Q_1", "meaning": "charge of the inner coating of the first jar (Art. 109; not the Art. 108 Q_1)" }, { "unit": null, "symbol": "K_1", "meaning": "mutual capacity of the first jar" }, { "unit": null, "symbol": "H_1", "meaning": "external part of the capacity of the inner coating of the first jar" }, { "unit": null, "symbol": "P", "meaning": "potential to which the connected inner and outer coatings are brought" } ], "sympy": "Eq(Q_1, (K_1+H_1)*P)", "physics": true, "states": [], "concepts": [ "instrument/condenser", "quantity/capacity", "quantity/electric-charge", "quantity/electric-potential" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/eq-9fe54f8926", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-viii", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 109", "location": "ON ELECTROSTATIC CAPACITY", "latex": "Q_2=-K_2 P", "name": null, "statement": "The inner coating of the second jar, with its outer coating at earth, carries charge minus K_2 times P.", "kind": "formula", "symbols": [ { "unit": null, "symbol": "Q_2", "meaning": "charge of the inner coating of the second jar" }, { "unit": null, "symbol": "K_2", "meaning": "mutual capacity of the second jar" }, { "unit": null, "symbol": "P", "meaning": "potential to which the connected coatings are brought" } ], "sympy": "Eq(Q_2, -K_2*P)", "physics": true, "states": [], "concepts": [ "instrument/condenser", "quantity/capacity", "quantity/electric-charge" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/eq-9539378b27", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-viii", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 109", "location": "ON ELECTROSTATIC CAPACITY", "latex": "Q_1 + Q_2 = {Q_1}' + {Q_2}'", "name": null, "statement": "The total charge on the two inner coatings is unchanged when they are joined together.", "kind": "law", "symbols": [ { "unit": null, "symbol": "Q_1", "meaning": "charge of the inner coating of the first jar before joining" }, { "unit": null, "symbol": "Q_2", "meaning": "charge of the inner coating of the second jar before joining" }, { "unit": null, "symbol": "Q_1p", "meaning": "charge of the inner coating of the first jar after joining (Q_1')" }, { "unit": null, "symbol": "Q_2p", "meaning": "charge of the inner coating of the second jar after joining (Q_2')" } ], "sympy": "Eq(Q_1 + Q_2, Q_1p + Q_2p)", "physics": true, "states": [], "concepts": [ "instrument/condenser", "law/conservation-of-electric-charge", "quantity/electric-charge" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/eq-9be60f31cf", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-viii", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 109", "location": "ON ELECTROSTATIC CAPACITY", "latex": "{P_1}' = {P_2}' = P'", "name": null, "statement": "After the inner coatings are joined, both jars have the same common potential P'.", "kind": "result", "symbols": [ { "unit": null, "symbol": "P_1p", "meaning": "potential of the first jar's inner coating after joining (P_1')" }, { "unit": null, "symbol": "P_2p", "meaning": "potential of the second jar's inner coating after joining (P_2')" }, { "unit": null, "symbol": "Pp", "meaning": "common potential of the inner coatings after joining (P')" } ], "sympy": "Eq(P_1p, P_2p)", "physics": true, "states": [], "concepts": [ "instrument/condenser", "quantity/electric-potential", "theorem/common-potential-after-contact" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/eq-23dca126d4", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-viii", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 109", "location": "ON ELECTROSTATIC CAPACITY", "latex": "(K_1+H_1-K_2)P=(K_1+H_1+K_2+H_2)P'", "name": null, "statement": "Charge conservation applied to the joined inner coatings gives the common potential P' in terms of P and the jar capacities.", "kind": "result", "symbols": [ { "unit": null, "symbol": "K_1", "meaning": "mutual capacity of the first jar" }, { "unit": null, "symbol": "H_1", "meaning": "external part of the capacity of the first jar's inner coating" }, { "unit": null, "symbol": "K_2", "meaning": "mutual capacity of the second jar" }, { "unit": null, "symbol": "H_2", "meaning": "external part of the capacity of the second jar's inner coating" }, { "unit": null, "symbol": "P", "meaning": "potential to which the coatings were first brought" }, { "unit": null, "symbol": "Pp", "meaning": "common potential of the inner coatings after joining (P')" } ], "sympy": "Eq((K_1+H_1-K_2)*P, (K_1+H_1+K_2+H_2)*Pp)", "physics": true, "states": [], "concepts": [ "law/conservation-of-electric-charge", "method/discharging-a-conductor", "quantity/capacity", "quantity/electric-potential" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/eq-0107660d5c", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-viii", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 109", "location": "ON ELECTROSTATIC CAPACITY", "latex": "K_1 + H_1 = K_2", "name": null, "statement": "When the first jar's total capacity equals the second jar's mutual capacity, the discharge between the jars is complete.", "kind": "result", "symbols": [ { "unit": null, "symbol": "K_1", "meaning": "mutual capacity of the first jar" }, { "unit": null, "symbol": "H_1", "meaning": "external part of the capacity of the first jar's inner coating" }, { "unit": null, "symbol": "K_2", "meaning": "mutual capacity of the second jar" } ], "sympy": "Eq(K_1 + H_1, K_2)", "physics": true, "states": [], "concepts": [ "instrument/condenser", "method/discharging-a-conductor", "quantity/capacity" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/eq-4e95d4778c", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-viii", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 112", "location": "ON ELECTROSTATIC CAPACITY", "latex": "a &= (P+R+\\alpha+\\eta)A-PB-RD-\\eta C", "name": null, "statement": "The charge of conductor alpha is its coefficient of capacity times its potential, minus the induction terms from the potentials of the adjacent conductors.", "kind": "formula", "symbols": [ { "unit": null, "symbol": "a", "meaning": "charge of conductor alpha (inner coatings of P and R with connecting wire)" }, { "unit": null, "symbol": "P", "meaning": "coefficient of induction between the inner coating of P and the outer coating of P" }, { "unit": null, "symbol": "R", "meaning": "coefficient of induction between alpha and delta" }, { "unit": null, "symbol": "alpha", "meaning": "excess of the coefficient of capacity of alpha over its three coefficients of induction" }, { "unit": null, "symbol": "eta", "meaning": "small coefficient of induction between alpha and gamma" }, { "unit": null, "symbol": "A", "meaning": "potential of conductor alpha" }, { "unit": null, "symbol": "B", "meaning": "potential of conductor beta" }, { "unit": null, "symbol": "C", "meaning": "potential of conductor gamma" }, { "unit": null, "symbol": "D", "meaning": "potential of conductor delta" } ], "sympy": "Eq(a, (P+R+alpha+eta)*A - P*B - R*D - eta*C)", "physics": true, "states": [], "concepts": [ "concept/coefficients-of-capacity", "instrument/wheatstone-s-bridge", "quantity/coefficient-of-induction", "quantity/electric-charge", "quantity/electric-potential" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/eq-738d3c1502", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-viii", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 112", "location": "ON ELECTROSTATIC CAPACITY", "latex": "b &= (P+Q+\\beta+\\xi)B-PA-QC-\\xi D", "name": null, "statement": "The charge of conductor beta is its coefficient of capacity times its potential, minus the induction terms from the adjacent conductors.", "kind": "formula", "symbols": [ { "unit": null, "symbol": "b", "meaning": "charge of conductor beta (outer coatings of P and Q with the stand)" }, { "unit": null, "symbol": "P", "meaning": "coefficient of induction between beta and alpha" }, { "unit": null, "symbol": "Q", "meaning": "coefficient of induction between beta and gamma" }, { "unit": null, "symbol": "beta", "meaning": "excess of the coefficient of capacity of beta over its coefficients of induction" }, { "unit": null, "symbol": "xi", "meaning": "small coefficient of induction between beta and delta" }, { "unit": null, "symbol": "A", "meaning": "potential of conductor alpha" }, { "unit": null, "symbol": "B", "meaning": "potential of conductor beta" }, { "unit": null, "symbol": "C", "meaning": "potential of conductor gamma" }, { "unit": null, "symbol": "D", "meaning": "potential of conductor delta" } ], "sympy": "Eq(b, (P+Q+beta+xi)*B - P*A - Q*C - xi*D)", "physics": true, "states": [], "concepts": [ "concept/coefficients-of-capacity", "quantity/coefficient-of-induction", "quantity/electric-charge", "quantity/electric-potential" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/eq-3c0f77dde6", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-viii", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 112", "location": "ON ELECTROSTATIC CAPACITY", "latex": "c &= (Q+S+\\gamma+\\eta)C-QB-SD-\\eta A", "name": null, "statement": "The charge of conductor gamma is its coefficient of capacity times its potential, minus the induction terms from the adjacent conductors.", "kind": "formula", "symbols": [ { "unit": null, "symbol": "c", "meaning": "charge of conductor gamma (inner coatings of Q and S with connecting wire)" }, { "unit": null, "symbol": "Q", "meaning": "coefficient of induction between gamma and beta" }, { "unit": null, "symbol": "S", "meaning": "coefficient of induction between gamma and delta" }, { "unit": null, "symbol": "gamma", "meaning": "excess of the coefficient of capacity of gamma over its coefficients of induction" }, { "unit": null, "symbol": "eta", "meaning": "small coefficient of induction between gamma and alpha" }, { "unit": null, "symbol": "A", "meaning": "potential of conductor alpha" }, { "unit": null, "symbol": "B", "meaning": "potential of conductor beta" }, { "unit": null, "symbol": "C", "meaning": "potential of conductor gamma" }, { "unit": null, "symbol": "D", "meaning": "potential of conductor delta" } ], "sympy": "Eq(c, (Q+S+gamma+eta)*C - Q*B - S*D - eta*A)", "physics": true, "states": [], "concepts": [ "concept/coefficients-of-capacity", "quantity/coefficient-of-induction", "quantity/electric-charge", "quantity/electric-potential" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/eq-ae8310db6c", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-viii", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 112", "location": "ON ELECTROSTATIC CAPACITY", "latex": "d &= (R+S+\\delta+\\xi)D-RA-SC-\\xi B", "name": null, "statement": "The charge of conductor delta is its coefficient of capacity times its potential, minus the induction terms from the adjacent conductors.", "kind": "formula", "symbols": [ { "unit": null, "symbol": "d", "meaning": "charge of conductor delta (outer coatings of R and S with the earth)" }, { "unit": null, "symbol": "R", "meaning": "coefficient of induction between delta and alpha" }, { "unit": null, "symbol": "S", "meaning": "coefficient of induction between delta and gamma" }, { "unit": null, "symbol": "delta", "meaning": "excess of the coefficient of capacity of delta over its coefficients of induction" }, { "unit": null, "symbol": "xi", "meaning": "small coefficient of induction between delta and beta" }, { "unit": null, "symbol": "A", "meaning": "potential of conductor alpha" }, { "unit": null, "symbol": "B", "meaning": "potential of conductor beta" }, { "unit": null, "symbol": "C", "meaning": "potential of conductor gamma" }, { "unit": null, "symbol": "D", "meaning": "potential of conductor delta" } ], "sympy": "Eq(d, (R+S+delta+xi)*D - R*A - S*C - xi*B)", "physics": true, "states": [], "concepts": [ "concept/coefficients-of-capacity", "quantity/coefficient-of-induction", "quantity/electric-charge", "quantity/electric-potential" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/eq-6248eca347", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-viii", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 112", "location": "ON ELECTROSTATIC CAPACITY", "latex": "a &= (P+R+\\alpha+\\eta)A-\\eta C", "name": null, "statement": "Before the discharge, with beta and delta at zero potential, the charge of alpha depends only on A and C.", "kind": "result", "symbols": [ { "unit": null, "symbol": "a", "meaning": "charge of conductor alpha before the discharge" }, { "unit": null, "symbol": "A", "meaning": "initial potential of conductor alpha" }, { "unit": null, "symbol": "C", "meaning": "initial potential of conductor gamma" }, { "unit": null, "symbol": "eta", "meaning": "small coefficient of induction between alpha and gamma" } ], "sympy": "Eq(a, (P+R+alpha+eta)*A - eta*C)", "physics": true, "states": [], "concepts": [ "concept/coefficients-of-capacity", "quantity/electric-charge", "quantity/electric-potential" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/eq-a653d55727", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-viii", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 112", "location": "ON ELECTROSTATIC CAPACITY", "latex": "b &= \\hphantom{(P+R+\\alpha}-PA-QC", "name": null, "statement": "Before the discharge, with beta at zero potential, the charge of beta depends on A and C through the induction terms.", "kind": "result", "symbols": [ { "unit": null, "symbol": "b", "meaning": "charge of conductor beta before the discharge" }, { "unit": null, "symbol": "P", "meaning": "coefficient of induction between beta and alpha" }, { "unit": null, "symbol": "Q", "meaning": "coefficient of induction between beta and gamma" }, { "unit": null, "symbol": "A", "meaning": "initial potential of conductor alpha" }, { "unit": null, "symbol": "C", "meaning": "initial potential of conductor gamma" } ], "sympy": "Eq(b, -P*A - Q*C)", "physics": true, "states": [], "concepts": [ "quantity/coefficient-of-induction", "quantity/electric-charge", "quantity/electric-potential" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/eq-204ec80eaa", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-viii", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 112", "location": "ON ELECTROSTATIC CAPACITY", "latex": "c &= (Q+S+\\gamma+\\eta)C-\\eta A", "name": null, "statement": "Before the discharge, with beta and delta at zero potential, the charge of gamma depends only on C and A.", "kind": "result", "symbols": [ { "unit": null, "symbol": "c", "meaning": "charge of conductor gamma before the discharge" }, { "unit": null, "symbol": "C", "meaning": "initial potential of conductor gamma" }, { "unit": null, "symbol": "A", "meaning": "initial potential of conductor alpha" }, { "unit": null, "symbol": "eta", "meaning": "small coefficient of induction between gamma and alpha" } ], "sympy": "Eq(c, (Q+S+gamma+eta)*C - eta*A)", "physics": true, "states": [], "concepts": [ "concept/coefficients-of-capacity", "quantity/electric-charge", "quantity/electric-potential" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/eq-3a6ae9ec79", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-viii", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 112", "location": "ON ELECTROSTATIC CAPACITY", "latex": "a' + c' = a + c", "name": null, "statement": "The total charge of the connected conductors alpha and gamma is the same after the discharge as before.", "kind": "law", "symbols": [ { "unit": null, "symbol": "a", "meaning": "charge of alpha before the discharge" }, { "unit": null, "symbol": "c", "meaning": "charge of gamma before the discharge" }, { "unit": null, "symbol": "ap", "meaning": "charge of alpha after the discharge (a')" }, { "unit": null, "symbol": "cp", "meaning": "charge of gamma after the discharge (c')" } ], "sympy": "Eq(ap + cp, a + c)", "physics": true, "states": [], "concepts": [ "law/conservation-of-electric-charge", "method/discharging-a-conductor", "quantity/electric-charge" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/eq-57b10d2396", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-viii", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 112", "location": "ON ELECTROSTATIC CAPACITY", "latex": "b' = b", "name": null, "statement": "The charge of conductor beta is unchanged by the discharge between alpha and gamma.", "kind": "law", "symbols": [ { "unit": null, "symbol": "b", "meaning": "charge of beta before the discharge" }, { "unit": null, "symbol": "bp", "meaning": "charge of beta after the discharge (b')" } ], "sympy": "Eq(bp, b)", "physics": true, "states": [], "concepts": [ "law/conservation-of-electric-charge", "quantity/electric-charge" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/eq-3d973a64e0", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-viii", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 112", "location": "ON ELECTROSTATIC CAPACITY", "latex": "A' = C' = y", "name": null, "statement": "After the discharge, alpha and gamma share the common potential y.", "kind": "definition", "symbols": [ { "unit": null, "symbol": "Ap", "meaning": "potential of alpha after the discharge (A')" }, { "unit": null, "symbol": "Cp", "meaning": "potential of gamma after the discharge (C')" }, { "unit": null, "symbol": "y", "meaning": "common potential of alpha and gamma after they are connected" } ], "sympy": "Eq(Ap, Cp)", "physics": true, "states": [], "concepts": [ "method/discharging-a-conductor", "quantity/electric-potential", "theorem/common-potential-after-contact" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/eq-0f829495e9", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-viii", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 112", "location": "ON ELECTROSTATIC CAPACITY", "latex": "a' &= (P+R+\\alpha)y-PB'", "name": null, "statement": "After the discharge, the charge of alpha is expressed through the common potential y and the potential B' of beta.", "kind": "formula", "symbols": [ { "unit": null, "symbol": "ap", "meaning": "charge of alpha after the discharge (a')" }, { "unit": null, "symbol": "y", "meaning": "common potential of alpha and gamma after connection" }, { "unit": null, "symbol": "Bp", "meaning": "potential of beta after the discharge (B')" }, { "unit": null, "symbol": "P", "meaning": "coefficient of induction between beta and alpha" }, { "unit": null, "symbol": "R", "meaning": "coefficient of induction between alpha and delta" }, { "unit": null, "symbol": "alpha", "meaning": "excess of the coefficient of capacity of alpha" } ], "sympy": "Eq(ap, (P+R+alpha)*y - P*Bp)", "physics": true, "states": [], "concepts": [ "concept/coefficients-of-capacity", "quantity/electric-charge", "quantity/electric-potential" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/eq-7c42fa0c4c", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-viii", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 112", "location": "ON ELECTROSTATIC CAPACITY", "latex": "b' &= (P+Q+\\beta+\\xi)B' - (P+Q)y", "name": null, "statement": "After the discharge, the charge of beta is expressed through its potential B' and the common potential y.", "kind": "formula", "symbols": [ { "unit": null, "symbol": "bp", "meaning": "charge of beta after the discharge (b')" }, { "unit": null, "symbol": "Bp", "meaning": "potential of beta after the discharge (B')" }, { "unit": null, "symbol": "y", "meaning": "common potential of alpha and gamma after connection" }, { "unit": null, "symbol": "P", "meaning": "coefficient of induction between beta and alpha" }, { "unit": null, "symbol": "Q", "meaning": "coefficient of induction between beta and gamma" }, { "unit": null, "symbol": "beta", "meaning": "excess of the coefficient of capacity of beta" }, { "unit": null, "symbol": "xi", "meaning": "small coefficient of induction between beta and delta" } ], "sympy": "Eq(bp, (P+Q+beta+xi)*Bp - (P+Q)*y)", "physics": true, "states": [], "concepts": [ "concept/coefficients-of-capacity", "quantity/electric-charge", "quantity/electric-potential" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/eq-3550752c46", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-viii", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 112", "location": "ON ELECTROSTATIC CAPACITY", "latex": "c' &= (Q+S+\\gamma)y-QB'", "name": null, "statement": "After the discharge, the charge of gamma is expressed through the common potential y and the potential B' of beta.", "kind": "formula", "symbols": [ { "unit": null, "symbol": "cp", "meaning": "charge of gamma after the discharge (c')" }, { "unit": null, "symbol": "y", "meaning": "common potential of alpha and gamma after connection" }, { "unit": null, "symbol": "Bp", "meaning": "potential of beta after the discharge (B')" }, { "unit": null, "symbol": "Q", "meaning": "coefficient of induction between gamma and beta" }, { "unit": null, "symbol": "S", "meaning": "coefficient of induction between gamma and delta" }, { "unit": null, "symbol": "gamma", "meaning": "excess of the coefficient of capacity of gamma" } ], "sympy": "Eq(cp, (Q+S+gamma)*y - Q*Bp)", "physics": true, "states": [], "concepts": [ "concept/coefficients-of-capacity", "quantity/electric-charge", "quantity/electric-potential" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/eq-5d880364aa", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-viii", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 113", "location": "ON ELECTROSTATIC CAPACITY", "latex": "(P+R+Q+S+\\alpha+\\gamma)y-(P+Q)B'=(P+R+\\alpha)A+(Q+S+\\gamma)C", "name": null, "statement": "Charge conservation for alpha and gamma after the connection relates the common potential y, the potential B', and the initial potentials A and C.", "kind": "law", "symbols": [ { "unit": null, "symbol": "y", "meaning": "common potential of alpha and gamma after connection" }, { "unit": null, "symbol": "Bp", "meaning": "potential of beta after the discharge (B')" }, { "unit": null, "symbol": "A", "meaning": "initial potential of conductor alpha" }, { "unit": null, "symbol": "C", "meaning": "initial potential of conductor gamma" }, { "unit": null, "symbol": "P", "meaning": "coefficient of induction between beta and alpha" }, { "unit": null, "symbol": "Q", "meaning": "coefficient of induction between beta and gamma" }, { "unit": null, "symbol": "R", "meaning": "coefficient of induction between alpha and delta" }, { "unit": null, "symbol": "S", "meaning": "coefficient of induction between gamma and delta" }, { "unit": null, "symbol": "alpha", "meaning": "excess of the coefficient of capacity of alpha" }, { "unit": null, "symbol": "gamma", "meaning": "excess of the coefficient of capacity of gamma" } ], "sympy": "Eq((P+R+Q+S+alpha+gamma)*y - (P+Q)*Bp, (P+R+alpha)*A + (Q+S+gamma)*C)", "physics": true, "states": [], "concepts": [ "law/conservation-of-electric-charge", "quantity/electric-charge", "quantity/electric-potential" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/eq-212db2de95", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-viii", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 113", "location": "ON ELECTROSTATIC CAPACITY", "latex": "(P+Q+\\beta+\\xi)B'-(P+Q)y = -PA-QC", "name": null, "statement": "The unchanged charge of beta, after the discharge, relates its potential B' and the common potential y to the initial potentials A and C.", "kind": "law", "symbols": [ { "unit": null, "symbol": "Bp", "meaning": "potential of beta after the discharge (B')" }, { "unit": null, "symbol": "y", "meaning": "common potential of alpha and gamma after connection" }, { "unit": null, "symbol": "A", "meaning": "initial potential of conductor alpha" }, { "unit": null, "symbol": "C", "meaning": "initial potential of conductor gamma" }, { "unit": null, "symbol": "P", "meaning": "coefficient of induction between beta and alpha" }, { "unit": null, "symbol": "Q", "meaning": "coefficient of induction between beta and gamma" }, { "unit": null, "symbol": "beta", "meaning": "excess of the coefficient of capacity of beta" }, { "unit": null, "symbol": "xi", "meaning": "small coefficient of induction between beta and delta" } ], "sympy": "Eq((P+Q+beta+xi)*Bp - (P+Q)*y, -P*A - Q*C)", "physics": true, "states": [], "concepts": [ "law/conservation-of-electric-charge", "quantity/electric-charge", "quantity/electric-potential" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/eq-e329b44aa5", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-viii", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 113", "location": "ON ELECTROSTATIC CAPACITY", "latex": "B'\\{(P+Q)(R+S)+(P+Q)(\\alpha+\\beta+\\gamma+\\xi)+(R+S+\\alpha+\\gamma)(\\beta+\\xi)\\}=\\{Q(R+\\alpha)-P(S+\\gamma)\\}(A-C)", "name": null, "statement": "Eliminating y gives the potential B' of beta after the discharge in terms of the initial potentials A and C and the coefficients.", "kind": "result", "symbols": [ { "unit": null, "symbol": "Bp", "meaning": "potential of beta after the discharge (B')" }, { "unit": null, "symbol": "A", "meaning": "initial potential of conductor alpha" }, { "unit": null, "symbol": "C", "meaning": "initial potential of conductor gamma" }, { "unit": null, "symbol": "P", "meaning": "coefficient of induction between beta and alpha" }, { "unit": null, "symbol": "Q", "meaning": "coefficient of induction between beta and gamma" }, { "unit": null, "symbol": "R", "meaning": "coefficient of induction between alpha and delta" }, { "unit": null, "symbol": "S", "meaning": "coefficient of induction between gamma and delta" }, { "unit": null, "symbol": "alpha", "meaning": "excess of the coefficient of capacity of alpha" }, { "unit": null, "symbol": "beta", "meaning": "excess of the coefficient of capacity of beta" }, { "unit": null, "symbol": "gamma", "meaning": "excess of the coefficient of capacity of gamma" }, { "unit": null, "symbol": "xi", "meaning": "small coefficient of induction between beta and delta" } ], "sympy": "Eq(Bp*((P+Q)*(R+S) + (P+Q)*(alpha+beta+gamma+xi) + (R+S+alpha+gamma)*(beta+xi)), (Q*(R+alpha) - P*(S+gamma))*(A-C))", "physics": true, "states": [], "concepts": [ "concept/coefficients-of-capacity", "instrument/wheatstone-s-bridge", "quantity/electric-potential" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/eq-d6fdc1e1db", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-viii", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 113", "location": "ON ELECTROSTATIC CAPACITY", "latex": "B' = 0", "name": null, "statement": "If the electrometer is undisturbed by the discharge, the potential of beta stays zero.", "kind": "result", "symbols": [ { "unit": null, "symbol": "Bp", "meaning": "potential of beta after the discharge (B')" } ], "sympy": "Eq(Bp, 0)", "physics": true, "states": [], "concepts": [ "instrument/electrometer", "instrument/wheatstone-s-bridge", "quantity/electric-potential" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/eq-015e300532", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-viii", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 113", "location": "ON ELECTROSTATIC CAPACITY", "latex": "P : Q :: R + \\alpha : S + \\gamma", "name": null, "statement": "The balance condition: when the electrometer is undisturbed, the capacities of the jars are in the same proportion as the sums of the coefficients on the two arms of the bridge.", "kind": "law", "symbols": [ { "unit": null, "symbol": "P", "meaning": "capacity of jar P (coefficient of induction on the first arm)" }, { "unit": null, "symbol": "Q", "meaning": "capacity of jar Q (coefficient of induction on the second arm)" }, { "unit": null, "symbol": "R", "meaning": "capacity of jar R (coefficient of induction on the other arm)" }, { "unit": null, "symbol": "S", "meaning": "capacity of jar S (coefficient of induction on the other arm)" }, { "unit": null, "symbol": "alpha", "meaning": "excess of the coefficient of capacity of conductor alpha" }, { "unit": null, "symbol": "gamma", "meaning": "excess of the coefficient of capacity of conductor gamma" } ], "sympy": "Eq(P/Q, (R+alpha)/(S+gamma))", "physics": true, "states": [], "concepts": [ "concept/coefficients-of-capacity", "instrument/electrometer", "instrument/wheatstone-s-bridge", "quantity/capacity" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/eq-184170045b", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-ix", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 117", "location": "THE ELECTRIC CURRENT", "latex": "\\text{Electromotive force} = \\text{Current} \\times \\text{Resistance,}", "name": "Ohm's law", "statement": "The electromotive force equals the current multiplied by the resistance, so the ratio of electromotive force to current is the resistance of the conductor.", "kind": "law", "symbols": [], "sympy": null, "physics": true, "states": [ "law/ohm-s-law" ], "concepts": [ "concept/electric-current", "quantity/electromotive-force", "quantity/resistance" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/eq-ee127e023d", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-ix", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 118", "location": "THE ELECTRIC CURRENT", "latex": "\\text{Heat generated measured in dynamical units}\\\\ = \\text{Square of Current} \\times \\text{Resistance} \\times \\text{Time.}", "name": "Joule's law", "statement": "The heat generated in a conductor carrying a steady current, measured in dynamical units, equals the square of the current times the resistance times the time.", "kind": "law", "symbols": [], "sympy": null, "physics": true, "states": [ "law/joule-s-law" ], "concepts": [ "concept/electric-current", "concept/thermal-effect-of-an-electric-current", "quantity/resistance", "quantity/time" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/eq-5d62bfe413", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-ix", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 144", "location": "THE ELECTRIC CURRENT", "latex": "E_{12} = CR_{12}\\text{,} \\quad E_{23} = CR_{23}\\text{,} \\quad E_{34} = CR_{34}\\text{.}", "name": null, "statement": "Ohm's law applied to each conductor of a series, all carrying the same current C.", "kind": "law", "symbols": [ { "unit": null, "symbol": "E_{12}", "meaning": "electromotive force along the first conductor, from A_1 to A_2" }, { "unit": null, "symbol": "E_{23}", "meaning": "electromotive force along the second conductor, from A_2 to A_3" }, { "unit": null, "symbol": "E_{34}", "meaning": "electromotive force along the third conductor, from A_3 to A_4" }, { "unit": null, "symbol": "C", "meaning": "the same current flowing through each conductor in series" }, { "unit": null, "symbol": "R_{12}", "meaning": "resistance of the first conductor" }, { "unit": null, "symbol": "R_{23}", "meaning": "resistance of the second conductor" }, { "unit": null, "symbol": "R_{34}", "meaning": "resistance of the third conductor" } ], "sympy": null, "physics": true, "states": [], "concepts": [ "concept/electric-current", "law/ohm-s-law", "quantity/electromotive-force", "theorem/resistance-of-conductors-in-series" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/eq-f5613a74fa", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-ix", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 143", "location": "THE ELECTRIC CURRENT", "latex": "E = CR \\text{.}", "name": "Ohm's law", "statement": "For the series system as a whole, the resultant electromotive force equals the current times the resultant resistance.", "kind": "law", "symbols": [ { "unit": null, "symbol": "E", "meaning": "resultant electromotive force of the series system" }, { "unit": null, "symbol": "C", "meaning": "current through the series system" }, { "unit": null, "symbol": "R", "meaning": "resultant resistance of the series system" } ], "sympy": "Eq(E, C*R)", "physics": true, "states": [ "law/ohm-s-law" ], "concepts": [ "concept/electric-current", "concept/linear-conductor", "quantity/electromotive-force", "quantity/resistance", "theorem/resistance-of-conductors-in-series" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/eq-c46a61d7b6", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-ix", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 144", "location": "THE ELECTRIC CURRENT", "latex": "E &= E_{12} + E_{23} + E_{34}\\text{,}", "name": null, "statement": "The resultant electromotive force of a series of conductors is the sum of the separate electromotive forces.", "kind": "result", "symbols": [ { "unit": null, "symbol": "E", "meaning": "resultant electromotive force of the series" }, { "unit": null, "symbol": "E_{12}", "meaning": "electromotive force along the first conductor" }, { "unit": null, "symbol": "E_{23}", "meaning": "electromotive force along the second conductor" }, { "unit": null, "symbol": "E_{34}", "meaning": "electromotive force along the third conductor" } ], "sympy": "Eq(E, E_12 + E_23 + E_34)", "physics": true, "states": [], "concepts": [ "quantity/electromotive-force", "theorem/resistance-of-conductors-in-series" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/eq-b81327c95f", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-ix", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 144", "location": "THE ELECTRIC CURRENT", "latex": "R = R_{12} + R_{23} + R_{34}", "name": null, "statement": "The resistance of a series of conductors is the sum of the resistances of the conductors taken separately.", "kind": "result", "symbols": [ { "unit": null, "symbol": "R", "meaning": "resultant resistance of the series" }, { "unit": null, "symbol": "R_{12}", "meaning": "resistance of the first conductor" }, { "unit": null, "symbol": "R_{23}", "meaning": "resistance of the second conductor" }, { "unit": null, "symbol": "R_{34}", "meaning": "resistance of the third conductor" } ], "sympy": "Eq(R, R_12 + R_23 + R_34)", "physics": true, "states": [], "concepts": [ "quantity/resistance", "theorem/resistance-of-conductors-in-series" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/eq-c7bc23ee13", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-ix", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 144", "location": "THE ELECTRIC CURRENT", "latex": "a - b = R_1C\\text{,} \\quad b - c = R_2C\\text{,}\\quad \\text{and} \\quad a - c = RC\\text{,}", "name": null, "statement": "The potential differences across the part from A to B, the part from B to C, and the whole from A to C are each the current times the corresponding resistance.", "kind": "formula", "symbols": [ { "unit": null, "symbol": "a", "meaning": "potential at point A" }, { "unit": null, "symbol": "b", "meaning": "potential at point B" }, { "unit": null, "symbol": "c", "meaning": "potential at point C" }, { "unit": null, "symbol": "R_1", "meaning": "resistance of the part from A to B" }, { "unit": null, "symbol": "R_2", "meaning": "resistance of the part from B to C" }, { "unit": null, "symbol": "R", "meaning": "resistance of the whole from A to C" }, { "unit": null, "symbol": "C", "meaning": "current in the series" } ], "sympy": null, "physics": true, "states": [], "concepts": [ "law/ohm-s-law", "quantity/electric-potential", "theorem/resistance-of-conductors-in-series" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/eq-6eeb6b1493", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-ix", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 144", "location": "THE ELECTRIC CURRENT", "latex": "b = \\frac {R_2a + R_1c}{R}\\text{,}", "name": null, "statement": "The potential at an intermediate point B of a series is a weighted combination of the potentials at its ends, weighted by the resistances.", "kind": "result", "symbols": [ { "unit": null, "symbol": "b", "meaning": "potential at point B between A and C" }, { "unit": null, "symbol": "a", "meaning": "potential at electrode A" }, { "unit": null, "symbol": "c", "meaning": "potential at electrode C" }, { "unit": null, "symbol": "R_1", "meaning": "resistance of the part from A to B" }, { "unit": null, "symbol": "R_2", "meaning": "resistance of the part from B to C" }, { "unit": null, "symbol": "R", "meaning": "resistance of the whole from A to C" } ], "sympy": "Eq(b, (R_2*a + R_1*c)/R)", "physics": true, "states": [], "concepts": [ "quantity/electric-potential", "theorem/resistance-of-conductors-in-series" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/eq-acfc970331", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-ix", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 145", "location": "THE ELECTRIC CURRENT", "latex": "E = C_1R_1 = C_2R_2 = C_3R_3 = CR\\text{,}", "name": null, "statement": "The same potential difference E between the common ends holds across each branch of a multiple arc, and across the multiple conductor as a whole.", "kind": "law", "symbols": [ { "unit": null, "symbol": "E", "meaning": "common potential difference between the two common points A and Z" }, { "unit": null, "symbol": "C_1", "meaning": "current in the first branch" }, { "unit": null, "symbol": "C_2", "meaning": "current in the second branch" }, { "unit": null, "symbol": "C_3", "meaning": "current in the third branch" }, { "unit": null, "symbol": "R_1", "meaning": "resistance of the first branch" }, { "unit": null, "symbol": "R_2", "meaning": "resistance of the second branch" }, { "unit": null, "symbol": "R_3", "meaning": "resistance of the third branch" }, { "unit": null, "symbol": "C", "meaning": "total current" }, { "unit": null, "symbol": "R", "meaning": "resistance of the multiple conductor" } ], "sympy": null, "physics": true, "states": [], "concepts": [ "law/ohm-s-law", "quantity/electromotive-force", "theorem/resistance-of-conductors-in-multiple-arc" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/eq-9e6da24093", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-ix", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 145", "location": "THE ELECTRIC CURRENT", "latex": "\\frac{1}{R} = \\frac{1}{R_1} + \\frac{1}{R_2} + \\frac{1}{R_3}\\text{.}", "name": null, "statement": "The reciprocal of the resistance of conductors in multiple arc is the sum of the reciprocals of the component resistances; equivalently, conductivities add.", "kind": "result", "symbols": [ { "unit": null, "symbol": "R", "meaning": "resistance of the multiple conductor" }, { "unit": null, "symbol": "R_1", "meaning": "resistance of the first branch" }, { "unit": null, "symbol": "R_2", "meaning": "resistance of the second branch" }, { "unit": null, "symbol": "R_3", "meaning": "resistance of the third branch" } ], "sympy": "Eq(1/R, 1/R_1 + 1/R_2 + 1/R_3)", "physics": true, "states": [], "concepts": [ "quantity/conductivity", "quantity/resistance", "theorem/resistance-of-conductors-in-multiple-arc" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/eq-0cdb2617b2", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-ix", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 145", "location": "THE ELECTRIC CURRENT", "latex": "C = C_1 + C_2 + C_3\\text{,}", "name": null, "statement": "The total current into a multiple arc is the sum of the currents in its branches.", "kind": "law", "symbols": [ { "unit": null, "symbol": "C", "meaning": "total current" }, { "unit": null, "symbol": "C_1", "meaning": "current in the first branch" }, { "unit": null, "symbol": "C_2", "meaning": "current in the second branch" }, { "unit": null, "symbol": "C_3", "meaning": "current in the third branch" } ], "sympy": "Eq(C, C_1 + C_2 + C_3)", "physics": true, "states": [], "concepts": [ "concept/electric-current", "theorem/resistance-of-conductors-in-multiple-arc" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/eq-4961708d1f", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-ix", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 145", "location": "THE ELECTRIC CURRENT", "latex": "C_1 = C\\frac{R}{R_1}\\text{,}", "name": null, "statement": "The current in any branch of a multiple conductor is the total current times the resistance of the whole divided by the resistance of that branch.", "kind": "result", "symbols": [ { "unit": null, "symbol": "C_1", "meaning": "current in a branch of the multiple conductor" }, { "unit": null, "symbol": "C", "meaning": "total current" }, { "unit": null, "symbol": "R", "meaning": "resistance of the multiple conductor" }, { "unit": null, "symbol": "R_1", "meaning": "resistance of that branch" } ], "sympy": "Eq(C_1, C*R/R_1)", "physics": true, "states": [], "concepts": [ "concept/electric-current", "theorem/resistance-of-conductors-in-multiple-arc" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/eq-baf87a6468", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-ix", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 146", "location": "THE ELECTRIC CURRENT", "latex": "R = \\frac{l\\rho}{s}\\text{.}", "name": null, "statement": "The resistance of a uniform conductor is its specific resistance times its length divided by its cross-section.", "kind": "result", "symbols": [ { "unit": null, "symbol": "R", "meaning": "resistance of the conductor of length l and uniform section s" }, { "unit": null, "symbol": "l", "meaning": "length of the conductor" }, { "unit": null, "symbol": "rho", "meaning": "specific resistance of the material for unit of volume" }, { "unit": null, "symbol": "s", "meaning": "uniform section (cross-sectional area) of the conductor" } ], "sympy": "Eq(R, l*rho/s)", "physics": true, "states": [], "concepts": [ "quantity/resistance", "quantity/specific-resistance", "theorem/resistance-of-conductors-in-multiple-arc", "theorem/resistance-of-conductors-in-series" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/eq-176abcfeb8", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-ix", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 146", "location": "THE ELECTRIC CURRENT", "latex": "R = \\frac{l^2r}{m}\\text{.}", "name": null, "statement": "The resistance of a wire is the square of its length times its specific resistance per unit of weight, divided by its mass.", "kind": "result", "symbols": [ { "unit": null, "symbol": "R", "meaning": "resistance of the wire" }, { "unit": null, "symbol": "l", "meaning": "length of the wire" }, { "unit": null, "symbol": "r", "meaning": "resistance of a wire of unit length and unit mass (specific resistance per unit of weight)" }, { "unit": null, "symbol": "m", "meaning": "mass of the wire" } ], "sympy": "Eq(R, l**2*r/m)", "physics": true, "states": [], "concepts": [ "quantity/resistance", "quantity/specific-resistance" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/eq-2015cf8f94", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-x", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 147", "location": "PHENOMENA OF AN ELECTRIC CURRENT WHICH FLOWS THROUGH HETEROGENEOUS MEDIA", "latex": "a - b - x = 0", "name": null, "statement": "Around a circuit of three metals A, B, C at one temperature, the total electromotive force is zero, so the force from B to A equals a minus b.", "kind": "law", "symbols": [ { "unit": null, "symbol": "a", "meaning": "electromotive force from C to A (potential of A with respect to C)" }, { "unit": null, "symbol": "b", "meaning": "electromotive force from C to B (potential of B with respect to C)" }, { "unit": null, "symbol": "x", "meaning": "electromotive force from B to A" } ], "sympy": "Eq(a - b - x, 0)", "physics": true, "states": [], "concepts": [ "concept/electric-circuit", "concept/thermo-electric-effect", "quantity/electric-potential", "quantity/electromotive-force" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/eq-b30a5840ec", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-x", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 154", "location": "PHENOMENA OF AN ELECTRIC CURRENT WHICH FLOWS THROUGH HETEROGENEOUS MEDIA", "latex": "(\\phi_2 - \\phi_1)(t - t_1)", "name": null, "statement": "The Peltier effect at a junction is of this form, the product of the increase in thermo-electric power and the temperature measured from a reference point below any observed temperature.", "kind": "formula", "symbols": [ { "unit": null, "symbol": "\\phi_1", "meaning": "thermo-electric power of the metal the current flows from" }, { "unit": null, "symbol": "\\phi_2", "meaning": "thermo-electric power of the metal the current flows to" }, { "unit": null, "symbol": "t", "meaning": "thermometer reading (temperature)" }, { "unit": null, "symbol": "t_1", "meaning": "constant temperature below all observed temperatures, found only by experiment" } ], "sympy": null, "physics": true, "states": [], "concepts": [ "concept/peltier-effect", "concept/thermal-effect-of-an-electric-current", "quantity/thermo-electric-power" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/eq-ebea931462", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-x", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 154", "location": "PHENOMENA OF AN ELECTRIC CURRENT WHICH FLOWS THROUGH HETEROGENEOUS MEDIA", "latex": "(\\phi_2 - \\phi_1) \\theta", "name": null, "statement": "By the second law of thermodynamics the heat absorbed at the junction may be written as the difference of thermo-electric powers times the absolute temperature.", "kind": "result", "symbols": [ { "unit": null, "symbol": "\\phi_1", "meaning": "thermo-electric power of the first metal" }, { "unit": null, "symbol": "\\phi_2", "meaning": "thermo-electric power of the second metal" }, { "unit": null, "symbol": "\\theta", "meaning": "temperature reckoned from absolute zero of the thermodynamic scale" } ], "sympy": null, "physics": true, "states": [], "concepts": [ "concept/peltier-effect", "law/second-law-of-thermodynamics", "quantity/absolute-temperature", "quantity/thermo-electric-power" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/eq-afcdb7bf0e", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-x", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 156", "location": "PHENOMENA OF AN ELECTRIC CURRENT WHICH FLOWS THROUGH HETEROGENEOUS MEDIA", "latex": "\\xp\\dfrac{H}{\\theta}", "name": null, "statement": "A body receiving a quantity of heat H at temperature theta increases its entropy by H divided by theta.", "kind": "definition", "symbols": [ { "unit": null, "symbol": "H", "meaning": "quantity of heat received or emitted by the body" }, { "unit": null, "symbol": "\\theta", "meaning": "temperature reckoned on the thermodynamic scale" } ], "sympy": null, "physics": true, "states": [], "concepts": [ "concept/heat", "quantity/absolute-temperature", "quantity/entropy" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/eq-6da1b77794", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-x", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 160", "location": "PHENOMENA OF AN ELECTRIC CURRENT WHICH FLOWS THROUGH HETEROGENEOUS MEDIA", "latex": "QE = H\\text{,}", "name": null, "statement": "The work done by a current Q carried across a region against an electromotive force E equals the heat H generated in that region, by conservation of energy.", "kind": "law", "symbols": [ { "unit": null, "symbol": "Q", "meaning": "total quantity of electricity transmitted from A to B" }, { "unit": null, "symbol": "E", "meaning": "electromotive force acting against the current from B to A" }, { "unit": null, "symbol": "H", "meaning": "quantity of heat generated in the portion AB, in dynamical measure" } ], "sympy": "Eq(Q*E, H)", "physics": true, "states": [], "concepts": [ "concept/electric-current", "concept/thermal-effect-of-an-electric-current", "concept/work", "law/conservation-of-energy", "quantity/electromotive-force" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/eq-08c1929c0e", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-x", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 164", "location": "PHENOMENA OF AN ELECTRIC CURRENT WHICH FLOWS THROUGH HETEROGENEOUS MEDIA", "latex": "(b-a)\\theta+B-A\\text{.}", "name": null, "statement": "The total electromotive force round the circuit ABC is the thermo-electric term (b minus a) times theta plus the electrolytic terms B minus A.", "kind": "result", "symbols": [ { "unit": null, "symbol": "a", "meaning": "thermo-electric power of metal A at temperature theta" }, { "unit": null, "symbol": "b", "meaning": "thermo-electric power of metal B at temperature theta" }, { "unit": null, "symbol": "\\theta", "meaning": "temperature of the junction" }, { "unit": null, "symbol": "A", "meaning": "electromotive force from metal A to electrolyte C" }, { "unit": null, "symbol": "B", "meaning": "electromotive force from metal B to electrolyte C" } ], "sympy": null, "physics": true, "states": [], "concepts": [ "concept/electric-circuit", "concept/electrolysis", "quantity/electromotive-force", "quantity/thermo-electric-power" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/eq-869922689f", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-x", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 163", "location": "PHENOMENA OF AN ELECTRIC CURRENT WHICH FLOWS THROUGH HETEROGENEOUS MEDIA", "latex": "JH &= Jh + E", "name": null, "statement": "The work equation at the anode: the chemical heat JH equals the heat generated there, Jh, plus the work E done in driving the current.", "kind": "law", "symbols": [ { "unit": null, "symbol": "J", "meaning": "Joule's equivalent, the mechanical equivalent of heat" }, { "unit": null, "symbol": "H", "meaning": "total heat from the chemical action at the anode per unit of electricity" }, { "unit": null, "symbol": "h", "meaning": "heat generated at the anode per unit of electricity transmitted" }, { "unit": null, "symbol": "E", "meaning": "electromotive force acting from the zinc to the electrolyte" } ], "sympy": "Eq(J*H, J*h + E)", "physics": true, "states": [], "concepts": [ "concept/electrolysis", "concept/energy", "concept/work", "law/conservation-of-energy", "quantity/electromotive-force" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/eq-a78274590c", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-x", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 163", "location": "PHENOMENA OF AN ELECTRIC CURRENT WHICH FLOWS THROUGH HETEROGENEOUS MEDIA", "latex": "E &= J(H - h)\\text{.}", "name": null, "statement": "The electromotive force from metal to electrolyte is the mechanical equivalent of heat times the difference between total chemical heat and heat generated at the electrode.", "kind": "result", "symbols": [ { "unit": null, "symbol": "E", "meaning": "electromotive force acting from the zinc to the electrolyte" }, { "unit": null, "symbol": "J", "meaning": "Joule's equivalent, the mechanical equivalent of heat" }, { "unit": null, "symbol": "H", "meaning": "total heat from the chemical action at the anode per unit of electricity" }, { "unit": null, "symbol": "h", "meaning": "heat generated at the anode per unit of electricity transmitted" } ], "sympy": "Eq(E, J*(H - h))", "physics": true, "states": [], "concepts": [ "concept/electrolysis", "concept/electrolyte", "law/conservation-of-energy", "quantity/electromotive-force" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/eq-36d75498d7", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-xi", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 185", "location": "METHODS OF MAINTAINING AN ELECTRIC CURRENT", "latex": "EE_1 aa_1\\sin\\theta\\left\\{\\frac{1}{r^3}-\\frac{1}{b^3}\\right\\}=M(\\theta-\\phi)", "name": null, "statement": "With the spherical case large compared with the spheres' distances, the total moment from the charges and their image balances the torsional moment of the fibre.", "kind": "result", "symbols": [ { "unit": null, "symbol": "E", "meaning": "charge on the suspended sphere" }, { "unit": null, "symbol": "E_1", "meaning": "charge on the fixed sphere" }, { "unit": null, "symbol": "a", "meaning": "radius of the torsion arm" }, { "unit": null, "symbol": "a_1", "meaning": "distance of the fixed sphere from the centre of the case" }, { "unit": null, "symbol": "b", "meaning": "radius of the spherical case" }, { "unit": null, "symbol": "r", "meaning": "distance between the two small spheres" }, { "unit": null, "symbol": "M", "meaning": "moment of torsion of the fibre" }, { "unit": "radian", "symbol": "theta", "meaning": "angle between the positions of the two spheres" }, { "unit": "radian", "symbol": "phi", "meaning": "equilibrium angle of the torsion arm with both spheres discharged" } ], "sympy": "Eq(E*E1*a*a1*sin(theta)*(1/r**3 - 1/b**3), M*(theta - phi))", "physics": true, "states": [], "concepts": [ "concept/electrical-image", "concept/instrument-coulomb-s-torsion-balance", "quantity/electromotive-force" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/eq-2ce575ef51", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-xi", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 177", "location": "METHODS OF MAINTAINING AN ELECTRIC CURRENT", "latex": "z = -QU", "name": null, "statement": "The charge on the carrier, while it is in contact with earth so that its potential is zero, is minus Q times the potential of the inductor it was in.", "kind": "result", "symbols": [ { "unit": null, "symbol": "z", "meaning": "charge on the carrier" }, { "unit": null, "symbol": "Q", "meaning": "coefficient of induction between the inductor and the carrier (taken positive)" }, { "unit": null, "symbol": "U", "meaning": "potential of the inductor A and the receiver D" } ], "sympy": "Eq(z, -Q*U)", "physics": true, "states": [], "concepts": [ "concept/electric-induction", "concept/instrument-carrier", "concept/quantity-coefficient-of-induction", "quantity/electric-charge", "quantity/electric-potential" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/eq-81bcfd42ef", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-xi", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 181", "location": "METHODS OF MAINTAINING AN ELECTRIC CURRENT", "latex": "(C'+c')U+C'V'=aV", "name": null, "statement": "Charge on the carrier while it is within the inductor C, with its capacity C' + c' and coefficient of induction -C'.", "kind": "law", "symbols": [ { "unit": null, "symbol": "C'", "meaning": "coefficient of induction between the carrier and the regenerator C' (with sign taken as in the text)" }, { "unit": null, "symbol": "c'", "meaning": "extra capacity of the carrier within the inductor C" }, { "unit": null, "symbol": "U", "meaning": "potential of the carrier" }, { "unit": null, "symbol": "V'", "meaning": "potential of the second Leyden jar" }, { "unit": null, "symbol": "a", "meaning": "small extra capacity of the carrier within the receiver A" }, { "unit": null, "symbol": "V", "meaning": "potential of the first Leyden jar" } ], "sympy": "Eq((Cp + cp)*U + Cp*Vp, a*V)", "physics": true, "states": [], "concepts": [ "concept/instrument-carrier", "concept/instrument-regenerator", "quantity/capacity", "quantity/electric-charge", "quantity/electric-potential" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/eq-5ca8187e13", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-xi", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 181", "location": "METHODS OF MAINTAINING AN ELECTRIC CURRENT", "latex": "C'V'=aV", "name": null, "statement": "Condition under which the carrier's potential is reduced to zero at the regenerator, so it can touch the earth spring without a spark.", "kind": "rule", "symbols": [ { "unit": null, "symbol": "C'", "meaning": "coefficient of induction of the regenerator C'" }, { "unit": null, "symbol": "V'", "meaning": "potential of the second Leyden jar" }, { "unit": null, "symbol": "a", "meaning": "small extra capacity of the carrier within the receiver A" }, { "unit": null, "symbol": "V", "meaning": "potential of the first Leyden jar" } ], "sympy": "Eq(Cp*Vp, a*V)", "physics": true, "states": [], "concepts": [ "concept/instrument-carrier", "concept/instrument-regenerator", "quantity/electric-potential" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/eq-6f9f640298", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-xi", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 182", "location": "METHODS OF MAINTAINING AN ELECTRIC CURRENT", "latex": "C'V'=aV\\text{,\\quad and\\quad}CV = a'V'", "name": null, "statement": "The two conditions the regenerators must satisfy so that the carrier can touch the earth spring without a spark at either regenerator.", "kind": "rule", "symbols": [ { "unit": null, "symbol": "C'", "meaning": "coefficient of induction of the regenerator C'" }, { "unit": null, "symbol": "C", "meaning": "coefficient of induction of the regenerator C" }, { "unit": null, "symbol": "V", "meaning": "potential of the first Leyden jar" }, { "unit": null, "symbol": "V'", "meaning": "potential of the second Leyden jar" }, { "unit": null, "symbol": "a", "meaning": "small extra capacity of the carrier within the receiver A" }, { "unit": null, "symbol": "a'", "meaning": "small extra capacity of the carrier within the receiver A'" } ], "sympy": "And(Eq(Cp*Vp, a*V), Eq(C*V, ap*Vp))", "physics": true, "states": [], "concepts": [ "concept/instrument-leyden-jar", "concept/instrument-regenerator", "quantity/electric-potential" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/eq-e0a7f361ef", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-xi", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 183", "location": "METHODS OF MAINTAINING AN ELECTRIC CURRENT", "latex": "Fa \\cos \\tfrac{1}{2} \\theta = M ( \\theta - \\phi )", "name": null, "statement": "Balance of the torsion arm: the moment of the electric force about the axis of torsion equals the torsional moment of the fibre acting through the twist theta minus phi.", "kind": "law", "symbols": [ { "unit": null, "symbol": "F", "meaning": "force between the two spheres" }, { "unit": null, "symbol": "a", "meaning": "radius of the torsion arm" }, { "unit": "radian", "symbol": "theta", "meaning": "angle between the torsion arm and the radius through the fixed sphere when the spheres are charged" }, { "unit": "radian", "symbol": "phi", "meaning": "angle of equilibrium of the torsion arm when both spheres are discharged" }, { "unit": null, "symbol": "M", "meaning": "moment of the torsional elasticity of the fibre" } ], "sympy": "Eq(F*a*cos(theta/2), M*(theta - phi))", "physics": true, "states": [], "concepts": [ "concept/instrument-coulomb-s-torsion-balance", "concept/law-coulomb-s-law", "instrument/coulomb-s-torsion-balance", "quantity/electromotive-force" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/eq-4f3e2e80ef", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-xi", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 183", "location": "METHODS OF MAINTAINING AN ELECTRIC CURRENT", "latex": "M = \\frac{4\\pi^2I}{T^2}", "name": null, "statement": "The moment of torsion equals four pi squared times the moment of inertia divided by the square of the period of a double vibration.", "kind": "formula", "symbols": [ { "unit": null, "symbol": "M", "meaning": "moment of torsion of the fibre" }, { "unit": null, "symbol": "I", "meaning": "moment of inertia of the torsion arm" }, { "unit": "second", "symbol": "T", "meaning": "time of a double vibration of the arm under torsional elasticity" } ], "sympy": "Eq(M, 4*pi**2*I/T**2)", "physics": true, "states": [], "concepts": [ "concept/instrument-coulomb-s-torsion-balance", "concept/moment-of-inertia", "concept/periodic-function" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/eq-cf7bf3881e", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-xi", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 184", "location": "METHODS OF MAINTAINING AN ELECTRIC CURRENT", "latex": "=\\frac{EE_1}{r^2}", "name": null, "statement": "The repulsion between the two small spheres, neglecting induction on them, equals the product of their charges divided by the square of the distance between them.", "kind": "law", "symbols": [ { "unit": null, "symbol": "E", "meaning": "charge on the suspended sphere" }, { "unit": null, "symbol": "E_1", "meaning": "charge on the fixed sphere" }, { "unit": null, "symbol": "r", "meaning": "distance between the two small spheres" } ], "sympy": "Eq(F_r, E*E1/r**2)", "physics": true, "states": [], "concepts": [ "concept/law-coulomb-s-law", "law/electrostatic-attraction-and-repulsion", "quantity/electric-charge" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/eq-60e4a6043b", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-xi", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 184", "location": "METHODS OF MAINTAINING AN ELECTRIC CURRENT", "latex": "\\frac{EE_1aa_1 \\sin \\theta}{ r^3}", "name": null, "statement": "The moment of that repulsion about the vertical axis through the centre of motion.", "kind": "formula", "symbols": [ { "unit": null, "symbol": "E", "meaning": "charge on the suspended sphere" }, { "unit": null, "symbol": "E_1", "meaning": "charge on the fixed sphere" }, { "unit": null, "symbol": "a", "meaning": "radius of the torsion arm" }, { "unit": null, "symbol": "a_1", "meaning": "distance of the fixed sphere from the centre of the case" }, { "unit": "radian", "symbol": "theta", "meaning": "angle between the positions of the two spheres" }, { "unit": null, "symbol": "r", "meaning": "distance between the two small spheres" } ], "sympy": "Eq(N_r, E*E1*a*a1*sin(theta)/r**3)", "physics": true, "states": [], "concepts": [ "concept/instrument-coulomb-s-torsion-balance", "concept/law-coulomb-s-law", "quantity/electromotive-force" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/eq-c6b8c744d0", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-xi", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 184", "location": "METHODS OF MAINTAINING AN ELECTRIC CURRENT", "latex": "= EE_1 \\frac{aa_1\\sin\\theta}{b^3 \\left\\{ 1 - 2 \\dfrac{aa_1}{b^2} \\cos \\theta + \\dfrac{a^2{a_1}^2}{b^4} \\right\\}^\\frac{3}{2}}", "name": null, "statement": "The moment about the axis of the attraction between the suspended sphere and the image of the fixed sphere in the spherical case, which is the second line of the displayed calculation.", "kind": "result", "symbols": [ { "unit": null, "symbol": "E", "meaning": "charge on the suspended sphere" }, { "unit": null, "symbol": "E_1", "meaning": "charge on the fixed sphere" }, { "unit": null, "symbol": "b", "meaning": "radius of the spherical case" }, { "unit": null, "symbol": "a", "meaning": "radius of the torsion arm" }, { "unit": null, "symbol": "a_1", "meaning": "distance of the fixed sphere from the centre of the case" }, { "unit": "radian", "symbol": "theta", "meaning": "angle between the positions of the two spheres" } ], "sympy": "Eq(N_i, E*E1*a*a1*sin(theta)/(b**3*(1 - 2*a*a1*cos(theta)/b**2 + a**2*a1**2/b**4)**Rational(3,2)))", "physics": true, "states": [], "concepts": [ "concept/electrical-image", "concept/law-coulomb-s-law", "quantity/electromotive-force" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/eq-6d6590beb4", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-xi", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 188", "location": "METHODS OF MAINTAINING AN ELECTRIC CURRENT", "latex": "Wg &= \\frac{V^2A}{8 \\pi D^2}", "name": null, "statement": "The weight W times gravity g balances the attraction between the disks, which is V squared times the area A over 8 pi D squared.", "kind": "law", "symbols": [ { "unit": null, "symbol": "W", "meaning": "numerical value of the weight placed on the suspended disk" }, { "unit": null, "symbol": "g", "meaning": "force of gravity" }, { "unit": "volt", "symbol": "V", "meaning": "difference of potentials between the disks" }, { "unit": null, "symbol": "A", "meaning": "area of the suspended disk (in this article, not the inductor A of Art. 198)" }, { "unit": null, "symbol": "D", "meaning": "distance between the disks" } ], "sympy": "Eq(W*g, V**2*A/(8*pi*D**2))", "physics": true, "states": [], "concepts": [ "concept/instrument-attracted-disk-electrometer", "quantity/electric-potential", "quantity/electromotive-force" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/eq-3b301c71ac", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-xi", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 188", "location": "METHODS OF MAINTAINING AN ELECTRIC CURRENT", "latex": "V = D\\, \\sqrt{\\frac{8 \\pi gW}{A}}", "name": null, "statement": "The potential difference between the disks in terms of the distance, the weight and the disk area.", "kind": "formula", "symbols": [ { "unit": "volt", "symbol": "V", "meaning": "difference of potentials between the disks" }, { "unit": null, "symbol": "D", "meaning": "distance between the disks" }, { "unit": null, "symbol": "g", "meaning": "force of gravity" }, { "unit": null, "symbol": "W", "meaning": "numerical value of the weight" }, { "unit": null, "symbol": "A", "meaning": "area of the suspended disk" } ], "sympy": "Eq(V, D*sqrt(8*pi*g*W/A))", "physics": true, "states": [], "concepts": [ "concept/instrument-attracted-disk-electrometer", "quantity/electric-potential" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/eq-0c4daf0b3a", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-xi", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 188", "location": "METHODS OF MAINTAINING AN ELECTRIC CURRENT", "latex": "A = \\tfrac{1}{2} \\pi (R^2 + R'^2)", "name": null, "statement": "For a circular suspended disk of radius R in a guard-ring aperture of radius R', the effective area is half pi times the sum of the squares of the two radii.", "kind": "formula", "symbols": [ { "unit": null, "symbol": "A", "meaning": "effective area of the suspended disk" }, { "unit": null, "symbol": "R", "meaning": "radius of the suspended disk" }, { "unit": null, "symbol": "R'", "meaning": "radius of the aperture of the guard-ring" } ], "sympy": "Eq(A, pi*(R**2 + Rp**2)/2)", "physics": false, "states": [], "concepts": [ "concept/guard-ring", "concept/instrument-attracted-disk-electrometer", "quantity/area" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/eq-e65f588127", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-xi", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 188", "location": "METHODS OF MAINTAINING AN ELECTRIC CURRENT", "latex": "V = 4D\\, \\sqrt{ \\frac{gW}{R^2 + R'^2}}", "name": null, "statement": "The potential difference between the disks for a circular suspended disk inside a guard-ring.", "kind": "formula", "symbols": [ { "unit": "volt", "symbol": "V", "meaning": "difference of potentials between the disks" }, { "unit": null, "symbol": "D", "meaning": "distance between the disks" }, { "unit": null, "symbol": "g", "meaning": "force of gravity" }, { "unit": null, "symbol": "W", "meaning": "numerical value of the weight" }, { "unit": null, "symbol": "R", "meaning": "radius of the suspended disk" }, { "unit": null, "symbol": "R'", "meaning": "radius of the aperture of the guard-ring" } ], "sympy": "Eq(V, 4*D*sqrt(g*W/(R**2 + Rp**2)))", "physics": true, "states": [], "concepts": [ "concept/guard-ring", "concept/instrument-attracted-disk-electrometer", "quantity/electric-potential" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/eq-288eb0bcb0", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-xi", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 188", "location": "METHODS OF MAINTAINING AN ELECTRIC CURRENT", "latex": "\\alpha = B \\frac{log_e2}{\\pi}", "name": null, "statement": "Defines alpha, a correction length, as the breadth B of the annular gap times log base e of 2 over pi.", "kind": "definition", "symbols": [ { "unit": null, "symbol": "alpha", "meaning": "correction length for the guard-ring field" }, { "unit": null, "symbol": "B", "meaning": "breadth of the annular gap between the disk and the ring, equal to R' - R" } ], "sympy": "Eq(alpha, B*log(2)/pi)", "physics": false, "states": [], "concepts": [ "concept/guard-ring", "concept/instrument-attracted-disk-electrometer", "concept/natural-logarithm" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/eq-adea4180e5", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-xi", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 188", "location": "METHODS OF MAINTAINING AN ELECTRIC CURRENT", "latex": "\\alpha = 0.220635 (R' - R)", "name": null, "statement": "Numerical value of the correction length alpha for the guard-ring gap, to the stated precision.", "kind": "approximation", "symbols": [ { "unit": null, "symbol": "alpha", "meaning": "correction length for the guard-ring field" }, { "unit": null, "symbol": "R", "meaning": "radius of the suspended disk" }, { "unit": null, "symbol": "R'", "meaning": "radius of the aperture of the guard-ring" } ], "sympy": "Eq(alpha, 0.220635*(Rp - R))", "physics": false, "states": [], "concepts": [ "concept/approximation", "concept/guard-ring" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/eq-7481ab0506", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-xi", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 188", "location": "METHODS OF MAINTAINING AN ELECTRIC CURRENT", "latex": "Q &= V \\left\\{ \\frac{R^2 + R'^2}{8D} - \\frac{R'^2 - R^2}{8D} \\frac{\\alpha}{D + \\alpha} \\right\\}", "name": null, "statement": "The charge on the suspended disk when the guard-ring surface lies in the same plane as the disk, for potential difference V between the disks.", "kind": "formula", "symbols": [ { "unit": null, "symbol": "Q", "meaning": "electric charge on the suspended disk" }, { "unit": "volt", "symbol": "V", "meaning": "potential difference between the fixed and suspended disks" }, { "unit": null, "symbol": "R", "meaning": "radius of the suspended disk" }, { "unit": null, "symbol": "R'", "meaning": "radius of the aperture of the guard-ring" }, { "unit": null, "symbol": "D", "meaning": "distance between the fixed and suspended disks" }, { "unit": null, "symbol": "alpha", "meaning": "correction length for the guard-ring field" } ], "sympy": "Eq(Q, V*((R**2 + Rp**2)/(8*D) - (Rp**2 - R**2)/(8*D)*alpha/(D + alpha)))", "physics": true, "states": [], "concepts": [ "concept/guard-ring", "concept/instrument-attracted-disk-electrometer", "quantity/electric-charge" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/eq-0310e4cdfb", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-xi", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 188", "location": "METHODS OF MAINTAINING AN ELECTRIC CURRENT", "latex": "Q = V \\left\\{ \\frac{R^2 + R'^2}{8D} - \\frac{R'^2 - R^2}{8D} \\frac{\\alpha}{D + \\alpha} + \\frac{R+R'}{D}(D'-D) \\log_e \\frac{4 \\pi(R+R')}{D'-D} \\right\\}", "name": null, "statement": "The charge on the suspended disk when the guard-ring surface is not exactly in the plane of the disk, with an extra term for the height difference z.", "kind": "formula", "symbols": [ { "unit": null, "symbol": "Q", "meaning": "electric charge on the suspended disk" }, { "unit": "volt", "symbol": "V", "meaning": "potential difference between the fixed and suspended disks" }, { "unit": null, "symbol": "R", "meaning": "radius of the suspended disk" }, { "unit": null, "symbol": "R'", "meaning": "radius of the aperture of the guard-ring" }, { "unit": null, "symbol": "D", "meaning": "distance between the fixed and suspended disks" }, { "unit": null, "symbol": "D'", "meaning": "distance between the fixed disk and the guard-ring" }, { "unit": null, "symbol": "alpha", "meaning": "correction length for the guard-ring field" } ], "sympy": "Eq(Q, V*((R**2 + Rp**2)/(8*D) - (Rp**2 - R**2)/(8*D)*alpha/(D + alpha) + (R + Rp)/D*(Dp - D)*log(4*pi*(R + Rp)/(Dp - D))))", "physics": true, "states": [], "concepts": [ "concept/guard-ring", "concept/instrument-attracted-disk-electrometer", "concept/natural-logarithm", "quantity/electric-charge" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/eq-9b0a6c7b47", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-xi", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 188", "location": "METHODS OF MAINTAINING AN ELECTRIC CURRENT", "latex": "A = \\tfrac{1}{2} \\pi \\left\\{R^2 + R'^2 -(R'^2 - R^2) \\frac{\\alpha}{D + \\alpha} + 8 (R + R')(D' - D) \\log_e \\frac{4 \\pi (R + R')}{D' - D} \\right\\}", "name": null, "statement": "The corrected effective area of the suspended disk, to be used in the attraction formula when the guard-ring is not exactly in the plane of the disk.", "kind": "formula", "symbols": [ { "unit": null, "symbol": "A", "meaning": "corrected effective area of the suspended disk" }, { "unit": null, "symbol": "R", "meaning": "radius of the suspended disk" }, { "unit": null, "symbol": "R'", "meaning": "radius of the aperture of the guard-ring" }, { "unit": null, "symbol": "D", "meaning": "distance between the fixed and suspended disks" }, { "unit": null, "symbol": "D'", "meaning": "distance between the fixed disk and the guard-ring" }, { "unit": null, "symbol": "alpha", "meaning": "correction length for the guard-ring field" } ], "sympy": "Eq(A, pi/2*(R**2 + Rp**2 - (Rp**2 - R**2)*alpha/(D + alpha) + 8*(R + Rp)*(Dp - D)*log(4*pi*(R + Rp)/(Dp - D))))", "physics": false, "states": [], "concepts": [ "concept/guard-ring", "concept/instrument-attracted-disk-electrometer", "concept/natural-logarithm", "quantity/area" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/eq-16a09aaac1", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-xi", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 189", "location": "METHODS OF MAINTAINING AN ELECTRIC CURRENT", "latex": "V - V' = (D - D') \\sqrt{ \\frac{8 \\pi g W}{A}}", "name": null, "statement": "The difference of two potentials is found from the difference of the two disk distances at which the suspended disk is in its sighted position, so that the uncertain zero of D is avoided.", "kind": "formula", "symbols": [ { "unit": "volt", "symbol": "V", "meaning": "first potential difference between the disks" }, { "unit": "volt", "symbol": "V'", "meaning": "second potential difference between the disks" }, { "unit": null, "symbol": "D", "meaning": "distance between the disks for the first potential" }, { "unit": null, "symbol": "D'", "meaning": "distance between the disks for the second potential" }, { "unit": null, "symbol": "g", "meaning": "force of gravity" }, { "unit": null, "symbol": "W", "meaning": "numerical value of the weight" }, { "unit": null, "symbol": "A", "meaning": "area of the suspended disk" } ], "sympy": "Eq(V - Vp, (D - Dp)*sqrt(8*pi*g*W/A))", "physics": true, "states": [], "concepts": [ "concept/difference", "concept/instrument-attracted-disk-electrometer", "quantity/electric-potential" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/eq-1af5b2593f", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-xi", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 191", "location": "METHODS OF MAINTAINING AN ELECTRIC CURRENT", "latex": "\\overline{V} = \\frac{KV + K'V'}{K + K'}\\text{.}", "name": null, "statement": "After a conductor of capacity K at potential V is put in contact with an electrometer part of capacity K' at potential V', their common potential is the capacity-weighted mean (KV + K'V')/(K + K').", "kind": "result", "symbols": [ { "unit": null, "symbol": "\\overline{V}", "meaning": "common potential after making contact" }, { "unit": null, "symbol": "K", "meaning": "capacity of the conductor" }, { "unit": null, "symbol": "V", "meaning": "potential of the conductor before making contact" }, { "unit": null, "symbol": "K'", "meaning": "capacity of the part of the electrometer put in contact with the conductor" }, { "unit": null, "symbol": "V'", "meaning": "potential of the electrometer part before making contact" } ], "sympy": "Eq(Vbar, (K*V + Kp*Vp)/(K + Kp))", "physics": true, "states": [], "concepts": [ "concept/theorem-common-potential-after-contact", "instrument/electrometer", "quantity/capacity", "quantity/electric-potential" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/eq-324b4c6e29", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-xi", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 191", "location": "METHODS OF MAINTAINING AN ELECTRIC CURRENT", "latex": "V = \\overline{V} + \\frac{K'}{K} (\\overline{V} - V')\\text{.}", "name": null, "statement": "The original potential of the conductor can be recovered from the measured common potential, the capacities, and the electrometer's original potential.", "kind": "result", "symbols": [ { "unit": null, "symbol": "V", "meaning": "original potential of the conductor before contact" }, { "unit": null, "symbol": "\\overline{V}", "meaning": "common potential after making contact" }, { "unit": null, "symbol": "K", "meaning": "capacity of the conductor" }, { "unit": null, "symbol": "K'", "meaning": "capacity of the part of the electrometer put in contact with the conductor" }, { "unit": null, "symbol": "V'", "meaning": "potential of the electrometer part before making contact" } ], "sympy": "Eq(V, Vbar + (Kp/K)*(Vbar - Vp))", "physics": true, "states": [], "concepts": [ "instrument/electrometer", "quantity/capacity", "quantity/electric-potential" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/eq-8fbe8426c8", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-xi", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 192", "location": "METHODS OF MAINTAINING AN ELECTRIC CURRENT", "latex": "Q = V'a\\text{,}", "name": null, "statement": "The charge on the sphere equals its radius times the potential the electrometer reads for the sphere after it is earthed, insulated and carried into the room.", "kind": "formula", "symbols": [ { "unit": null, "symbol": "Q", "meaning": "total charge on the sphere" }, { "unit": null, "symbol": "V'", "meaning": "potential of the sphere as measured by an electrometer in the earthed room" }, { "unit": null, "symbol": "a", "meaning": "radius of the sphere" } ], "sympy": "Eq(Q, Vp*a)", "physics": true, "states": [], "concepts": [ "instrument/electrometer", "quantity/electric-charge", "quantity/electric-potential", "quantity/radius" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/eq-f01c164397", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-xi", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 192", "location": "METHODS OF MAINTAINING AN ELECTRIC CURRENT", "latex": "V + V' = 0\\text{,}", "name": null, "statement": "The potential of the air at the sphere's centre is equal in magnitude and opposite in sign to the sphere's measured potential, so the two sum to zero.", "kind": "result", "symbols": [ { "unit": null, "symbol": "V", "meaning": "potential of the air at the given point where the sphere's centre was placed" }, { "unit": null, "symbol": "V'", "meaning": "potential of the sphere as measured by an electrometer after earthing, insulating and carrying into the room" } ], "sympy": "Eq(V + Vp, 0)", "physics": true, "states": [], "concepts": [ "concept/electrical-earth", "instrument/electrometer", "quantity/electric-potential" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/eq-378c477504", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-xi", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 192", "location": "METHODS OF MAINTAINING AN ELECTRIC CURRENT", "latex": "-Va = Q", "name": null, "statement": "The charge on the sphere, placed with its centre at a point of potential V, equals minus the potential times the sphere's radius.", "kind": "result", "symbols": [ { "unit": null, "symbol": "V", "meaning": "potential at the given point in the air" }, { "unit": null, "symbol": "a", "meaning": "radius of the sphere" }, { "unit": null, "symbol": "Q", "meaning": "charge of the sphere" } ], "sympy": "Eq(-V*a, Q)", "physics": true, "states": [], "concepts": [ "quantity/electric-charge", "quantity/electric-potential", "quantity/radius" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/eq-d876ae1035", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-xi", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 178", "location": "METHODS OF MAINTAINING AN ELECTRIC CURRENT", "latex": "p^2 = \\xp\\dfrac {Q}{B}", "name": null, "statement": "Defines p as the square root of the coefficient of induction Q divided by the capacity B.", "kind": "definition", "symbols": [ { "unit": null, "symbol": "p", "meaning": "auxiliary constant defined from Q and B" }, { "unit": null, "symbol": "Q", "meaning": "coefficient of induction between the carrier and an inductor (taken positive)" }, { "unit": null, "symbol": "B", "meaning": "capacity of receiver B and inductor C" } ], "sympy": "Eq(p**2, Q/B)", "physics": false, "states": [], "concepts": [ "concept/constant", "concept/instrument-carrier", "quantity/capacity", "quantity/coefficient-of-induction" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/eq-7034dcff4a", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-xi", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 178", "location": "METHODS OF MAINTAINING AN ELECTRIC CURRENT", "latex": "q^2 = \\xp\\dfrac {Q'}{A}", "name": null, "statement": "Defines q as the square root of the coefficient of induction Q' divided by the capacity A.", "kind": "definition", "symbols": [ { "unit": null, "symbol": "q", "meaning": "auxiliary constant defined from Q' and A" }, { "unit": null, "symbol": "Q'", "meaning": "coefficient of induction between the carrier and C" }, { "unit": null, "symbol": "A", "meaning": "capacity of inductor A and receiver D" } ], "sympy": "Eq(q**2, Qp/A)", "physics": false, "states": [], "concepts": [ "concept/constant", "concept/instrument-carrier", "quantity/capacity", "quantity/coefficient-of-induction" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/eq-36acb3d76e", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-xi", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 178", "location": "METHODS OF MAINTAINING AN ELECTRIC CURRENT", "latex": "U_{n + 1} &= U_n - \\frac {Q'}{A} V_n", "name": null, "statement": "The potential of inductor A after n+1 half revolutions equals its potential after n half revolutions minus Q'/A times the potential of C.", "kind": "rule", "symbols": [ { "unit": null, "symbol": "U_n", "meaning": "potential of inductor A after n half revolutions" }, { "unit": null, "symbol": "V_n", "meaning": "potential of inductor C after n half revolutions" }, { "unit": null, "symbol": "Q'", "meaning": "coefficient of induction between the carrier and C" }, { "unit": null, "symbol": "A", "meaning": "capacity of inductor A and receiver D" } ], "sympy": null, "physics": true, "states": [], "concepts": [ "concept/cycle-of-operations", "concept/inductor", "concept/instrument-carrier", "concept/instrument-leyden-jar", "instrument/carrier", "quantity/coefficient-of-induction", "quantity/electric-potential" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/eq-fdf305cdc2", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-xi", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 178", "location": "METHODS OF MAINTAINING AN ELECTRIC CURRENT", "latex": "V_{n + 1} &= V_n - \\frac {Q}{B} U_n", "name": null, "statement": "The potential of inductor C after n+1 half revolutions equals its previous potential minus Q/B times the potential of A.", "kind": "rule", "symbols": [ { "unit": null, "symbol": "V_n", "meaning": "potential of inductor C after n half revolutions" }, { "unit": null, "symbol": "U_n", "meaning": "potential of inductor A after n half revolutions" }, { "unit": null, "symbol": "Q", "meaning": "coefficient of induction between the carrier and A (taken positive)" }, { "unit": null, "symbol": "B", "meaning": "capacity of receiver B and inductor C" } ], "sympy": null, "physics": true, "states": [], "concepts": [ "concept/cycle-of-operations", "concept/inductor", "concept/instrument-carrier", "concept/instrument-leyden-jar", "instrument/carrier", "quantity/capacity", "quantity/coefficient-of-induction", "quantity/electric-potential" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/eq-99cd191488", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-xi", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 178", "location": "METHODS OF MAINTAINING AN ELECTRIC CURRENT", "latex": "pU_{n + 1} + qV_{n + 1} &= \\left(pU_n + qV_n \\right) \\left( 1 - pq \\right) = \\left(pU_0 + qV_0 \\right) \\left( 1 - pq \\right)^{n + 1}", "name": null, "statement": "The combination pU + qV is multiplied by (1 - pq) at each half revolution, so after n+1 half revolutions it equals its initial value times (1 - pq) to the power n+1.", "kind": "result", "symbols": [ { "unit": null, "symbol": "p", "meaning": "auxiliary constant, p^2 = Q/B" }, { "unit": null, "symbol": "q", "meaning": "auxiliary constant, q^2 = Q'/A" }, { "unit": null, "symbol": "U_n", "meaning": "potential of inductor A after n half revolutions" }, { "unit": null, "symbol": "V_n", "meaning": "potential of inductor C after n half revolutions" }, { "unit": null, "symbol": "U_0", "meaning": "initial potential of inductor A" }, { "unit": null, "symbol": "V_0", "meaning": "initial potential of inductor C" } ], "sympy": null, "physics": true, "states": [], "concepts": [ "concept/cycle-of-operations", "concept/geometrical-progression", "concept/instrument-carrier", "quantity/electric-potential" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/eq-f923256305", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-xi", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 178", "location": "METHODS OF MAINTAINING AN ELECTRIC CURRENT", "latex": "pU_{n + 1} - qV_{n + 1} &= \\left( pU_n - qV_n \\right) \\left( 1 + pq \\right) = \\left( pU_0 - qV_0 \\right) \\left( 1 + pq \\right)^{n + 1}", "name": null, "statement": "The combination pU - qV is multiplied by (1 + pq) at each half revolution, so it grows geometrically with the number of revolutions.", "kind": "result", "symbols": [ { "unit": null, "symbol": "p", "meaning": "auxiliary constant, p^2 = Q/B" }, { "unit": null, "symbol": "q", "meaning": "auxiliary constant, q^2 = Q'/A" }, { "unit": null, "symbol": "U_0", "meaning": "initial potential of inductor A" }, { "unit": null, "symbol": "V_0", "meaning": "initial potential of inductor C" } ], "sympy": null, "physics": true, "states": [], "concepts": [ "concept/cycle-of-operations", "concept/geometrical-progression", "concept/instrument-carrier", "quantity/electric-potential" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/eq-43b029a35d", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-xi", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 178", "location": "METHODS OF MAINTAINING AN ELECTRIC CURRENT", "latex": "U_n &= U_0 \\left\\{ ( 1 - pq )^n + ( 1 + pq )^n \\right\\} + \\frac{q}{p} V_0 \\left\\{ ( 1 - pq )^n - ( 1 + pq )^n \\right\\}", "name": null, "statement": "Closed form for the potential of inductor A after n half revolutions, in terms of the initial potentials.", "kind": "result", "symbols": [ { "unit": null, "symbol": "U_n", "meaning": "potential of inductor A after n half revolutions" }, { "unit": null, "symbol": "U_0", "meaning": "initial potential of inductor A" }, { "unit": null, "symbol": "V_0", "meaning": "initial potential of inductor C" }, { "unit": null, "symbol": "p", "meaning": "auxiliary constant, p^2 = Q/B" }, { "unit": null, "symbol": "q", "meaning": "auxiliary constant, q^2 = Q'/A" }, { "unit": null, "symbol": "n", "meaning": "number of half revolutions" } ], "sympy": null, "physics": true, "states": [], "concepts": [ "concept/cycle-of-operations", "concept/geometrical-progression", "concept/instrument-carrier", "concept/power", "quantity/electric-potential" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/eq-25ff1430f1", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-xi", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 178", "location": "METHODS OF MAINTAINING AN ELECTRIC CURRENT", "latex": "V_n &= \\frac{p}{q} U_0 \\left\\{ ( 1 - pq )^n - ( 1 + pq )^n \\right\\} + V_0 \\left\\{ ( 1 - pq )^n + ( 1 + pq )^n \\right\\}", "name": null, "statement": "Closed form for the potential of inductor C after n half revolutions, in terms of the initial potentials.", "kind": "result", "symbols": [ { "unit": null, "symbol": "V_n", "meaning": "potential of inductor C after n half revolutions" }, { "unit": null, "symbol": "U_0", "meaning": "initial potential of inductor A" }, { "unit": null, "symbol": "V_0", "meaning": "initial potential of inductor C" }, { "unit": null, "symbol": "p", "meaning": "auxiliary constant, p^2 = Q/B" }, { "unit": null, "symbol": "q", "meaning": "auxiliary constant, q^2 = Q'/A" }, { "unit": null, "symbol": "n", "meaning": "number of half revolutions" } ], "sympy": null, "physics": true, "states": [], "concepts": [ "concept/cycle-of-operations", "concept/geometrical-progression", "concept/instrument-carrier", "concept/power", "quantity/electric-potential" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/eq-66eb24d4a1", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-xi", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 181", "location": "METHODS OF MAINTAINING AN ELECTRIC CURRENT", "latex": "C'V'=aV\\text{,}", "name": null, "statement": "Condition that the carrier, leaving the regenerator C, is brought to zero potential so it can touch the earth spring without a spark.", "kind": "rule", "symbols": [ { "unit": null, "symbol": "C'", "meaning": "coefficient of induction between the carrier and regenerator C (magnitude)" }, { "unit": null, "symbol": "V'", "meaning": "potential of the second Leyden jar (negative inductors A', B', C')" }, { "unit": null, "symbol": "a", "meaning": "charge-producing coefficient of the small receiver spring connection to A, with a aV the charge carried away" }, { "unit": null, "symbol": "V", "meaning": "potential of the first Leyden jar (inductors A, B, C)" } ], "sympy": "Eq(Cp*Vp, a*V)", "physics": true, "states": [], "concepts": [ "concept/electrical-earth", "instrument/carrier", "instrument/regenerator", "quantity/electric-charge", "quantity/electric-potential" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/eq-cdbc851e26", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-xi", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 181", "location": "METHODS OF MAINTAINING AN ELECTRIC CURRENT", "latex": "(C'+c')U+C'V'=aV\\text{.}", "name": null, "statement": "The charge on the carrier when it is in regenerator C equals aV, where U is the carrier's potential.", "kind": "result", "symbols": [ { "unit": null, "symbol": "C'", "meaning": "coefficient of induction between the carrier and regenerator C (magnitude)" }, { "unit": null, "symbol": "c'", "meaning": "extra capacity of the carrier in that position" }, { "unit": null, "symbol": "U", "meaning": "potential of the carrier" }, { "unit": null, "symbol": "V'", "meaning": "potential of the second Leyden jar" }, { "unit": null, "symbol": "a", "meaning": "small capacity of the carrier when in receiver A" }, { "unit": null, "symbol": "V", "meaning": "potential of the first Leyden jar" } ], "sympy": "Eq((Cp + cp)*U + Cp*Vp, a*V)", "physics": true, "states": [], "concepts": [ "instrument/regenerator", "quantity/capacity", "quantity/electric-charge", "quantity/electric-potential" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/eq-1ff057ea96", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-xi", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 182", "location": "METHODS OF MAINTAINING AN ELECTRIC CURRENT", "latex": "-\\frac{A'V'+BV}{A'+a'}\\text{,}", "name": null, "statement": "The potential the carrier would have at the middle of receiver A' if it kept its charge, found from the charges and capacities involved.", "kind": "formula", "symbols": [ { "unit": null, "symbol": "A'", "meaning": "capacity of the negative receiver A'" }, { "unit": null, "symbol": "V'", "meaning": "potential of the second Leyden jar" }, { "unit": null, "symbol": "B", "meaning": "coefficient of induction between the carrier and inductor B" }, { "unit": null, "symbol": "V", "meaning": "potential of the first Leyden jar" }, { "unit": null, "symbol": "a'", "meaning": "extra capacity of the carrier in receiver A'" } ], "sympy": null, "physics": true, "states": [], "concepts": [ "quantity/capacity", "quantity/electric-charge", "quantity/electric-potential" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/eq-d8e2fdaef0", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-xi", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 182", "location": "METHODS OF MAINTAINING AN ELECTRIC CURRENT", "latex": "C'V'=aV\\text{,\\quad and\\quad}CV = a'V'\\text{.}", "name": null, "statement": "The two conditions that the regenerators must satisfy so that the carrier leaves each receiver at zero potential without sparking.", "kind": "rule", "symbols": [ { "unit": null, "symbol": "C'", "meaning": "coefficient of induction between the carrier and regenerator C (magnitude)" }, { "unit": null, "symbol": "C", "meaning": "coefficient of induction between the carrier and inductor C" }, { "unit": null, "symbol": "a", "meaning": "small extra capacity of the carrier in receiver A" }, { "unit": null, "symbol": "a'", "meaning": "small extra capacity of the carrier in receiver A'" }, { "unit": null, "symbol": "V", "meaning": "potential of the first Leyden jar" }, { "unit": null, "symbol": "V'", "meaning": "potential of the second Leyden jar" } ], "sympy": null, "physics": true, "states": [], "concepts": [ "instrument/regenerator", "quantity/capacity", "quantity/coefficient-of-induction", "quantity/electric-potential" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/eq-15304f59ef", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-xi", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 183", "location": "METHODS OF MAINTAINING AN ELECTRIC CURRENT", "latex": "Fa \\cos \\tfrac{1}{2} \\theta = M ( \\theta - \\phi )\\text{.}", "name": null, "statement": "The electric force between the spheres, times the lever arm, balances the torsional moment of the fibre, which is proportional to the twist angle theta minus phi.", "kind": "law", "symbols": [ { "unit": null, "symbol": "F", "meaning": "force between the two spheres" }, { "unit": null, "symbol": "a", "meaning": "radius of the torsion-arm" }, { "unit": "degree", "symbol": "theta", "meaning": "angle between the torsion-arm and the radius through the fixed sphere" }, { "unit": null, "symbol": "M", "meaning": "moment of the torsional elasticity of the fibre" }, { "unit": "degree", "symbol": "phi", "meaning": "equilibrium angle of the torsion-arm after discharge" } ], "sympy": "Eq(F*a*cos(theta/2), M*(theta - phi))", "physics": true, "states": [], "concepts": [ "concept/equation", "concept/torque", "instrument/coulomb-s-torsion-balance", "quantity/electromotive-force", "quantity/force" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/eq-b91787a4c5", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-xi", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 183", "location": "METHODS OF MAINTAINING AN ELECTRIC CURRENT", "latex": "M = \\frac{4\\pi^2I}{T^2}\\text{.}", "name": null, "statement": "The moment of torsion equals four pi squared times the moment of inertia of the arm divided by the square of the period of its double vibration.", "kind": "formula", "symbols": [ { "unit": null, "symbol": "M", "meaning": "moment of the torsional elasticity of the fibre" }, { "unit": null, "symbol": "I", "meaning": "moment of inertia of the torsion-arm" }, { "unit": "second", "symbol": "T", "meaning": "time of a double vibration of the arm under torsional elasticity" } ], "sympy": "Eq(M, 4*pi**2*I/T**2)", "physics": true, "states": [], "concepts": [ "concept/constant", "concept/moment-of-inertia", "instrument/coulomb-s-torsion-balance", "quantity/time" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/eq-f29f90f57e", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-xi", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 185", "location": "METHODS OF MAINTAINING AN ELECTRIC CURRENT", "latex": "EE_1 aa_1\\sin\\theta\\left\\{\\frac{1}{r^3}-\\frac{1}{b^3}\\right\\}=M(\\theta-\\phi)\\text{.}", "name": null, "statement": "With the spherical case included, the total moment tending to turn the torsion-arm equals the torsional moment M times the twist angle theta minus phi.", "kind": "result", "symbols": [ { "unit": null, "symbol": "E", "meaning": "charge on the suspended sphere" }, { "unit": null, "symbol": "E_1", "meaning": "charge on the fixed sphere" }, { "unit": null, "symbol": "a", "meaning": "radius of the torsion-arm" }, { "unit": null, "symbol": "a_1", "meaning": "distance of the fixed sphere from the centre of the case" }, { "unit": "degree", "symbol": "theta", "meaning": "angle between the positions of the two spheres" }, { "unit": null, "symbol": "r", "meaning": "distance between the two small spheres" }, { "unit": null, "symbol": "b", "meaning": "radius of the spherical case" }, { "unit": null, "symbol": "M", "meaning": "moment of the torsional elasticity of the fibre" }, { "unit": "degree", "symbol": "phi", "meaning": "equilibrium angle of the torsion-arm after discharge" } ], "sympy": "Eq(E*E1*a*a1*sin(theta)*(1/r**3 - 1/b**3), M*(theta - phi))", "physics": true, "states": [], "concepts": [ "concept/electrical-image", "concept/moment-of-inertia", "concept/plane-angle", "instrument/coulomb-s-torsion-balance", "quantity/electric-charge" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/eq-8ff385375c", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-xi", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 188", "location": "METHODS OF MAINTAINING AN ELECTRIC CURRENT", "latex": "V = 4D\\, \\sqrt{ \\frac{gW}{R^2 + R'^2}}.", "name": null, "statement": "For a circular suspended disk inside a guard-ring, the potential difference between the disks equals 4D times the square root of gW over R squared plus R' squared.", "kind": "formula", "symbols": [ { "unit": null, "symbol": "V", "meaning": "difference of the potentials of the disks" }, { "unit": null, "symbol": "D", "meaning": "distance between the disks" }, { "unit": null, "symbol": "g", "meaning": "force of gravity" }, { "unit": null, "symbol": "W", "meaning": "numerical value of the weight balancing the attraction" }, { "unit": null, "symbol": "R", "meaning": "radius of the suspended disk" }, { "unit": null, "symbol": "R'", "meaning": "radius of the aperture of the guard-ring" } ], "sympy": "Eq(V, 4*D*sqrt(g*W/(R**2 + Rp**2)))", "physics": true, "states": [], "concepts": [ "concept/guard-ring", "concept/weight", "instrument/attracted-disk-electrometer", "quantity/area", "quantity/distance", "quantity/electric-potential" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/eq-6904475e4b", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-xi", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 188", "location": "METHODS OF MAINTAINING AN ELECTRIC CURRENT", "latex": "Wg &= \\frac{V^2A}{8 \\pi D^2}\\text{,}", "name": null, "statement": "The attraction between the two disks, of area A at distance D and potential difference V, equals the weight W times gravity g that balances it.", "kind": "law", "symbols": [ { "unit": null, "symbol": "W", "meaning": "numerical value of the weight balancing the attraction" }, { "unit": null, "symbol": "g", "meaning": "force of gravity" }, { "unit": null, "symbol": "V", "meaning": "difference of the potentials of the disks" }, { "unit": null, "symbol": "A", "meaning": "area of the suspended disk" }, { "unit": null, "symbol": "D", "meaning": "distance between the disks" } ], "sympy": "Eq(W*g, V**2*A/(8*pi*D**2))", "physics": true, "states": [], "concepts": [ "concept/weight", "instrument/attracted-disk-electrometer", "quantity/area", "quantity/distance", "quantity/electric-potential", "quantity/electromotive-force", "quantity/force" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/eq-824047d55e", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-xi", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 188", "location": "METHODS OF MAINTAINING AN ELECTRIC CURRENT", "latex": "V &= D\\, \\sqrt{\\frac{8 \\pi gW}{A}}\\text{.}", "name": null, "statement": "The potential difference between the disks equals D times the square root of 8 pi g W over A.", "kind": "formula", "symbols": [ { "unit": null, "symbol": "V", "meaning": "difference of the potentials of the disks" }, { "unit": null, "symbol": "D", "meaning": "distance between the disks" }, { "unit": null, "symbol": "g", "meaning": "force of gravity" }, { "unit": null, "symbol": "W", "meaning": "numerical value of the weight balancing the attraction" }, { "unit": null, "symbol": "A", "meaning": "area of the suspended disk" } ], "sympy": "Eq(V, D*sqrt(8*pi*g*W/A))", "physics": true, "states": [], "concepts": [ "concept/weight", "instrument/attracted-disk-electrometer", "quantity/area", "quantity/distance", "quantity/electric-potential" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/eq-8295cebfea", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-xi", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 189", "location": "METHODS OF MAINTAINING AN ELECTRIC CURRENT", "latex": "V - V' = (D - D') \\sqrt{ \\frac{8 \\pi g W}{A}}\\text{.}", "name": null, "statement": "The difference of two potentials equals the difference of the corresponding disk distances times the same constant factor, so only differences of readings are needed.", "kind": "formula", "symbols": [ { "unit": null, "symbol": "V", "meaning": "a potential difference between the disks" }, { "unit": null, "symbol": "V'", "meaning": "a second potential difference between the disks" }, { "unit": null, "symbol": "D", "meaning": "distance between the disks for V" }, { "unit": null, "symbol": "D'", "meaning": "distance between the disks for V'" }, { "unit": null, "symbol": "g", "meaning": "force of gravity" }, { "unit": null, "symbol": "W", "meaning": "numerical value of the weight balancing the attraction" }, { "unit": null, "symbol": "A", "meaning": "area of the suspended disk" } ], "sympy": "Eq(V - Vp, (D - Dp)*sqrt(8*pi*g*W/A))", "physics": true, "states": [], "concepts": [ "concept/difference", "instrument/attracted-disk-electrometer", "quantity/distance", "quantity/electric-potential" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/eq-9af0520009", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-xi", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 189", "location": "METHODS OF MAINTAINING AN ELECTRIC CURRENT", "latex": "v = (D - D') \\sqrt{ \\frac{8 \\pi gW}{A}}\\text{.}", "name": null, "statement": "The electromotive force v of the battery equals the difference of the micrometer readings times the constant factor sqrt(8 pi g W / A).", "kind": "formula", "symbols": [ { "unit": null, "symbol": "v", "meaning": "electromotive force of the battery" }, { "unit": null, "symbol": "D", "meaning": "micrometer distance with the battery connected" }, { "unit": null, "symbol": "D'", "meaning": "micrometer distance with the suspended disk to earth" }, { "unit": null, "symbol": "g", "meaning": "force of gravity" }, { "unit": null, "symbol": "W", "meaning": "numerical value of the weight balancing the attraction" }, { "unit": null, "symbol": "A", "meaning": "area of the suspended disk" } ], "sympy": "Eq(v, (D - Dp)*sqrt(8*pi*g*W/A))", "physics": true, "states": [], "concepts": [ "concept/small-electromotive-force-measured", "instrument/attracted-disk-electrometer", "quantity/electric-potential", "quantity/electromotive-force" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/eq-6955ac08ac", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-xi", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 188", "location": "METHODS OF MAINTAINING AN ELECTRIC CURRENT", "latex": "Q &= V \\left\\{ \\frac{R^2 + R'^2}{8D} - \\frac{R'^2 - R^2}{8D} \\frac{\\alpha}{D + \\alpha} \\right\\}\\text{,}", "name": null, "statement": "The quantity of electricity on the suspended disk, with the guard-ring present, in terms of the potential difference V and the disk dimensions.", "kind": "result", "symbols": [ { "unit": null, "symbol": "Q", "meaning": "quantity of electricity on the suspended disk" }, { "unit": null, "symbol": "V", "meaning": "difference of potentials between the disks" }, { "unit": null, "symbol": "R", "meaning": "radius of the suspended disk" }, { "unit": null, "symbol": "R'", "meaning": "radius of the aperture in the guard-ring" }, { "unit": null, "symbol": "D", "meaning": "distance between the fixed and suspended disks" }, { "unit": null, "symbol": "alpha", "meaning": "width-dependent correction length, B log_e 2 / pi" } ], "sympy": "Eq(Q, V*((R**2 + Rp**2)/(8*D) - (Rp**2 - R**2)/(8*D)*alpha/(D + alpha)))", "physics": true, "states": [], "concepts": [ "concept/guard-ring", "instrument/attracted-disk-electrometer", "quantity/area", "quantity/electric-charge", "quantity/electric-potential" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/eq-def5e68130", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-xii", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 200", "location": "THE MEASUREMENT OF ELECTRIC RESISTANCE", "latex": "E = IR = I_1( R + r_1 ) = I_2( R + r_2 )", "name": "Ohm's law", "statement": "The battery's electromotive force equals the current times the total circuit resistance, and so it also equals each current times the resistance with the extra resistance added.", "kind": "law", "symbols": [ { "unit": null, "symbol": "E", "meaning": "electromotive force of the battery" }, { "unit": null, "symbol": "I", "meaning": "strength of the current when the battery connexions are closed" }, { "unit": "ohm", "symbol": "R", "meaning": "resistance of the battery and its connexions, including the galvanometer" }, { "unit": null, "symbol": "I_1", "meaning": "current when additional resistance r_1 is introduced" }, { "unit": null, "symbol": "I_2", "meaning": "current when additional resistance r_2 is introduced" }, { "unit": "ohm", "symbol": "r_1", "meaning": "first additional resistance introduced into the circuit" }, { "unit": "ohm", "symbol": "r_2", "meaning": "second additional resistance introduced into the circuit" } ], "sympy": "Eq(E, I*R)", "physics": true, "states": [ "law/ohm-s-law" ], "concepts": [ "concept/battery", "concept/electric-current", "quantity/electromotive-force", "quantity/resistance" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/eq-3d0f752e76", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-xii", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 200", "location": "THE MEASUREMENT OF ELECTRIC RESISTANCE", "latex": "\\frac{r_1}{r_2} = \\frac{(I-I_1)I_2}{(I-I_2)I_1}", "name": "Ohm's formula", "statement": "The ratio of two unknown resistances is found from the ratios of the measured currents, with the battery's own resistance and emf eliminated.", "kind": "formula", "symbols": [ { "unit": "ohm", "symbol": "r_1", "meaning": "first additional resistance" }, { "unit": "ohm", "symbol": "r_2", "meaning": "second additional resistance" }, { "unit": null, "symbol": "I", "meaning": "current with battery connexions closed" }, { "unit": null, "symbol": "I_1", "meaning": "current with resistance r_1 introduced" }, { "unit": null, "symbol": "I_2", "meaning": "current with resistance r_2 introduced" } ], "sympy": "Eq(r_1/r_2, ((I-I_1)*I_2)/((I-I_2)*I_1))", "physics": true, "states": [ "theorem/ohm-s-formula" ], "concepts": [ "concept/comparison-of-resistances", "concept/electric-current", "law/ohm-s-law", "quantity/resistance" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/eq-c58b07ec95", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-xii", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 201", "location": "THE MEASUREMENT OF ELECTRIC RESISTANCE", "latex": "\\delta = mI_1 - nI_2", "name": null, "statement": "The deflexion of the differential galvanometer needle is the difference between the two coil currents, each weighted by its coil constant.", "kind": "formula", "symbols": [ { "unit": null, "symbol": "delta", "meaning": "deflexion of the galvanometer needle" }, { "unit": null, "symbol": "I_1", "meaning": "current through the first galvanometer coil" }, { "unit": null, "symbol": "I_2", "meaning": "current through the second galvanometer coil" }, { "unit": null, "symbol": "m", "meaning": "effect of the first coil per unit current on the needle" }, { "unit": null, "symbol": "n", "meaning": "effect of the second coil per unit current on the needle" } ], "sympy": "Eq(delta, m*I_1 - n*I_2)", "physics": true, "states": [], "concepts": [ "instrument/differential-galvanometer", "instrument/galvanometer", "method/null-method" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/eq-af9963254a", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-xii", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 201", "location": "THE MEASUREMENT OF ELECTRIC RESISTANCE", "latex": "C-D = I_1(A+\\alpha) = I_2(B+\\beta) = E-Ir", "name": null, "statement": "The potential difference between C and D equals the current in each galvanometer branch times that branch's total resistance, and also equals the emf less the drop across the battery's internal resistance.", "kind": "law", "symbols": [ { "unit": "volt", "symbol": "C-D", "meaning": "difference of potentials between points C and D" }, { "unit": null, "symbol": "I_1", "meaning": "current through the first galvanometer coil branch" }, { "unit": null, "symbol": "I_2", "meaning": "current through the second galvanometer coil branch" }, { "unit": "ohm", "symbol": "A", "meaning": "resistance introduced into the first coil" }, { "unit": "ohm", "symbol": "B", "meaning": "resistance introduced into the second coil" }, { "unit": "ohm", "symbol": "alpha", "meaning": "remaining resistance of the first coil and its connexions" }, { "unit": "ohm", "symbol": "beta", "meaning": "remaining resistance of the second coil and its connexions" }, { "unit": null, "symbol": "E", "meaning": "electromotive force of the battery" }, { "unit": null, "symbol": "I", "meaning": "battery current" }, { "unit": "ohm", "symbol": "r", "meaning": "resistance of the battery between C and D" } ], "sympy": "Eq(C - D, I_1*(A + alpha))", "physics": true, "states": [], "concepts": [ "instrument/differential-galvanometer", "law/ohm-s-law", "quantity/electric-potential", "quantity/electromotive-force" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/eq-9b4afbeb40", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-xii", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 201", "location": "THE MEASUREMENT OF ELECTRIC RESISTANCE", "latex": "I_1 + I_2 = I", "name": null, "statement": "The battery current divides between the two galvanometer coils so that the two branch currents add up to the total current.", "kind": "result", "symbols": [ { "unit": null, "symbol": "I_1", "meaning": "current through the first galvanometer coil" }, { "unit": null, "symbol": "I_2", "meaning": "current through the second galvanometer coil" }, { "unit": null, "symbol": "I", "meaning": "battery current" } ], "sympy": "Eq(I_1 + I_2, I)", "physics": true, "states": [], "concepts": [ "concept/electric-current", "instrument/differential-galvanometer", "law/kirchhoff-s-laws" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/eq-c59a6c1945", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-xii", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 201", "location": "THE MEASUREMENT OF ELECTRIC RESISTANCE", "latex": "I_1 = E\\,\\frac {B + \\beta}{D}", "name": null, "statement": "The current through the first coil equals the emf times the second branch's total resistance divided by the common denominator D.", "kind": "result", "symbols": [ { "unit": null, "symbol": "I_1", "meaning": "current through the first galvanometer coil" }, { "unit": null, "symbol": "E", "meaning": "electromotive force of the battery" }, { "unit": "ohm", "symbol": "B", "meaning": "resistance introduced into the second coil" }, { "unit": "ohm", "symbol": "beta", "meaning": "remaining resistance of the second coil and its connexions" }, { "unit": null, "symbol": "D", "meaning": "common denominator of the branch-current expressions" } ], "sympy": "Eq(I_1, E*(B + beta)/D)", "physics": true, "states": [], "concepts": [ "concept/electric-current", "instrument/differential-galvanometer", "quantity/electromotive-force" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/eq-cec2a5607e", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-xii", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 201", "location": "THE MEASUREMENT OF ELECTRIC RESISTANCE", "latex": "D = (A + \\alpha)(B + \\beta) + r(A + \\alpha + B + \\beta)", "name": null, "statement": "D is the common denominator for the branch currents, built from the two coil branch resistances and the battery resistance.", "kind": "definition", "symbols": [ { "unit": "ohm squared", "symbol": "D", "meaning": "common denominator for the currents in the galvanometer branches" }, { "unit": "ohm", "symbol": "A", "meaning": "resistance introduced into the first coil" }, { "unit": "ohm", "symbol": "B", "meaning": "resistance introduced into the second coil" }, { "unit": "ohm", "symbol": "alpha", "meaning": "remaining resistance of the first coil and its connexions" }, { "unit": "ohm", "symbol": "beta", "meaning": "remaining resistance of the second coil and its connexions" }, { "unit": "ohm", "symbol": "r", "meaning": "resistance of the battery between C and D" } ], "sympy": "Eq(D, (A + alpha)*(B + beta) + r*(A + alpha + B + beta))", "physics": true, "states": [], "concepts": [ "concept/conjugate-conductors", "instrument/differential-galvanometer", "quantity/resistance" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/eq-253b85f181", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-xii", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 201", "location": "THE MEASUREMENT OF ELECTRIC RESISTANCE", "latex": "\\delta =\\frac{E}{D} \\{m(B + \\beta) - n(A + \\alpha)\\}", "name": null, "statement": "The galvanometer deflexion is the emf over D times the difference between the two weighted branch resistances; zero deflexion means that bracket is nearly zero.", "kind": "formula", "symbols": [ { "unit": null, "symbol": "delta", "meaning": "deflexion of the galvanometer needle" }, { "unit": null, "symbol": "E", "meaning": "electromotive force of the battery" }, { "unit": "ohm squared", "symbol": "D", "meaning": "common denominator for the branch currents" }, { "unit": null, "symbol": "m", "meaning": "effect of the first coil per unit current on the needle" }, { "unit": null, "symbol": "n", "meaning": "effect of the second coil per unit current on the needle" }, { "unit": "ohm", "symbol": "A", "meaning": "resistance introduced into the first coil" }, { "unit": "ohm", "symbol": "B", "meaning": "resistance introduced into the second coil" }, { "unit": "ohm", "symbol": "alpha", "meaning": "remaining resistance of the first coil and its connexions" }, { "unit": "ohm", "symbol": "beta", "meaning": "remaining resistance of the second coil and its connexions" } ], "sympy": "Eq(delta, E/D*(m*(B + beta) - n*(A + alpha)))", "physics": true, "states": [], "concepts": [ "concept/comparison-of-resistances", "instrument/differential-galvanometer", "instrument/galvanometer", "method/null-method" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/eq-9d3003fc2f", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-xii", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 202", "location": "THE MEASUREMENT OF ELECTRIC RESISTANCE", "latex": "n(A' - A) = \\frac{D}{E} \\delta - \\frac{D'}{E'} \\delta'", "name": null, "statement": "The difference between the two substituted resistances is set by the two observed deflexions, each corrected by its own D and emf.", "kind": "result", "symbols": [ { "unit": "ohm", "symbol": "A", "meaning": "first resistance introduced into the first coil" }, { "unit": "ohm", "symbol": "A'", "meaning": "substituted resistance for A in the second observation" }, { "unit": null, "symbol": "n", "meaning": "effect of the second coil per unit current on the needle" }, { "unit": "ohm squared", "symbol": "D", "meaning": "common denominator in the first observation" }, { "unit": "ohm squared", "symbol": "D'", "meaning": "common denominator in the second observation" }, { "unit": null, "symbol": "E", "meaning": "electromotive force in the first observation" }, { "unit": null, "symbol": "E'", "meaning": "electromotive force in the second observation" }, { "unit": null, "symbol": "delta", "meaning": "deflexion in the first observation" }, { "unit": null, "symbol": "delta'", "meaning": "deflexion in the second observation" } ], "sympy": "Eq(n*(A_p - A), D/E*delta - D_p/E_p*delta_p)", "physics": true, "states": [], "concepts": [ "concept/comparison-of-resistances", "instrument/differential-galvanometer", "method/null-method", "quantity/electromotive-force" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/eq-782a494c92", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-xii", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 203", "location": "THE MEASUREMENT OF ELECTRIC RESISTANCE", "latex": "(m + n)(B - A) = \\frac{D}{E} \\delta - \\frac{D'}{ E} \\delta'", "name": null, "statement": "After exchanging the resistances A and B, the difference between them is set by the two observed deflexions, with the sum of the coil constants as a factor.", "kind": "result", "symbols": [ { "unit": null, "symbol": "m", "meaning": "effect of the first coil per unit current on the needle" }, { "unit": null, "symbol": "n", "meaning": "effect of the second coil per unit current on the needle" }, { "unit": "ohm", "symbol": "A", "meaning": "resistance in the first coil" }, { "unit": "ohm", "symbol": "B", "meaning": "resistance in the second coil" }, { "unit": "ohm squared", "symbol": "D", "meaning": "common denominator in the first observation" }, { "unit": "ohm squared", "symbol": "D'", "meaning": "common denominator in the exchanged observation" }, { "unit": null, "symbol": "E", "meaning": "electromotive force" }, { "unit": null, "symbol": "delta", "meaning": "deflexion in the first observation" }, { "unit": null, "symbol": "delta'", "meaning": "deflexion in the exchanged observation" } ], "sympy": "Eq((m + n)*(B - A), D/E*delta - D_p/E*delta_p)", "physics": true, "states": [], "concepts": [ "concept/comparison-of-resistances", "instrument/differential-galvanometer", "method/null-method" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/eq-f97cd3de6d", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-xii", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 203", "location": "THE MEASUREMENT OF ELECTRIC RESISTANCE", "latex": "B - A = \\frac{1}{2nE} (A + \\alpha)(A + \\alpha + 2r)(\\delta - \\delta')", "name": null, "statement": "When the coil constants and resistances are nearly equal, the difference B minus A is approximately given by the smallest observable deflexion difference.", "kind": "approximation", "symbols": [ { "unit": "ohm", "symbol": "B", "meaning": "resistance in the second coil" }, { "unit": "ohm", "symbol": "A", "meaning": "resistance in the first coil" }, { "unit": null, "symbol": "n", "meaning": "effect of the second coil per unit current on the needle" }, { "unit": null, "symbol": "E", "meaning": "electromotive force of the battery" }, { "unit": "ohm", "symbol": "alpha", "meaning": "remaining resistance of the first coil and its connexions" }, { "unit": "ohm", "symbol": "r", "meaning": "resistance of the battery" }, { "unit": null, "symbol": "delta", "meaning": "deflexion in the first observation" }, { "unit": null, "symbol": "delta'", "meaning": "deflexion in the exchanged observation" } ], "sympy": "Eq(B - A, (1/(2*n*E))*(A + alpha)*(A + alpha + 2*r)*(delta - delta_p))", "physics": true, "states": [], "concepts": [ "concept/comparison-of-resistances", "instrument/differential-galvanometer", "instrument/galvanometer", "quantity/resistance" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/eq-93fa00a148", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-xii", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 203", "location": "THE MEASUREMENT OF ELECTRIC RESISTANCE", "latex": "\\alpha = \\tfrac{1}{3}(A + r) \\left\\{2 \\sqrt{1 - \\frac{3}{4}\\frac{r^2}{(A + r)^2}}-1\\right\\}", "name": null, "statement": "The galvanometer coil resistance alpha that minimises the sensitivity-error factor is given by this expression in terms of A and the battery resistance r.", "kind": "result", "symbols": [ { "unit": "ohm", "symbol": "alpha", "meaning": "remaining resistance of a galvanometer coil and its connexions" }, { "unit": "ohm", "symbol": "A", "meaning": "resistance to be measured in the first coil" }, { "unit": "ohm", "symbol": "r", "meaning": "resistance of the battery" } ], "sympy": "Eq(alpha, Rational(1,3)*(A + r)*(2*sqrt(1 - Rational(3,4)*r**2/(A + r)**2) - 1))", "physics": true, "states": [], "concepts": [ "concept/minimum", "instrument/differential-galvanometer", "instrument/galvanometer", "quantity/resistance" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/eq-b09442fa97", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-xii", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 203", "location": "THE MEASUREMENT OF ELECTRIC RESISTANCE", "latex": "\\alpha = \\tfrac{1}{3} A", "name": null, "statement": "When the battery resistance r is small compared with A, each galvanometer coil should have one-third of the resistance to be measured.", "kind": "result", "symbols": [ { "unit": "ohm", "symbol": "alpha", "meaning": "remaining resistance of a galvanometer coil and its connexions" }, { "unit": "ohm", "symbol": "A", "meaning": "resistance to be measured" } ], "sympy": "Eq(alpha, Rational(1,3)*A)", "physics": true, "states": [], "concepts": [ "instrument/differential-galvanometer", "instrument/galvanometer", "quantity/resistance" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/eq-6795c0715e", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-xii", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 203", "location": "THE MEASUREMENT OF ELECTRIC RESISTANCE", "latex": "B - A = \\frac{8}{9}\\frac{A^2}{nE}(\\delta - \\delta')", "name": null, "statement": "With the optimal galvanometer coil resistance, the difference B minus A is approximately 8/9 times A squared over nE, times the difference of the smallest observable deflexions.", "kind": "approximation", "symbols": [ { "unit": "ohm", "symbol": "B", "meaning": "resistance in the second coil" }, { "unit": "ohm", "symbol": "A", "meaning": "resistance in the first coil" }, { "unit": null, "symbol": "n", "meaning": "effect of the second coil per unit current on the needle" }, { "unit": null, "symbol": "E", "meaning": "electromotive force of the battery" }, { "unit": null, "symbol": "delta", "meaning": "deflexion in the first observation" }, { "unit": null, "symbol": "delta'", "meaning": "deflexion in the exchanged observation" } ], "sympy": "Eq(B - A, Rational(8,9)*A**2/(n*E)*(delta - delta_p))", "physics": true, "states": [], "concepts": [ "concept/comparison-of-resistances", "instrument/differential-galvanometer", "quantity/resistance" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/eq-47524b189e", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-xii", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 203", "location": "THE MEASUREMENT OF ELECTRIC RESISTANCE", "latex": "\\Delta = \\frac{mE}{A + \\alpha + r} = \\frac{3}{4}\\frac{nE}{A}", "name": null, "statement": "The deflexion from one coil alone is mE over the total circuit resistance; with r zero and alpha one-third of A, this equals three-quarters of nE over A.", "kind": "formula", "symbols": [ { "unit": null, "symbol": "Delta", "meaning": "deflexion of the needle when current flows through one coil only" }, { "unit": null, "symbol": "m", "meaning": "effect of the first coil per unit current on the needle" }, { "unit": null, "symbol": "E", "meaning": "electromotive force of the battery" }, { "unit": "ohm", "symbol": "A", "meaning": "resistance to be measured" }, { "unit": "ohm", "symbol": "alpha", "meaning": "remaining resistance of the galvanometer coil and its connexions" }, { "unit": "ohm", "symbol": "r", "meaning": "resistance of the battery" }, { "unit": null, "symbol": "n", "meaning": "effect of the second coil per unit current on the needle" } ], "sympy": "Eq(Delta, m*E/(A + alpha + r))", "physics": true, "states": [], "concepts": [ "instrument/differential-galvanometer", "instrument/galvanometer", "law/ohm-s-law", "quantity/resistance" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/eq-12fd21e886", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-xii", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 203", "location": "THE MEASUREMENT OF ELECTRIC RESISTANCE", "latex": "\\frac{B - A}{A} = \\frac{2}{3}\\frac{\\delta - \\delta'}{\\Delta}", "name": null, "statement": "The fractional error in the comparison of A and B is two-thirds of the smallest observable deflexion difference divided by the single-coil deflexion.", "kind": "approximation", "symbols": [ { "unit": "ohm", "symbol": "B", "meaning": "resistance in the second coil" }, { "unit": "ohm", "symbol": "A", "meaning": "resistance in the first coil" }, { "unit": null, "symbol": "delta", "meaning": "deflexion in the first observation" }, { "unit": null, "symbol": "delta'", "meaning": "deflexion in the exchanged observation" }, { "unit": null, "symbol": "Delta", "meaning": "deflexion when current flows through one coil only" } ], "sympy": "Eq((B - A)/A, Rational(2,3)*(delta - delta_p)/Delta)", "physics": true, "states": [], "concepts": [ "concept/comparison-of-resistances", "instrument/differential-galvanometer", "method/null-method", "quantity/resistance" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/eq-cfb3423057", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-xii", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 204", "location": "THE MEASUREMENT OF ELECTRIC RESISTANCE", "latex": "O = \\frac{B \\gamma + C \\beta}{ \\beta + \\gamma}", "name": null, "statement": "With no current in OA, the potential at O is the average of the potentials at B and C, weighted by the opposite resistances beta and gamma.", "kind": "result", "symbols": [ { "unit": "volt", "symbol": "O", "meaning": "potential at point O" }, { "unit": "volt", "symbol": "B", "meaning": "potential at point B" }, { "unit": "volt", "symbol": "C", "meaning": "potential at point C" }, { "unit": "ohm", "symbol": "beta", "meaning": "resistance of conductor BO" }, { "unit": "ohm", "symbol": "gamma", "meaning": "resistance of conductor OC" } ], "sympy": "Eq(O, (B*gamma + C*beta)/(beta + gamma))", "physics": true, "states": [], "concepts": [ "concept/conjugate-conductors", "instrument/wheatstone-s-bridge", "law/ohm-s-law", "quantity/electric-potential" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/eq-155e956d4f", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-xii", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 204", "location": "THE MEASUREMENT OF ELECTRIC RESISTANCE", "latex": "A = \\frac{Bb + Cc}{b + c}", "name": null, "statement": "With no current in OA, the potential at A is the average of the potentials at B and C, weighted by the opposite resistances c and b.", "kind": "result", "symbols": [ { "unit": "volt", "symbol": "A", "meaning": "potential at point A" }, { "unit": "volt", "symbol": "B", "meaning": "potential at point B" }, { "unit": "volt", "symbol": "C", "meaning": "potential at point C" }, { "unit": "ohm", "symbol": "b", "meaning": "resistance of conductor CA" }, { "unit": "ohm", "symbol": "c", "meaning": "resistance of conductor AB" } ], "sympy": "Eq(A, (B*b + C*c)/(b + c))", "physics": true, "states": [], "concepts": [ "concept/conjugate-conductors", "instrument/wheatstone-s-bridge", "law/ohm-s-law", "quantity/electric-potential" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/eq-5f7a73da2f", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-xii", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 204", "location": "THE MEASUREMENT OF ELECTRIC RESISTANCE", "latex": "b \\beta = c \\gamma", "name": null, "statement": "The bridge is balanced, with no current in OA, when the products of opposite arm resistances are equal, so the two conductors are conjugate.", "kind": "result", "symbols": [ { "unit": "ohm", "symbol": "b", "meaning": "resistance of conductor CA" }, { "unit": "ohm", "symbol": "c", "meaning": "resistance of conductor AB" }, { "unit": "ohm", "symbol": "beta", "meaning": "resistance of conductor BO" }, { "unit": "ohm", "symbol": "gamma", "meaning": "resistance of conductor OC" } ], "sympy": "Eq(b*beta, c*gamma)", "physics": true, "states": [], "concepts": [ "concept/conjugate-conductors", "concept/electric-current", "instrument/wheatstone-s-bridge", "quantity/resistance" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/eq-ef872efefc", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-xii", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 213", "location": "THE MEASUREMENT OF ELECTRIC RESISTANCE", "latex": "x_1 = y \\left(1 + \\frac{b}{\\alpha + \\gamma} \\right)", "name": null, "statement": "With the key up, the actual current through the battery equals the galvanometer current times one plus b over alpha plus gamma.", "kind": "formula", "symbols": [ { "unit": null, "symbol": "x_1", "meaning": "actual current through the battery with the key up" }, { "unit": null, "symbol": "y", "meaning": "current through the galvanometer" }, { "unit": null, "symbol": "b", "meaning": "resistance of the bridge arm b" }, { "unit": null, "symbol": "alpha", "meaning": "resistance of the galvanometer" }, { "unit": null, "symbol": "gamma", "meaning": "resistance of the arm gamma" } ], "sympy": "Eq(x1, y*(1 + b/(alpha + gamma)))", "physics": true, "states": [], "concepts": [ "concept/battery", "concept/electric-current", "method/determining-battery-resistance-by-mance-s-method" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/eq-a46b771fc2", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-xii", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 209", "location": "THE MEASUREMENT OF ELECTRIC RESISTANCE", "latex": "\\frac{c + x}{b - x} = \\frac{\\beta}{\\gamma}", "name": null, "statement": "With the coils in their first position, the bridge balances when the ratio of the two arm resistances equals the ratio of the standard coil to the coil being adjusted.", "kind": "formula", "symbols": [ { "unit": null, "symbol": "c", "meaning": "resistance of coil c, including the part of wire PR up to its zero reading" }, { "unit": null, "symbol": "x", "meaning": "scale reading of the contact point Q in the first position" }, { "unit": null, "symbol": "b", "meaning": "resistance of coil b, including the part of wire PR up to its zero reading" }, { "unit": null, "symbol": "beta", "meaning": "resistance of the standard resistance coil" }, { "unit": null, "symbol": "gamma", "meaning": "resistance of the coil being adjusted to equal beta" } ], "sympy": "Eq((c + x)/(b - x), beta/gamma)", "physics": true, "states": [], "concepts": [ "instrument/wheatstone-s-bridge", "method/comparing-two-equal-resistances-with-wheatstone-s-bridge", "method/null-method", "quantity/resistance" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/eq-0cf23e8fdd", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-xii", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 209", "location": "THE MEASUREMENT OF ELECTRIC RESISTANCE", "latex": "\\frac{c + y}{b - y} = \\frac{\\gamma}{\\beta}", "name": null, "statement": "With the coils beta and gamma interchanged, the bridge balances at the second scale reading y, with the ratio of arm resistances now equal to gamma over beta.", "kind": "formula", "symbols": [ { "unit": null, "symbol": "c", "meaning": "resistance of coil c, including the part of wire PR up to its zero reading" }, { "unit": null, "symbol": "y", "meaning": "scale reading of the contact point Q after beta and gamma are interchanged" }, { "unit": null, "symbol": "b", "meaning": "resistance of coil b, including the part of wire PR up to its zero reading" }, { "unit": null, "symbol": "gamma", "meaning": "resistance of the coil being adjusted" }, { "unit": null, "symbol": "beta", "meaning": "resistance of the standard resistance coil" } ], "sympy": "Eq((c + y)/(b - y), gamma/beta)", "physics": true, "states": [], "concepts": [ "instrument/wheatstone-s-bridge", "method/comparing-two-equal-resistances-with-wheatstone-s-bridge", "method/null-method", "quantity/resistance" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/eq-e44bdd033f", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-xii", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 209", "location": "THE MEASUREMENT OF ELECTRIC RESISTANCE", "latex": "\\frac{\\gamma ^2}{\\beta ^2} = 1 + \\frac{(b+c)(y-x)}{(c+x)(b-y)}", "name": null, "statement": "Combining the two balance conditions gives the ratio of the squares of the two resistances in terms of the two scale readings and the arm resistances.", "kind": "result", "symbols": [ { "unit": null, "symbol": "gamma", "meaning": "resistance of the coil being adjusted" }, { "unit": null, "symbol": "beta", "meaning": "resistance of the standard resistance coil" }, { "unit": null, "symbol": "b", "meaning": "resistance of coil b, including the part of wire PR up to its zero reading" }, { "unit": null, "symbol": "c", "meaning": "resistance of coil c, including the part of wire PR up to its zero reading" }, { "unit": null, "symbol": "x", "meaning": "scale reading of the contact point Q in the first position" }, { "unit": null, "symbol": "y", "meaning": "scale reading of the contact point Q after beta and gamma are interchanged" } ], "sympy": "Eq(gamma**2/beta**2, 1 + (b + c)*(y - x)/((c + x)*(b - y)))", "physics": true, "states": [], "concepts": [ "instrument/wheatstone-s-bridge", "method/comparing-two-equal-resistances-with-wheatstone-s-bridge", "quantity/resistance" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/eq-87be207383", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-xii", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 209", "location": "THE MEASUREMENT OF ELECTRIC RESISTANCE", "latex": "\\frac{\\gamma^2}{\\beta^2} = 1 + 4\\frac{y - x}{b + c}", "name": null, "statement": "When b and c are nearly equal and large compared with x and y, the ratio of the squares of the resistances is approximately one plus four times the scale difference over b plus c.", "kind": "approximation", "symbols": [ { "unit": null, "symbol": "gamma", "meaning": "resistance of the coil being adjusted" }, { "unit": null, "symbol": "beta", "meaning": "resistance of the standard resistance coil" }, { "unit": null, "symbol": "y", "meaning": "scale reading of the contact point Q after beta and gamma are interchanged" }, { "unit": null, "symbol": "x", "meaning": "scale reading of the contact point Q in the first position" }, { "unit": null, "symbol": "b", "meaning": "resistance of coil b, including the part of wire PR up to its zero reading" }, { "unit": null, "symbol": "c", "meaning": "resistance of coil c, including the part of wire PR up to its zero reading" } ], "sympy": "Eq(gamma**2/beta**2, 1 + 4*(y - x)/(b + c))", "physics": true, "states": [], "concepts": [ "concept/approximation", "instrument/wheatstone-s-bridge", "method/comparing-two-equal-resistances-with-wheatstone-s-bridge", "quantity/resistance" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/eq-b068590bb6", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-xii", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 209", "location": "THE MEASUREMENT OF ELECTRIC RESISTANCE", "latex": "\\gamma = \\beta\\left(1 + 2 \\frac{y - x}{b + c}\\right)", "name": null, "statement": "To first order, the resistance to be adjusted equals the standard resistance times one plus twice the scale difference over b plus c.", "kind": "approximation", "symbols": [ { "unit": null, "symbol": "gamma", "meaning": "resistance of the coil being adjusted" }, { "unit": null, "symbol": "beta", "meaning": "resistance of the standard resistance coil" }, { "unit": null, "symbol": "y", "meaning": "scale reading of the contact point Q after beta and gamma are interchanged" }, { "unit": null, "symbol": "x", "meaning": "scale reading of the contact point Q in the first position" }, { "unit": null, "symbol": "b", "meaning": "resistance of coil b, including the part of wire PR up to its zero reading" }, { "unit": null, "symbol": "c", "meaning": "resistance of coil c, including the part of wire PR up to its zero reading" } ], "sympy": "Eq(gamma, beta*(1 + 2*(y - x)/(b + c)))", "physics": true, "states": [], "concepts": [ "concept/approximation", "instrument/wheatstone-s-bridge", "method/comparing-two-equal-resistances-with-wheatstone-s-bridge", "quantity/resistance" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/eq-d69896bcb5", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-xii", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 210", "location": "THE MEASUREMENT OF ELECTRIC RESISTANCE", "latex": "c=\\sqrt{a\\alpha}", "name": null, "statement": "The best value of the bridge arm c, given the battery and galvanometer resistances, is the square root of their product, as shown by Heaviside.", "kind": "result", "symbols": [ { "unit": null, "symbol": "c", "meaning": "resistance of the bridge arm chosen as best value" }, { "unit": null, "symbol": "a", "meaning": "resistance of the battery" }, { "unit": null, "symbol": "alpha", "meaning": "resistance of the galvanometer" } ], "sympy": "Eq(c, sqrt(a*alpha))", "physics": true, "states": [], "concepts": [ "concept/battery", "instrument/galvanometer", "instrument/wheatstone-s-bridge", "quantity/resistance" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/eq-ba61ae24b2", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-xii", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 210", "location": "THE MEASUREMENT OF ELECTRIC RESISTANCE", "latex": "b=\\sqrt{a\\gamma\\frac{\\alpha + \\gamma}{a + \\gamma}}", "name": null, "statement": "The best value of the bridge arm b, given the battery, galvanometer, and measured resistances, is the square root of a gamma times the ratio of alpha plus gamma to a plus gamma.", "kind": "result", "symbols": [ { "unit": null, "symbol": "b", "meaning": "resistance of the bridge arm chosen as best value" }, { "unit": null, "symbol": "a", "meaning": "resistance of the battery" }, { "unit": null, "symbol": "gamma", "meaning": "resistance to be measured" }, { "unit": null, "symbol": "alpha", "meaning": "resistance of the galvanometer" } ], "sympy": "Eq(b, sqrt(a*gamma*(alpha + gamma)/(a + gamma)))", "physics": true, "states": [], "concepts": [ "concept/battery", "instrument/galvanometer", "instrument/wheatstone-s-bridge", "quantity/resistance" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/eq-41c016ab5c", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-xii", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 210", "location": "THE MEASUREMENT OF ELECTRIC RESISTANCE", "latex": "\\beta = \\sqrt{\\alpha \\gamma \\frac{a + \\gamma }{\\alpha + \\gamma}}", "name": null, "statement": "The best value of the standard coil beta, given the battery, galvanometer, and measured resistances, is the square root of alpha gamma times the ratio of a plus gamma to alpha plus gamma.", "kind": "result", "symbols": [ { "unit": null, "symbol": "beta", "meaning": "resistance of the standard coil chosen as best value" }, { "unit": null, "symbol": "alpha", "meaning": "resistance of the galvanometer" }, { "unit": null, "symbol": "gamma", "meaning": "resistance to be measured" }, { "unit": null, "symbol": "a", "meaning": "resistance of the battery" } ], "sympy": "Eq(beta, sqrt(alpha*gamma*(a + gamma)/(alpha + gamma)))", "physics": true, "states": [], "concepts": [ "concept/battery", "instrument/galvanometer", "instrument/wheatstone-s-bridge", "quantity/resistance" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/eq-b59162bc3d", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-xii", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 211", "location": "THE MEASUREMENT OF ELECTRIC RESISTANCE", "latex": "b = \\frac{c\\gamma}{\\beta}", "name": null, "statement": "When the galvanometer in CA gives the same deflexion whether or not O and A are joined, the galvanometer resistance b equals c times gamma over beta.", "kind": "result", "symbols": [ { "unit": null, "symbol": "b", "meaning": "resistance of the galvanometer coil" }, { "unit": null, "symbol": "c", "meaning": "resistance of the known coil c" }, { "unit": null, "symbol": "gamma", "meaning": "resistance of the known coil gamma" }, { "unit": null, "symbol": "beta", "meaning": "resistance of the known coil beta" } ], "sympy": "Eq(b, c*gamma/beta)", "physics": true, "states": [], "concepts": [ "concept/conjugate-conductors", "instrument/galvanometer", "instrument/wheatstone-s-bridge", "method/determining-galvanometer-resistance-by-thomson-s-method", "quantity/resistance" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/eq-6bff70ac2b", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-xii", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 212", "location": "THE MEASUREMENT OF ELECTRIC RESISTANCE", "latex": "y = \\frac{E\\alpha}{b\\alpha + c(b+\\alpha+\\gamma)}", "name": null, "statement": "When the bridge condition is satisfied, the current through the galvanometer equals the battery emf times alpha divided by a combination of the arm resistances, and does not depend on beta.", "kind": "result", "symbols": [ { "unit": null, "symbol": "y", "meaning": "current through the galvanometer" }, { "unit": "volt", "symbol": "E", "meaning": "electromotive force of the battery" }, { "unit": null, "symbol": "alpha", "meaning": "resistance of the galvanometer" }, { "unit": null, "symbol": "b", "meaning": "resistance of the bridge arm b" }, { "unit": null, "symbol": "c", "meaning": "resistance of the bridge arm c" }, { "unit": null, "symbol": "gamma", "meaning": "resistance to be measured" } ], "sympy": "Eq(y, E*alpha/(b*alpha + c*(b + alpha + gamma)))", "physics": true, "states": [], "concepts": [ "concept/battery", "concept/electric-current", "instrument/galvanometer", "method/determining-battery-resistance-by-mance-s-method", "quantity/electromotive-force" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/eq-d1de377c70", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-xii", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 212", "location": "THE MEASUREMENT OF ELECTRIC RESISTANCE", "latex": "\\frac{y_0-y_1}{y} = \\frac{\\alpha}{\\gamma}\\frac{c\\gamma-a\\alpha}{(c+\\alpha )(\\alpha+\\gamma)}", "name": null, "statement": "The sensitivity of Mance's method: the relative change in galvanometer current between the two switch positions is proportional to the departure of c gamma from a alpha.", "kind": "result", "symbols": [ { "unit": null, "symbol": "y_0", "meaning": "galvanometer current when O and B are joined by a conductor of no sensible resistance" }, { "unit": null, "symbol": "y_1", "meaning": "galvanometer current when O and B are completely disconnected" }, { "unit": null, "symbol": "y", "meaning": "galvanometer current when the adjustment is perfect" }, { "unit": null, "symbol": "alpha", "meaning": "resistance of the galvanometer" }, { "unit": null, "symbol": "gamma", "meaning": "resistance of the arm gamma" }, { "unit": null, "symbol": "c", "meaning": "resistance of the conductor AB" }, { "unit": null, "symbol": "a", "meaning": "resistance of the battery" } ], "sympy": "Eq((y0 - y1)/y, alpha/gamma*(c*gamma - a*alpha)/((c + alpha)*(alpha + gamma)))", "physics": true, "states": [], "concepts": [ "concept/sensibility-of-a-method", "instrument/galvanometer", "method/determining-battery-resistance-by-mance-s-method", "quantity/resistance" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/eq-e0107d09ec", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-xii", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 212", "location": "THE MEASUREMENT OF ELECTRIC RESISTANCE", "latex": "c\\gamma=a\\alpha", "name": null, "statement": "The condition under which the galvanometer deflexion is unchanged when O and B are connected or disconnected: the product of c and gamma equals the product of a and alpha.", "kind": "rule", "symbols": [ { "unit": null, "symbol": "c", "meaning": "resistance of the conductor AB" }, { "unit": null, "symbol": "gamma", "meaning": "resistance of the arm gamma" }, { "unit": null, "symbol": "a", "meaning": "resistance of the battery" }, { "unit": null, "symbol": "alpha", "meaning": "resistance of the galvanometer" } ], "sympy": "Eq(c*gamma, a*alpha)", "physics": true, "states": [], "concepts": [ "concept/conjugate-conductors", "instrument/wheatstone-s-bridge", "method/determining-battery-resistance-by-mance-s-method", "method/null-method" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/eq-f6931ea895", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-xii", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 213", "location": "THE MEASUREMENT OF ELECTRIC RESISTANCE", "latex": "x_0 = y \\left(1 + \\frac{b}{\\gamma} + \\frac{\\alpha c}{\\gamma (\\alpha + c)} \\right)", "name": null, "statement": "With the key down, the actual current through the battery equals the galvanometer current times a sum of terms in the bridge resistances.", "kind": "formula", "symbols": [ { "unit": null, "symbol": "x_0", "meaning": "actual current through the battery with the key down" }, { "unit": null, "symbol": "y", "meaning": "current through the galvanometer" }, { "unit": null, "symbol": "b", "meaning": "resistance of the bridge arm b" }, { "unit": null, "symbol": "gamma", "meaning": "resistance of the arm gamma" }, { "unit": null, "symbol": "alpha", "meaning": "resistance of the galvanometer" }, { "unit": null, "symbol": "c", "meaning": "resistance of the conductor AB" } ], "sympy": "Eq(x0, y*(1 + b/gamma + alpha*c/(gamma*(alpha + c))))", "physics": true, "states": [], "concepts": [ "concept/battery", "concept/electric-current", "method/determining-battery-resistance-by-mance-s-method" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/eq-571717dfb6", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-xii", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 213", "location": "THE MEASUREMENT OF ELECTRIC RESISTANCE", "latex": "a = \\frac{c \\gamma}{\\alpha}", "name": null, "statement": "The resistance of the battery equals c times gamma divided by alpha.", "kind": "result", "symbols": [ { "unit": null, "symbol": "a", "meaning": "resistance of the battery" }, { "unit": null, "symbol": "c", "meaning": "resistance of the conductor AB" }, { "unit": null, "symbol": "gamma", "meaning": "resistance of the arm gamma" }, { "unit": null, "symbol": "alpha", "meaning": "resistance of the galvanometer" } ], "sympy": "Eq(a, c*gamma/alpha)", "physics": true, "states": [], "concepts": [ "concept/battery", "method/determining-battery-resistance-by-mance-s-method", "quantity/resistance" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/eq-f3315449ec", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-xii", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 213", "location": "THE MEASUREMENT OF ELECTRIC RESISTANCE", "latex": "E = y \\left( b + c + \\frac{c}{\\alpha} ( b + \\gamma ) \\right)", "name": null, "statement": "The electromotive force of the battery equals the galvanometer current times a combination of the bridge resistances.", "kind": "result", "symbols": [ { "unit": "volt", "symbol": "E", "meaning": "electromotive force of the battery" }, { "unit": null, "symbol": "y", "meaning": "current through the galvanometer" }, { "unit": null, "symbol": "b", "meaning": "resistance of the bridge arm b" }, { "unit": null, "symbol": "c", "meaning": "resistance of the conductor AB" }, { "unit": null, "symbol": "alpha", "meaning": "resistance of the galvanometer" }, { "unit": null, "symbol": "gamma", "meaning": "resistance of the arm gamma" } ], "sympy": "Eq(E, y*(b + c + c/alpha*(b + gamma)))", "physics": true, "states": [], "concepts": [ "concept/battery", "concept/electric-current", "method/determining-battery-resistance-by-mance-s-method", "quantity/electromotive-force" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/eq-e6023668b0", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-xii", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 213", "location": "THE MEASUREMENT OF ELECTRIC RESISTANCE", "latex": "\\frac{y_0 - y_1}{y} = \\frac{\\beta}{\\gamma} \\frac{c \\gamma - b \\beta}{(c + \\beta)(\\beta + \\gamma)}", "name": null, "statement": "For the galvanometer-resistance arrangement, obtained from the battery case by exchanging alpha and beta, the relative change in galvanometer current has the same form with b beta in place of a alpha.", "kind": "result", "symbols": [ { "unit": null, "symbol": "y_0", "meaning": "galvanometer current when O and A are joined by a conductor of no sensible resistance" }, { "unit": null, "symbol": "y_1", "meaning": "galvanometer current when O and A are disconnected" }, { "unit": null, "symbol": "y", "meaning": "galvanometer current when the adjustment is perfect" }, { "unit": null, "symbol": "beta", "meaning": "resistance exchanged with alpha in the galvanometer arrangement" }, { "unit": null, "symbol": "gamma", "meaning": "resistance of the arm gamma" }, { "unit": null, "symbol": "c", "meaning": "resistance of the conductor CA or AB" }, { "unit": null, "symbol": "b", "meaning": "resistance of the galvanometer coil" } ], "sympy": "Eq((y0 - y1)/y, beta/gamma*(c*gamma - b*beta)/((c + beta)*(beta + gamma)))", "physics": true, "states": [], "concepts": [ "concept/sensibility-of-a-method", "instrument/galvanometer", "method/determining-galvanometer-resistance-by-thomson-s-method", "quantity/resistance" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/eq-9df34973ed", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-xii", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 214", "location": "THE MEASUREMENT OF ELECTRIC RESISTANCE", "latex": "E_1 = R_1C", "name": null, "statement": "When no current flows through the electromotor E1, its emf equals the resistance R1 between A1 and B1 times the primary-circuit current C.", "kind": "law", "symbols": [ { "unit": "volt", "symbol": "E_1", "meaning": "electromotive force of the first electromotor" }, { "unit": null, "symbol": "R_1", "meaning": "resistance between A1 and B1 at balance" }, { "unit": "ampere", "symbol": "C", "meaning": "strength of the current in the primary circuit" } ], "sympy": "Eq(E_1, R_1*C)", "physics": true, "states": [], "concepts": [ "concept/electric-current", "method/comparing-electromotive-forces-by-poggendorff-s-compensation-method", "quantity/electromotive-force", "quantity/resistance" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/eq-e96101c536", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-xii", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 214", "location": "THE MEASUREMENT OF ELECTRIC RESISTANCE", "latex": "E_2 = R_2C", "name": null, "statement": "When no current flows through the electromotor E2, its emf equals the resistance R2 between A2 and B2 times the primary-circuit current C.", "kind": "law", "symbols": [ { "unit": "volt", "symbol": "E_2", "meaning": "electromotive force of the second electromotor" }, { "unit": null, "symbol": "R_2", "meaning": "resistance between A2 and B2 at balance" }, { "unit": "ampere", "symbol": "C", "meaning": "strength of the current in the primary circuit" } ], "sympy": "Eq(E_2, R_2*C)", "physics": true, "states": [], "concepts": [ "concept/electric-current", "method/comparing-electromotive-forces-by-poggendorff-s-compensation-method", "quantity/electromotive-force", "quantity/resistance" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/eq-f0bd12c32a", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-xii", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 214", "location": "THE MEASUREMENT OF ELECTRIC RESISTANCE", "latex": "E_1 : E_2 :: R_1 : R_2", "name": null, "statement": "Two electromotive forces are in the same ratio as the resistances that balance them against the same primary current.", "kind": "result", "symbols": [ { "unit": "volt", "symbol": "E_1", "meaning": "electromotive force of the first electromotor" }, { "unit": "volt", "symbol": "E_2", "meaning": "electromotive force of the second electromotor" }, { "unit": null, "symbol": "R_1", "meaning": "resistance between A1 and B1 at balance" }, { "unit": null, "symbol": "R_2", "meaning": "resistance between A2 and B2 at balance" } ], "sympy": "Eq(E_1/E_2, R_1/R_2)", "physics": true, "states": [], "concepts": [ "concept/common-ratio", "concept/proportion", "method/comparing-electromotive-forces-by-poggendorff-s-compensation-method", "quantity/electromotive-force" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/eq-95cfd2348c", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-xii", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 200", "location": "THE MEASUREMENT OF ELECTRIC RESISTANCE", "latex": "E = IR = I_1( R + r_1 ) = I_2( R + r_2 )\\text{.}", "name": "Ohm's law", "statement": "By Ohm's law, the battery's electromotive force equals the current times the total circuit resistance in each of the three states: no added resistance, and with r_1 or r_2 added.", "kind": "law", "symbols": [ { "unit": null, "symbol": "E", "meaning": "electromotive force of the battery" }, { "unit": null, "symbol": "I", "meaning": "strength of the current when the battery connexions are closed" }, { "unit": null, "symbol": "R", "meaning": "resistance of the battery and its connexions, including the galvanometer used in measuring the current" }, { "unit": null, "symbol": "I_1", "meaning": "current when additional resistance r_1 is introduced" }, { "unit": null, "symbol": "I_2", "meaning": "current when additional resistance r_2 is introduced" }, { "unit": null, "symbol": "r_1", "meaning": "first additional resistance introduced into the circuit" }, { "unit": null, "symbol": "r_2", "meaning": "second additional resistance introduced into the circuit" } ], "sympy": null, "physics": true, "states": [ "law/ohm-s-law" ], "concepts": [ "concept/battery", "concept/electric-circuit", "concept/electric-current", "quantity/electromotive-force", "quantity/resistance" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/eq-87d335477c", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-xii", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 200", "location": "THE MEASUREMENT OF ELECTRIC RESISTANCE", "latex": "\\frac{r_1}{r_2} = \\frac{(I-I_1)I_2}{(I-I_2)I_1}\\text{.}", "name": "Ohm's formula", "statement": "The ratio of two resistances can be found from the ratio of the currents measured with each one in the circuit, without knowing E or R.", "kind": "result", "symbols": [ { "unit": null, "symbol": "r_1", "meaning": "first additional resistance" }, { "unit": null, "symbol": "r_2", "meaning": "second additional resistance" }, { "unit": null, "symbol": "I", "meaning": "strength of the current with the battery connexions closed" }, { "unit": null, "symbol": "I_1", "meaning": "current with r_1 introduced" }, { "unit": null, "symbol": "I_2", "meaning": "current with r_2 introduced" } ], "sympy": "Eq(r_1/r_2, (I - I_1)*I_2/((I - I_2)*I_1))", "physics": true, "states": [ "theorem/ohm-s-formula" ], "concepts": [ "concept/comparison-of-resistances", "concept/electric-current", "law/ohm-s-law", "quantity/resistance" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/eq-72d35a878e", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-xii", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 201", "location": "THE MEASUREMENT OF ELECTRIC RESISTANCE", "latex": "\\delta = mI_1 - nI_2\\text{.}", "name": null, "statement": "The deflexion of the differential galvanometer needle is the difference between the two coil currents, each weighted by its coil constant.", "kind": "law", "symbols": [ { "unit": null, "symbol": "delta", "meaning": "deflexion of the galvanometer needle" }, { "unit": null, "symbol": "m", "meaning": "coefficient of action of the first coil on the needle" }, { "unit": null, "symbol": "n", "meaning": "coefficient of action of the second coil on the needle" }, { "unit": null, "symbol": "I_1", "meaning": "current through the first coil of the galvanometer" }, { "unit": null, "symbol": "I_2", "meaning": "current through the second coil of the galvanometer" } ], "sympy": "Eq(delta, m*I_1 - n*I_2)", "physics": true, "states": [], "concepts": [ "concept/electric-current", "instrument/differential-galvanometer", "instrument/galvanometer" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/eq-e500ab6f04", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-xii", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 201", "location": "THE MEASUREMENT OF ELECTRIC RESISTANCE", "latex": "\\delta =\\frac{E}{D} \\{m(B + \\beta) - n(A + \\alpha)\\}\\text{,}", "name": null, "statement": "The needle deflexion in the differential galvanometer arrangement is proportional to the bracketed difference of the coil-resistance combinations, so zero deflexion means that bracket vanishes.", "kind": "result", "symbols": [ { "unit": null, "symbol": "delta", "meaning": "deflexion of the galvanometer needle" }, { "unit": null, "symbol": "E", "meaning": "electromotive force of the battery" }, { "unit": null, "symbol": "D", "meaning": "combined resistance determinant of the circuit" }, { "unit": null, "symbol": "m", "meaning": "coefficient of action of the first galvanometer coil" }, { "unit": null, "symbol": "n", "meaning": "coefficient of action of the second galvanometer coil" }, { "unit": null, "symbol": "A", "meaning": "resistance introduced into the first coil" }, { "unit": null, "symbol": "B", "meaning": "resistance introduced into the second coil" }, { "unit": null, "symbol": "alpha", "meaning": "remainder of the resistance of the first coil and its connexions" }, { "unit": null, "symbol": "beta", "meaning": "remainder of the resistance of the second coil and its connexions" } ], "sympy": "Eq(delta, E/D*(m*(B + beta) - n*(A + alpha)))", "physics": true, "states": [], "concepts": [ "concept/comparison-of-resistances", "instrument/differential-galvanometer", "method/null-method", "quantity/electromotive-force" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/eq-ce8d135990", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-xii", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 201", "location": "THE MEASUREMENT OF ELECTRIC RESISTANCE", "latex": "D = (A + \\alpha)(B + \\beta) + r(A + \\alpha + B + \\beta)\\text{.}", "name": null, "statement": "D is defined as the combined resistance quantity of the differential galvanometer circuit, built from the two coil branches and the battery resistance r.", "kind": "definition", "symbols": [ { "unit": null, "symbol": "D", "meaning": "combined resistance quantity of the circuit" }, { "unit": null, "symbol": "A", "meaning": "resistance introduced into the first coil" }, { "unit": null, "symbol": "B", "meaning": "resistance introduced into the second coil" }, { "unit": null, "symbol": "alpha", "meaning": "remainder of the resistance of the first coil and its connexions" }, { "unit": null, "symbol": "beta", "meaning": "remainder of the resistance of the second coil and its connexions" }, { "unit": null, "symbol": "r", "meaning": "resistance of the battery between C and D" } ], "sympy": "Eq(D, (A + alpha)*(B + beta) + r*(A + alpha + B + beta))", "physics": false, "states": [], "concepts": [ "concept/formula", "instrument/differential-galvanometer", "quantity/resistance" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/eq-83478d15e6", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-xii", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 203", "location": "THE MEASUREMENT OF ELECTRIC RESISTANCE", "latex": "B - A = \\frac{1}{2nE} (A + \\alpha)(A + \\alpha + 2r)(\\delta - \\delta')\\text{.}", "name": null, "statement": "When the resistances and coil constants are approximately equal, the difference B - A is approximately given by the smallest observable deflexion difference times a factor depending on the circuit.", "kind": "approximation", "symbols": [ { "unit": null, "symbol": "B", "meaning": "resistance introduced into the second coil" }, { "unit": null, "symbol": "A", "meaning": "resistance introduced into the first coil" }, { "unit": null, "symbol": "n", "meaning": "coefficient of action of the second galvanometer coil" }, { "unit": null, "symbol": "E", "meaning": "electromotive force of the battery" }, { "unit": null, "symbol": "alpha", "meaning": "remainder of the resistance of the first coil and its connexions" }, { "unit": null, "symbol": "r", "meaning": "resistance of the battery between C and D" }, { "unit": null, "symbol": "delta", "meaning": "deflexion in the first observation" }, { "unit": null, "symbol": "delta'", "meaning": "deflexion in the second observation after exchange" } ], "sympy": null, "physics": true, "states": [], "concepts": [ "concept/approximation", "concept/comparison-of-resistances", "concept/small-variation", "instrument/differential-galvanometer", "method/null-method" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/eq-535fbd3eaa", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-xii", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 203", "location": "THE MEASUREMENT OF ELECTRIC RESISTANCE", "latex": "\\alpha = \\tfrac{1}{3} A\\text{;}", "name": null, "statement": "For a battery of negligible resistance, the galvanometer coil resistance should be one-third of the resistance being measured.", "kind": "result", "symbols": [ { "unit": null, "symbol": "alpha", "meaning": "remainder of the resistance of the galvanometer coil and its connexions" }, { "unit": null, "symbol": "A", "meaning": "resistance to be measured in the first coil" } ], "sympy": "Eq(alpha, A/3)", "physics": true, "states": [], "concepts": [ "concept/comparison-of-resistances", "concept/optimal-design", "instrument/galvanometer", "quantity/resistance" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/eq-9ba64bdcaa", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-xii", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 203", "location": "THE MEASUREMENT OF ELECTRIC RESISTANCE", "latex": "\\frac{B - A}{A} = \\frac{2}{3}\\frac{\\delta - \\delta'}{\\Delta}\\text{.}", "name": null, "statement": "The fractional difference between the two resistances is two-thirds of the smallest observable deflexion divided by the deflexion produced by one coil alone.", "kind": "result", "symbols": [ { "unit": null, "symbol": "B", "meaning": "resistance introduced into the second coil" }, { "unit": null, "symbol": "A", "meaning": "resistance introduced into the first coil" }, { "unit": null, "symbol": "delta", "meaning": "deflexion in the first observation" }, { "unit": null, "symbol": "delta'", "meaning": "deflexion in the second observation after exchange" }, { "unit": null, "symbol": "Delta", "meaning": "deflexion produced when the current flows through one coil only" } ], "sympy": "Eq((B - A)/A, Rational(2, 3)*(delta - delta_p)/Delta)", "physics": true, "states": [], "concepts": [ "concept/comparison-of-resistances", "concept/small-variation", "instrument/differential-galvanometer", "method/null-method" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/eq-e630cd921f", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-xii", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 203", "location": "THE MEASUREMENT OF ELECTRIC RESISTANCE", "latex": "\\Delta = \\frac{mE}{A + \\alpha + r} = \\frac{3}{4}\\frac{nE}{A}\\text{ if }r = 0\\text{ and }\\alpha = \\frac{1}{3} A\\text{.}", "name": null, "statement": "The deflexion produced by one galvanometer coil alone is mE over the total resistance, which reduces to three-quarters of nE/A when r is zero and alpha is one-third of A.", "kind": "result", "symbols": [ { "unit": null, "symbol": "Delta", "meaning": "deflexion produced when the current flows through one coil only" }, { "unit": null, "symbol": "m", "meaning": "coefficient of action of the first galvanometer coil" }, { "unit": null, "symbol": "n", "meaning": "coefficient of action of the second galvanometer coil" }, { "unit": null, "symbol": "E", "meaning": "electromotive force of the battery" }, { "unit": null, "symbol": "A", "meaning": "resistance introduced into the first coil" }, { "unit": null, "symbol": "alpha", "meaning": "remainder of the resistance of the galvanometer coil and its connexions" }, { "unit": null, "symbol": "r", "meaning": "resistance of the battery and its connexions" } ], "sympy": null, "physics": true, "states": [], "concepts": [ "instrument/differential-galvanometer", "instrument/galvanometer", "quantity/electromotive-force", "quantity/resistance" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/eq-dd955426fe", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-xii", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 204", "location": "THE MEASUREMENT OF ELECTRIC RESISTANCE", "latex": "b \\beta = c \\gamma\\text{,}", "name": "Wheatstone's bridge balance condition", "statement": "The bridge gives no current in the galvanometer branch when the product of the opposite arm resistances b and beta equals the product of c and gamma.", "kind": "law", "symbols": [ { "unit": null, "symbol": "b", "meaning": "resistance of conductor CA" }, { "unit": null, "symbol": "c", "meaning": "resistance of conductor AB" }, { "unit": null, "symbol": "beta", "meaning": "resistance of conductor BO" }, { "unit": null, "symbol": "gamma", "meaning": "resistance of conductor OC" } ], "sympy": "Eq(b*beta, c*gamma)", "physics": true, "states": [ "law/wheatstone-s-bridge-balance-condition" ], "concepts": [ "concept/comparison-of-resistances", "concept/conjugate-conductors", "instrument/wheatstone-s-bridge", "method/null-method", "quantity/resistance" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/eq-1ed5ae6afb", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-xii", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 204", "location": "THE MEASUREMENT OF ELECTRIC RESISTANCE", "latex": "O = \\frac{B \\gamma + C \\beta}{ \\beta + \\gamma}\\text{,}", "name": null, "statement": "The potential at O is the weighted average of the potentials at B and C, weighted by the opposite resistances.", "kind": "result", "symbols": [ { "unit": null, "symbol": "O", "meaning": "potential at the point O" }, { "unit": null, "symbol": "B", "meaning": "potential at the point B" }, { "unit": null, "symbol": "C", "meaning": "potential at the point C" }, { "unit": null, "symbol": "beta", "meaning": "resistance of conductor BO" }, { "unit": null, "symbol": "gamma", "meaning": "resistance of conductor OC" } ], "sympy": "Eq(O, (B*gamma + C*beta)/(beta + gamma))", "physics": true, "states": [], "concepts": [ "concept/point", "instrument/wheatstone-s-bridge", "quantity/electric-potential", "quantity/resistance" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/eq-a8d2c270f2", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-xii", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 205", "location": "THE MEASUREMENT OF ELECTRIC RESISTANCE", "latex": "\\xi = \\frac{E}{D}(b\\beta - c\\gamma)\\text{,}", "name": null, "statement": "The current along OA in the bridge is proportional to the departure of the bridge from balance, b beta minus c gamma.", "kind": "result", "symbols": [ { "unit": null, "symbol": "xi", "meaning": "current along the conductor OA" }, { "unit": null, "symbol": "E", "meaning": "electromotive force acting along BC" }, { "unit": null, "symbol": "D", "meaning": "determinant of the bridge system of equations" }, { "unit": null, "symbol": "b", "meaning": "resistance of conductor CA" }, { "unit": null, "symbol": "c", "meaning": "resistance of conductor AB" }, { "unit": null, "symbol": "beta", "meaning": "resistance of conductor BO" }, { "unit": null, "symbol": "gamma", "meaning": "resistance of conductor OC" } ], "sympy": "Eq(xi, E/D*(b*beta - c*gamma))", "physics": true, "states": [], "concepts": [ "concept/electric-current", "instrument/wheatstone-s-bridge", "method/null-method", "quantity/electromotive-force" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/eq-f75a775690", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-xii", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 205", "location": "THE MEASUREMENT OF ELECTRIC RESISTANCE", "latex": "D = abc + bc(\\beta+\\gamma)+ca(\\gamma+\\alpha)+ab(\\alpha+\\beta)+(a+b+c)(\\beta\\gamma+\\gamma\\alpha+\\alpha\\beta)", "name": null, "statement": "The bridge determinant D is written in a symmetrical form in the six conductor resistances.", "kind": "definition", "symbols": [ { "unit": null, "symbol": "D", "meaning": "determinant of the bridge system of equations" }, { "unit": null, "symbol": "a", "meaning": "resistance of the conductor BC" }, { "unit": null, "symbol": "b", "meaning": "resistance of the conductor CA" }, { "unit": null, "symbol": "c", "meaning": "resistance of the conductor AB" }, { "unit": null, "symbol": "alpha", "meaning": "resistance of the conductor OA" }, { "unit": null, "symbol": "beta", "meaning": "resistance of the conductor OB" }, { "unit": null, "symbol": "gamma", "meaning": "resistance of the conductor OC" } ], "sympy": "Eq(D, a*b*c + b*c*(beta + gamma) + c*a*(gamma + alpha) + a*b*(alpha + beta) + (a + b + c)*(beta*gamma + gamma*alpha + alpha*beta))", "physics": false, "states": [], "concepts": [ "concept/determinant", "concept/symmetry", "instrument/wheatstone-s-bridge", "law/kirchhoff-s-laws", "quantity/resistance" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/eq-5abcd1a512", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-xii", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 207", "location": "THE MEASUREMENT OF ELECTRIC RESISTANCE", "latex": "G = n(1 - n)(R + S)\\text{.}", "name": null, "statement": "The best galvanometer resistance for a bridge with m equal to n is n(1 - n) times the sum of the total bridge resistance R and the total resistance S of BOC.", "kind": "result", "symbols": [ { "unit": null, "symbol": "G", "meaning": "resistance of the galvanometer and its connexions" }, { "unit": null, "symbol": "n", "meaning": "fraction of the BOC wire read off on the slide" }, { "unit": null, "symbol": "R", "meaning": "whole resistance of BAC" }, { "unit": null, "symbol": "S", "meaning": "whole resistance of BOC" } ], "sympy": "Eq(G, n*(1 - n)*(R + S))", "physics": true, "states": [], "concepts": [ "concept/optimal-design", "instrument/galvanometer", "instrument/wheatstone-s-bridge", "quantity/resistance" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/eq-7bc463f847", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-xii", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 208", "location": "THE MEASUREMENT OF ELECTRIC RESISTANCE", "latex": "B =\\frac{RS}{R + S}\\text{.}", "name": null, "statement": "For a battery of given total electrode area, the most advantageous battery resistance is RS over R plus S.", "kind": "result", "symbols": [ { "unit": null, "symbol": "B", "meaning": "resistance of the battery and its connexions" }, { "unit": null, "symbol": "R", "meaning": "whole resistance of BAC" }, { "unit": null, "symbol": "S", "meaning": "whole resistance of BOC" } ], "sympy": "Eq(B, R*S/(R + S))", "physics": true, "states": [], "concepts": [ "concept/battery", "concept/optimal-design", "instrument/wheatstone-s-bridge", "quantity/resistance" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/eq-9bd792f824", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-xii", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 208", "location": "THE MEASUREMENT OF ELECTRIC RESISTANCE", "latex": "S^2 = \\frac{BR}{B + R}\\left(R +\\frac{G}{n(1 - n)}\\right)\\text{.}", "name": null, "statement": "The value of S that makes a given change in n produce the greatest galvanometer deflexion is found from this relation, obtained by differentiating the current expression.", "kind": "result", "symbols": [ { "unit": null, "symbol": "S", "meaning": "whole resistance of BOC" }, { "unit": null, "symbol": "B", "meaning": "resistance of the battery and its connexions" }, { "unit": null, "symbol": "R", "meaning": "whole resistance of BAC" }, { "unit": null, "symbol": "G", "meaning": "resistance of the galvanometer and its connexions" }, { "unit": null, "symbol": "n", "meaning": "fraction of the BOC wire read off on the slide" } ], "sympy": "Eq(S**2, B*R/(B + R)*(R + G/(n*(1 - n))))", "physics": true, "states": [], "concepts": [ "concept/optimal-design", "instrument/galvanometer", "instrument/wheatstone-s-bridge", "method/differentiation", "quantity/resistance" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/eq-02ef363089", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-xii", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 208", "location": "THE MEASUREMENT OF ELECTRIC RESISTANCE", "latex": "G = 2n(1-n)R\\text{,}", "name": null, "statement": "For many determinations of nearly equal resistance, the best galvanometer resistance is 2n(1-n) times R, with S equal to R and B equal to half of R.", "kind": "result", "symbols": [ { "unit": null, "symbol": "G", "meaning": "resistance of the galvanometer and its connexions" }, { "unit": null, "symbol": "n", "meaning": "fraction of the BOC wire read off on the slide" }, { "unit": null, "symbol": "R", "meaning": "whole resistance of BAC" } ], "sympy": "Eq(G, 2*n*(1 - n)*R)", "physics": true, "states": [], "concepts": [ "concept/optimal-design", "instrument/galvanometer", "instrument/wheatstone-s-bridge", "quantity/resistance" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/eq-68850259e4", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-xii", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 207", "location": "THE MEASUREMENT OF ELECTRIC RESISTANCE", "latex": "\\delta = C \\sqrt{G} \\xi\\text{,}", "name": null, "statement": "The deviation of the galvanometer needle is proportional to the square root of the galvanometer resistance times the current in its wire.", "kind": "law", "symbols": [ { "unit": null, "symbol": "delta", "meaning": "deviation of the galvanometer needle" }, { "unit": null, "symbol": "C", "meaning": "a constant of the galvanometer" }, { "unit": null, "symbol": "G", "meaning": "resistance of the galvanometer wire" }, { "unit": null, "symbol": "xi", "meaning": "current in the galvanometer wire" } ], "sympy": "Eq(delta, C*sqrt(G)*xi)", "physics": true, "states": [], "concepts": [ "concept/electric-current", "concept/proportionality", "instrument/galvanometer", "quantity/resistance" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/eq-0c2541ef19", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-xiii", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 216", "location": "ON THE ELECTRIC RESISTANCE OF SUBSTANCES", "latex": "r = \\alpha T^{\\frac{1}{2}} + \\beta T + \\gamma", "name": null, "statement": "Siemens's empirical formula gives the resistance of a metal as a function of absolute temperature, with three constants fitted to the data.", "kind": "formula", "symbols": [ { "unit": null, "symbol": "r", "meaning": "electric resistance of the metal (as used in this formula; the book gives no unit here)" }, { "unit": null, "symbol": "T", "meaning": "absolute temperature reckoned from -273°C" }, { "unit": null, "symbol": "\\alpha", "meaning": "constant in Siemens's formula" }, { "unit": null, "symbol": "\\beta", "meaning": "constant in Siemens's formula" }, { "unit": null, "symbol": "\\gamma", "meaning": "constant in Siemens's formula" } ], "sympy": "Eq(r, alpha*T**(1/2) + beta*T + gamma)", "physics": true, "states": [], "concepts": [ "concept/conduction-of-heat", "concept/metal", "concept/temperature", "quantity/absolute-temperature", "quantity/resistance" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/eq-6fa9caabb2", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-xiii", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 218", "location": "ON THE ELECTRIC RESISTANCE OF SUBSTANCES", "latex": "\\rho = \\frac{R_1 - R_2}{{R_1}' - {R_2}'}", "name": null, "statement": "Paalzow's ratio: the resistance of an electrolyte divided by that of mercury of the same form at 0°C, found from two siphons of different lengths, with the polarization-cancelling difference taken in each case.", "kind": "formula", "symbols": [ { "unit": null, "symbol": "\\rho", "meaning": "ratio of the resistance of the electrolyte to that of mercury at 0°C of the same form" }, { "unit": null, "symbol": "R_1", "meaning": "observed resistance of the electrolyte in the first (shorter) siphon" }, { "unit": null, "symbol": "R_2", "meaning": "observed resistance of the electrolyte in the second (longer) siphon" }, { "unit": null, "symbol": "{R_1}'", "meaning": "resistance of the first siphon when filled with mercury" }, { "unit": null, "symbol": "{R_2}'", "meaning": "resistance of the second siphon when filled with mercury" } ], "sympy": "Eq(rho, (R_1 - R_2)/(Rp_1 - Rp_2))", "physics": true, "states": [], "concepts": [ "concept/common-ratio", "concept/electrolyte", "concept/mercury", "concept/polarization", "quantity/resistance" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/eq-1c10bf3661", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-xiii", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 216", "location": "ON THE ELECTRIC RESISTANCE OF SUBSTANCES", "latex": "r &= 0.039369T^{\\frac{1}{2}} + 0.00216407T - 0.2413\\text{,}", "name": null, "statement": "The fitted resistance formula for platinum, with its numerical constants.", "kind": "formula", "symbols": [ { "unit": null, "symbol": "r", "meaning": "resistance of platinum" }, { "unit": null, "symbol": "T", "meaning": "absolute temperature reckoned from -273°C" } ], "sympy": "Eq(r, 0.039369*T**(1/2) + 0.00216407*T - 0.2413)", "physics": true, "states": [], "concepts": [ "concept/metal", "concept/temperature", "quantity/absolute-temperature", "quantity/resistance" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/eq-c70d5f336b", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-xiii", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 216", "location": "ON THE ELECTRIC RESISTANCE OF SUBSTANCES", "latex": "r &= 0.026577T^{\\frac{1}{2}} + 0.0031443T - 0.22751\\text{,}", "name": null, "statement": "The fitted resistance formula for copper, with its numerical constants.", "kind": "formula", "symbols": [ { "unit": null, "symbol": "r", "meaning": "resistance of copper" }, { "unit": null, "symbol": "T", "meaning": "absolute temperature reckoned from -273°C" } ], "sympy": "Eq(r, 0.026577*T**(1/2) + 0.0031443*T - 0.22751)", "physics": true, "states": [], "concepts": [ "concept/metal", "concept/temperature", "quantity/absolute-temperature", "quantity/resistance" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/eq-45c9d1f410", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-xiii", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 216", "location": "ON THE ELECTRIC RESISTANCE OF SUBSTANCES", "latex": "r &= 0.072545T^{\\frac{1}{2}} + 0.0038133T - 1.23971\\text{.}", "name": null, "statement": "The fitted resistance formula for iron, with its numerical constants.", "kind": "formula", "symbols": [ { "unit": null, "symbol": "r", "meaning": "resistance of iron" }, { "unit": null, "symbol": "T", "meaning": "absolute temperature reckoned from -273°C" } ], "sympy": "Eq(r, 0.072545*T**(1/2) + 0.0038133*T - 1.23971)", "physics": true, "states": [], "concepts": [ "concept/metal", "concept/temperature", "quantity/absolute-temperature", "quantity/resistance" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/eq-a5e80daab9", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-xiii", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 216", "location": "ON THE ELECTRIC RESISTANCE OF SUBSTANCES", "latex": "r = \\alpha T^{\\frac{1}{2}} + \\beta T + \\gamma\\text{,}", "name": null, "statement": "Siemens's empirical formula gives a metal's resistance r as a function of absolute temperature T, with constants alpha, beta and gamma fitted to each metal.", "kind": "formula", "symbols": [ { "unit": null, "symbol": "r", "meaning": "resistance of the metal" }, { "unit": null, "symbol": "T", "meaning": "absolute temperature reckoned from -273°C" }, { "unit": null, "symbol": "\\alpha", "meaning": "constant of the formula" }, { "unit": null, "symbol": "\\beta", "meaning": "constant of the formula" }, { "unit": null, "symbol": "\\gamma", "meaning": "constant of the formula" } ], "sympy": "Eq(r, alpha*T**(1/2) + beta*T + gamma)", "physics": true, "states": [], "concepts": [ "concept/constant", "concept/metal", "quantity/absolute-temperature", "quantity/resistance" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/eq-24dc874c31", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-xiii", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 218", "location": "ON THE ELECTRIC RESISTANCE OF SUBSTANCES", "latex": "\\rho = \\frac{R_1 - R_2}{{R_1}' - {R_2}'}.", "name": null, "statement": "The ratio of an electrolyte's resistance to that of mercury of the same form is found from the difference of the two siphon resistances filled with electrolyte divided by the difference of the two filled with mercury.", "kind": "formula", "symbols": [ { "unit": null, "symbol": "\\rho", "meaning": "ratio of the resistance of the electrolyte to that of mercury at 0°C of the same form" }, { "unit": null, "symbol": "R_1", "meaning": "observed resistance of the electrolyte in the first siphon" }, { "unit": null, "symbol": "R_2", "meaning": "observed resistance of the electrolyte in the second siphon" }, { "unit": null, "symbol": "{R_1}'", "meaning": "resistance of the first siphon when filled with mercury" }, { "unit": null, "symbol": "{R_2}'", "meaning": "resistance of the second siphon when filled with mercury" } ], "sympy": "Eq(rho, (R_1 - R_2)/(Rp_1 - Rp_2))", "physics": true, "states": [], "concepts": [ "concept/electrolyte", "concept/mercury", "concept/polarization", "quantity/resistance" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/eq-9d52bb38e0", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-xiii", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 222", "location": "ON THE ELECTRIC RESISTANCE OF SUBSTANCES", "latex": "R = r \\times 0.8878^t\\text{,}", "name": null, "statement": "The resistance of gutta-percha at temperature T+t is the resistance r at T multiplied by 0.8878 raised to the power t, an empirical formula found by Bright and Clark.", "kind": "approximation", "symbols": [ { "unit": null, "symbol": "R", "meaning": "resistance of gutta-percha at temperature T + t" }, { "unit": null, "symbol": "r", "meaning": "resistance of gutta-percha at temperature T" }, { "unit": null, "symbol": "t", "meaning": "change of temperature in degrees centigrade" } ], "sympy": "Eq(R, r*0.8878**t)", "physics": true, "states": [], "concepts": [ "concept/dielectric", "concept/temperature", "quantity/resistance" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/eq-2edecd0101", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-xiii", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 223", "location": "ON THE ELECTRIC RESISTANCE OF SUBSTANCES", "latex": "E = E_0 + RC\\text{.}", "name": null, "statement": "In a rarefied gas the electromotive force is a constant E_0 (the polarization of the electrodes) plus the part that drives the current C through the resistance R according to Ohm's law.", "kind": "law", "symbols": [ { "unit": null, "symbol": "E", "meaning": "electromotive force applied to the rarefied gas" }, { "unit": null, "symbol": "E_0", "meaning": "constant electromotive force of the electrode polarization" }, { "unit": null, "symbol": "R", "meaning": "resistance of the rarefied gas" }, { "unit": null, "symbol": "C", "meaning": "intensity of the current" } ], "sympy": "Eq(E, E_0 + R*C)", "physics": true, "states": [], "concepts": [ "concept/constant", "concept/electric-current", "concept/polarization", "law/ohm-s-law", "quantity/electromotive-force", "quantity/resistance" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/eq-d1b8647405", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-xiii", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 225", "location": "ON THE ELECTRIC RESISTANCE OF SUBSTANCES", "latex": "( P + G + Q )\\overline{ x + y} - Gy - Qz &= 0", "name": null, "statement": "First current equation for the bridge: Ohm's law applied to circuit PGQ, with the sum of the resistances around that circuit times its current, minus the neighbouring circuit currents times the shared resistances, equals zero.", "kind": "law", "symbols": [ { "unit": null, "symbol": "P", "meaning": "resistance of conductor P" }, { "unit": null, "symbol": "Q", "meaning": "resistance of conductor Q" }, { "unit": null, "symbol": "G", "meaning": "resistance of conductor G (galvanometer arm)" }, { "unit": null, "symbol": "x", "meaning": "current in circuit PGQ" }, { "unit": null, "symbol": "y", "meaning": "current in circuit RSG" }, { "unit": null, "symbol": "z", "meaning": "current in circuit QSB" } ], "sympy": "Eq((P + G + Q)*(x + y) - G*y - Q*z, 0)", "physics": true, "states": [], "concepts": [ "concept/electric-circuit", "concept/electric-current", "concept/linear-conductor", "instrument/wheatstone-s-bridge", "law/ohm-s-law", "quantity/resistance" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/eq-2ac0395ca5", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-xiii", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 225", "location": "ON THE ELECTRIC RESISTANCE OF SUBSTANCES", "latex": " ( R + S + G )y - Sz - G \\overline{x + y} &= 0", "name": null, "statement": "Second current equation for the bridge: Ohm's law applied to circuit RSG, equal to zero since its electromotive force is zero.", "kind": "law", "symbols": [ { "unit": null, "symbol": "R", "meaning": "resistance of conductor R" }, { "unit": null, "symbol": "S", "meaning": "resistance of conductor S" }, { "unit": null, "symbol": "G", "meaning": "resistance of conductor G (galvanometer arm)" }, { "unit": null, "symbol": "x", "meaning": "current in circuit PGQ" }, { "unit": null, "symbol": "y", "meaning": "current in circuit RSG" }, { "unit": null, "symbol": "z", "meaning": "current in circuit QSB" } ], "sympy": "Eq(-G*(x + y) + (R + S + G)*y - S*z, 0)", "physics": true, "states": [], "concepts": [ "concept/electric-circuit", "concept/electric-current", "concept/linear-conductor", "instrument/wheatstone-s-bridge", "law/ohm-s-law", "quantity/resistance" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/eq-5518a7e0ae", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-xiii", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 225", "location": "ON THE ELECTRIC RESISTANCE OF SUBSTANCES", "latex": "( Q + S + B )z - Sy - Q \\overline{x + y} &= E", "name": null, "statement": "Third current equation for the bridge: Ohm's law applied to circuit QSB, whose total electromotive force is the battery electromotive force E.", "kind": "law", "symbols": [ { "unit": null, "symbol": "Q", "meaning": "resistance of conductor Q" }, { "unit": null, "symbol": "S", "meaning": "resistance of conductor S" }, { "unit": null, "symbol": "B", "meaning": "resistance of conductor B" }, { "unit": null, "symbol": "E", "meaning": "electromotive force of the battery" }, { "unit": null, "symbol": "x", "meaning": "current in circuit PGQ" }, { "unit": null, "symbol": "y", "meaning": "current in circuit RSG" }, { "unit": null, "symbol": "z", "meaning": "current in circuit QSB" } ], "sympy": "Eq((Q + S + B)*z - S*y - Q*(x + y), E)", "physics": true, "states": [], "concepts": [ "concept/electric-circuit", "concept/electric-current", "instrument/wheatstone-s-bridge", "law/ohm-s-law", "quantity/electromotive-force", "quantity/resistance" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/eq-63c64b3508", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-xiii", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 225", "location": "ON THE ELECTRIC RESISTANCE OF SUBSTANCES", "latex": "( P + G + Q )x + ( P + Q )y - Qz &= 0 ", "name": null, "statement": "First current equation of the bridge in solved (rearranged) form, with the currents x, y, z as the unknowns.", "kind": "law", "symbols": [ { "unit": null, "symbol": "P", "meaning": "resistance of conductor P" }, { "unit": null, "symbol": "Q", "meaning": "resistance of conductor Q" }, { "unit": null, "symbol": "G", "meaning": "resistance of conductor G (galvanometer arm)" }, { "unit": null, "symbol": "x", "meaning": "current in circuit PGQ" }, { "unit": null, "symbol": "y", "meaning": "current in circuit RSG" }, { "unit": null, "symbol": "z", "meaning": "current in circuit QSB" } ], "sympy": "Eq((P + G + Q)*x + (P + Q)*y - Q*z, 0)", "physics": true, "states": [], "concepts": [ "concept/electric-current", "concept/linear-conductor", "instrument/wheatstone-s-bridge", "law/ohm-s-law", "quantity/resistance" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/eq-bd97b7d277", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-xiii", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 225", "location": "ON THE ELECTRIC RESISTANCE OF SUBSTANCES", "latex": "-Gx + ( R + S )y - Sz &= 0", "name": null, "statement": "Second current equation of the bridge in solved form.", "kind": "law", "symbols": [ { "unit": null, "symbol": "G", "meaning": "resistance of conductor G (galvanometer arm)" }, { "unit": null, "symbol": "R", "meaning": "resistance of conductor R" }, { "unit": null, "symbol": "S", "meaning": "resistance of conductor S" }, { "unit": null, "symbol": "x", "meaning": "current in circuit PGQ" }, { "unit": null, "symbol": "y", "meaning": "current in circuit RSG" }, { "unit": null, "symbol": "z", "meaning": "current in circuit QSB" } ], "sympy": "Eq(-G*x + (R + S)*y - S*z, 0)", "physics": true, "states": [], "concepts": [ "concept/electric-current", "concept/linear-conductor", "instrument/wheatstone-s-bridge", "law/ohm-s-law", "quantity/resistance" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/eq-e2e6655f2b", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-xiii", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 225", "location": "ON THE ELECTRIC RESISTANCE OF SUBSTANCES", "latex": "-Qx - ( S + Q )y + ( Q + S + B )z &= E", "name": null, "statement": "Third current equation of the bridge in solved form, equal to the battery electromotive force E.", "kind": "law", "symbols": [ { "unit": null, "symbol": "Q", "meaning": "resistance of conductor Q" }, { "unit": null, "symbol": "S", "meaning": "resistance of conductor S" }, { "unit": null, "symbol": "B", "meaning": "resistance of conductor B" }, { "unit": null, "symbol": "E", "meaning": "electromotive force of the battery" }, { "unit": null, "symbol": "x", "meaning": "current in circuit PGQ" }, { "unit": null, "symbol": "y", "meaning": "current in circuit RSG" }, { "unit": null, "symbol": "z", "meaning": "current in circuit QSB" } ], "sympy": "Eq(-Q*x - (S + Q)*y + (Q + S + B)*z, E)", "physics": true, "states": [], "concepts": [ "concept/electric-current", "instrument/wheatstone-s-bridge", "law/ohm-s-law", "quantity/electromotive-force", "quantity/resistance" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/eq-901085aa7b", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-xiii", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 225", "location": "ON THE ELECTRIC RESISTANCE OF SUBSTANCES", "latex": "& = \\frac{E(QR-PS)}{\\Delta}\\text{,}", "name": null, "statement": "The current x in the galvanometer arm, found by solving the system (II) by determinants, equals E(QR-PS) divided by the determinant Delta of the system.", "kind": "result", "symbols": [ { "unit": null, "symbol": "x", "meaning": "current in circuit PGQ, i.e. the current in the galvanometer G" }, { "unit": null, "symbol": "E", "meaning": "electromotive force of the battery" }, { "unit": null, "symbol": "P", "meaning": "resistance of conductor P" }, { "unit": null, "symbol": "Q", "meaning": "resistance of conductor Q" }, { "unit": null, "symbol": "R", "meaning": "resistance of conductor R" }, { "unit": null, "symbol": "S", "meaning": "resistance of conductor S" }, { "unit": null, "symbol": "\\Delta", "meaning": "determinant of the system of equations (II)" } ], "sympy": "Eq(x, E*(Q*R - P*S)/Delta)", "physics": true, "states": [], "concepts": [ "concept/determinant", "concept/electric-current", "instrument/galvanometer", "instrument/wheatstone-s-bridge", "quantity/electromotive-force" ] }, { "id": "maxwell-elementary-treatise-electricity-1888/eq-d803c495fa", "chapter": "maxwell-elementary-treatise-electricity-1888/ch-xiii", "book": "maxwell-elementary-treatise-electricity-1888", "edition": "Clarendon Press, 2nd ed., 1888, edited by William Garnett", "page": "scan 225", "location": "ON THE ELECTRIC RESISTANCE OF SUBSTANCES", "latex": "QR - PS = 0 \\text{, or } \\frac{P}{Q} =\\frac{R}{S}\\text{.}", "name": null, "statement": "The condition for no current in the galvanometer of the bridge: QR - PS = 0, equivalently P/Q = R/S.", "kind": "result", "symbols": [ { "unit": null, "symbol": "P", "meaning": "resistance of conductor P" }, { "unit": null, "symbol": "Q", "meaning": "resistance of conductor Q" }, { "unit": null, "symbol": "R", "meaning": "resistance of conductor R" }, { "unit": null, "symbol": "S", "meaning": "resistance of conductor S" } ], "sympy": "Eq(Q*R - P*S, 0)", "physics": true, "states": [], "concepts": [ "concept/electric-current", "instrument/galvanometer", "instrument/wheatstone-s-bridge", "quantity/resistance" ] } ], "exercise_sets": [], "problems": [], "errata_statuses": [ "transcriber_marked", "candidate", "probable", "confirmed", "dismissed", "note" ], "errata": [] }