{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Off-Axis Field of a Current Loop" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "*This simple formula can be obtained using the \n", "[Law of Biot Savart](../basics/biotsavart.html), \n", "integrated over a \n", "circular current loop to obrtain the magnetic field at any point in space. Compare this\n", "to the much simpler formula for calculating the \n", "[on-axis magnetic field due to a current loop](../solenoids/current_loop.html).*" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "![Magnetic field in vicinity of a current loop. Point is located at axial distance, x, and radius, r.](./offaxisloop.png \"Field due to a current loop\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Axial, Radial Components\n", "\n", "\n", "$B_x = B_0 \\frac 1 {\\pi \\sqrt Q} \\left[E(k) \\frac {1-\\alpha^2-\\beta^2}{Q-4\\alpha} + K(k) \\right]$\n", "\n", "\n", "$B_r = B_0 \\frac {\\gamma} {\\pi \\sqrt Q} \\left[E(k) \\frac {1+\\alpha^2+\\beta^2}{Q-4\\alpha} - K(k) \\right]$\n", "\n", "\n", "**$B$** is the magnetic field (Tesla) at any point in space that isn't on the current loop. It is equal to the sum of two field components: **$B_x$** the field component that is aligned with the axis and **$B_r$**, the field component that is in a radial direction. Symbols are defined:\n", "\n", "$\\alpha = \\frac r a $ and $\\beta = \\frac x a $ and $\\gamma = \\frac x r$\n", "\n", "$Q = \\left[\\left(1 + \\alpha\\right)^2 + \\beta^2 \\right]$\n", "\n", "$k = \\sqrt {\\frac {4 \\alpha} Q}$\n", "\n", "**$B_0$** is the magnetic field at the center of the coil: $B_0 = \\frac {i \\mu_0} {2a}$\n", " \n", "**$i$** is the current in the loop wire (Amperes)\n", "\n", "**$a$** is the loop radius (meters)\n", "\n", "**$\\mu_0$** is the permeability constant (approx. 1.26 x 10-6 or *exactly* π4 x 10-7)\n", "\n", "**$x$** is the distance in the axial direction from the center of the current loop to the field measurement point.\n", "\n", "**$r$** is the distance in the radial direction from the axis of the current loop to the field measurement point.\n", "\n", "**$K(k)$** is the complete elliptic integral function, of the first kind\n", "\n", "**$E(k)$** is the complete elliptic integral function, of the second kind.\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Online Calculator\n", "\n", "Please see the [online calculator](http://tiggerntatie.github.io/emagnet/offaxis/iloopcalculator.htm) for finding fields at any point in space due to a current loop.\n", "\n", "## Example Application\n", "\n", "The following Python code implements the formulas on this page and presents curves that show axial and radial field\n", "strength components in the vicinity of a 1m radius loop of wire carrying 1A of current.\n", "\n", "\n", "### Credits ###\n", "\n", "Formulas on this page are adapted from [SOME USEFUL INFORMATION FOR THE DESIGN OF AIR-CORE SOLENOIDS](https://drive.google.com/file/d/0Bw_DfnQIfCa-cWUxNzFOam1HeFk/view?usp=sharing&resourcekey=0-47IaCE6bVBVL4QbjV-QYgQ) by D. Bruce Montgomery \n", "and J. Terrell.\n", " \n" ] }, { "cell_type": "code", "execution_count": 24, "metadata": { "collapsed": false }, "outputs": [], "source": [ "%matplotlib inline\n", "from scipy.special import ellipk, ellipe, ellipkm1\n", "from numpy import pi, sqrt, linspace\n", "from pylab import plot, xlabel, ylabel, suptitle, legend, show\n", "\n", "uo = 4E-7*pi # Permeability constant - units of H/m\n", "Bo = lambda i, a, u=uo: i*u/2./a # Central field = f(current, loop radius, perm. constant)\n", "al = lambda r, a: r/a # Alpha = f(radius of measurement point, radius of loop)\n", "be = lambda x, a: x/a # Beta = f(axial distance to meas. point, radius of loop)\n", "ga = lambda x, r: x/r # Gamma = f(axial distance, radius to meas. point)\n", "Q = lambda r, x, a: (1 + al(r,a))**2 + be(x,a)**2 # Q = f(radius, distance to meas. point, loop radius)\n", "k = lambda r, x, a: sqrt(4*al(r,a)/Q(r,x,a)) # k = f(radius, distance to meas. point, loop radius)\n", "K = lambda k: ellipk(k**2.0) # Elliptic integral, first kind, as a function of k\n", "E = lambda k: ellipe(k**2.0) # Elliptic integral, second kind, as a function of k\n", "\n", "# On-Axis field = f(current and radius of loop, x of measurement point)\n", "def Baxial(i, a, x, u=uo):\n", " if a == 0:\n", " if x == 0:\n", " return NaN\n", " else:\n", " return 0.0\n", " else:\n", " return (u*i*a**2)/2.0/(a**2 + x**2)**(1.5)\n", "\n", "# Axial field component = f(current and radius of loop, r and x of meas. point)\n", "def Bx(i, a, x, r):\n", " if r == 0:\n", " if x == 0:\n", " return Bo(i,a) # central field\n", " else:\n", " return Baxial(i,a,x) # axial field\n", " else: # axial component, any location\n", " return Bo(i,a)*\\\n", " (E(k(r,x,a))*((1.0-al(r,a)**2-be(x,a)**2)/(Q(r,x,a)-4*al(r,a))) + K(k(r,x,a)))\\\n", " /pi/sqrt(Q(r,x,a))\n", " \n", "# Radial field component = f(current and radius of loop, r and x of meas. point)\n", "def Br(i, a, x, r):\n", " if r == 0:\n", " return 0 # no radial component on axis!\n", " else: # radial component, any location other than axis.\n", " return Bo(i,a)*ga(x,r)*\\\n", " (E(k(r,x,a))*((1.0+al(r,a)**2+be(x,a)**2)/(Q(r,x,a)-4*al(r,a))) - K(k(r,x,a)))\\\n", " /pi/sqrt(Q(r,x,a))\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Construct a family of field strength curves, as a function of radius and axial distance, for a unit coil (1m radius, 1A current):" ] }, { "cell_type": "code", "execution_count": 25, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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zaNkS/OtcZPvpbWw9uZXNJzez8shK6vvVp1/TfvRt2pd6fvUKX8qGDTBqlH7E\n5dtvoUmTAkf9NzmZnrt3803jxvSqUeOa32MHxOJWx42GHze0MrUQjkECZ/mQwCmsURcuKJKS4OJF\ncv9fvKifPNmxQ/8lJ5uDaMuWcFu7TI47R/Nz3M/8uvdXgn2Dc4NoA/8G1peUkwNffQXjxukgOmqU\nvh5qxZaUFLrv2sW00FD6BATk+S3zQiabIzfTdH5TqnW0fjOREJWdBM7yIYFTWFOsu2rPnzcH0e3b\n9U20/v7wwAPQo2cWaTVWs3DPLyzcu5CwGmG8fPvLdA/tjpPByj1ZR4/Cf/4DiYm69hkZaXWZ21NT\n6bZzJ581akT/wMC86Vl8noMvHKRNTBtcvKQ3ReF4JHCWD0cPnMK6Yr3MNb/sbKU2bFBq9GilQkOV\nqltXqWeeUeqPZRlq7o4fVauvW6nGXzRWX2/5Wl3KuHTtDHJylJo1S6kaNZQaO1apq1etLicmNVXV\nXLdOLTp37prf4h6NU/uG7ytV+oWwd6U9diuqCxcuqAceeEB5enqq4OBg9eOPPxY47uzZs1Xr1q2V\nj4+Puummm9Srr76a58XUnTp1Uu7u7srLy0t5eXmpJk2alDpdBa1nHORF1o6qGvALsAeIA9rm+73U\nO5SlPXuUeu89pW65RambblJq4sQc9ev2VarHjz1UzQ9qqvGrxquzaWevnfD4caV69FAqIkKp2Fir\n896cnKwC1q1TKxIT8wzPSMpQ629arxJXJFqdTojKrKyO3RspMzOz2OMOGDBADRgwQKWnp6t169Yp\nX19fFVvAOeGrr75S69atU5mZmerEiROqdevW6v3338/9PSoqSs2aNeu606+UBE5HNQd43PjZBcj/\nHEeZ7FyWtm9X6vHHlapWTalHH1Xql+g96sn/e1L5ve+nRv89Wl28fDHvBJa1z7lzrc4zOilJBaxb\npzYmJ+cZfv7382pDyAaVmVr8A1SIyuBGHLtlITg4WE2ePFlFREQod3f3PDXBgqSlpakqVaqoAwcO\n5A4bMmSIGjNmTLGW+fHHH6v7778/93tUVJSaOXNmyRNvRUHrGQcJnI7YAYIv0AH41vg9C0i+0Qtt\n0UL3wnfwIISFwUtDmrD7vRlMrLubM2nnaDy1MdM2TzN3vGAwwOOPw4oV8M478NRTcOVKnnl2qlaN\n75o0oeeuXexOS8sdXv2+6lSLqsbh0YdvdLaEEMW0YMECli5dSlJSEr169cLPz8/qX8+ePQHYv38/\nLi4uNGzp1qNWAAAgAElEQVRovlO+efPmxMbGFmt5q1evvubdna+99hoBAQG0b9+e1atXl13mRKXX\nAtgIfAdsA74BPPKNUyalssJkZiq1cKFSHToo1bixUh/O3aE6z+msmkxtohbvW6xycnLMIycnK9Wv\nn1ItWyp18OA18/rx9GlV959/1MFL5uum0mQrHFGRx65++Ov6/0ooJCREfffddyWaZs2aNapWrVp5\nhs2YMUNFRUUVOe2sWbNUUFCQunDhQu6wjRs3qrS0NJWRkaHmzJmjvL291aFDh0qUJpOC1jMOUuN0\nxFsvXYBWwLPAZuBTYAww1nKk8ePH536OiooiKiqqbBPhAr176ztw//4bxoxpjpPzXwx+ZSmv/j2K\nT/79hI/u/YgWtVrozuJ/+gm+/BJuvx2+/lpPbDSwZk2Ss7K4JyaGdS1bUsfNDddqroR+Hcq+Yfto\ns0vushUCuK53516voKCgEo3v5eVFSr7uOZOTk4t8ufSiRYt4/fXXWbFiBf4WvY3deuutuZ+HDBnC\n/Pnz+eOPP3j22WdLlC5L0dHRREdHl3p6YT9qAUcsvrcHluQbp1SlsOuRna3UTz8p1aiRUnfenale\n/XmaqvlBTfXSspdUeka6ecSNG5UKDlbqpZd0tdXC+/HxqunGjep8RkbusD1D96h9z8hdtsIx2OLY\nLY6QkBC1YsWK3O9du3bNvbs1/999992nlLJ+jXPw4MHqtddeK3A5S5cuVQEBAWrz5s1Fpqlr167q\niy++KFV+ClrPOEiN01GtAUKNn8cDk/P9XqqdqSxkZCg1Y4Z+lKV7v3Oq15yHVYPPGqjoI9HmkS5c\nUKpzZ6W6ddPNuBZGHzyobt2yRaUZbz6QJlvhSGx57BYmf+AsrgEDBqiBAweq9PR0tXbtWuXr66vi\n4uKsjrtixQrl7++v1q5de81vFy9eVMuWLVOXL19WmZmZ6ocfflCenp55gnJJFLSekcBZqTVHN9PG\nAAsph7tqS+rSJaUmTFCqenWlHp30m6r7UV01fMlwlXIlRY+QkaHUU08pFR6u1NGjudPl5OSooXv2\nqO4xMSozO1spZbzLtp7cZSsqv4pw7FpT2sCZmJiY5znO+fPn5/4WHx+vvLy81LFjx5RSSt15553K\n1dXVau317Nmz6pZbblHe3t6qWrVq6vbbb1fLly8vdX4KWs84SOCUHh6sM+4DtnfwIDzzDJxMvEj9\np0cRk/Y3X/f4mq4Nu+rrNZ9/DpMnw8KF0FY/jpqZk8P9u3Zxs7s7X4eGYjAY2PvYXpw8nAj9MrSI\nJQphv6TnoPLh6D0HVfoMllKFCZyg4+OCBfDSS9Cm/9/E3PwknRvcxWddP8PbzRt+/x2GDoUvvoAB\nAwBIzcoiascOetWowdiQEDIvZrIlYgtN5jTB7y4/22ZIiBtEAmf5cPTA6YjPcdodgwEGDoS4OKhz\n+R4yPtvF0SMGWs9ozfZT26F7d/285+jR+plPpfB2ceH3iAhmnz7Nt6dO5bnLNiv1Ol/SLYQQDqzS\nlwxKqULVOPNbvx6GDQO/jvPZ32AkYzu9xXO3PofhzBno1QtCQ3VvC1WqsO/SJTpt3853TZrQrXp1\n9g7bi8HVQOPpjW2dDSHKnNQ4y4fUOIXdadcOtm6FVq4DqfL9Br5c9z29f+pNom8ViI7W7zvr2RPS\n02ns4cGv4eEM2buXLSkpNPy4IYl/JJL4V6KtsyGEEHZJAqed8vCAqVNh1gcNSf10Pcd316fF9Jas\nO7dV3yhUpw7cfTdcuMDtvr58ExpKz927ia+SSeOZjdn35D6ykqXJVgghSkoCp53r1g1itlUhKPZj\nXP78kgd+7MukDVPImfkNREVB+/aQkMADAQG8GRzMfTt3ou70xr+bPwdfOmjr5AshhN2p9G3RpVSh\nr3Fao5R+//UrE07g+2RfWjWsw+wHZuM9bSZ88gksWwZNm/LKoUNsTElhWf1m7GyxjUZfNqL6fdVt\nnXwhyoRc4ywfjn6Ns9JnsJTsLnCaHDwI/QZeJfmOZ3FruJ7/G7iIRks3wssvw6JF5LRty0Oxsbg5\nOfHF6VrsHbKXW3bdgqufq62TLsR1k8BZPhw9cEpTbSXTsCFsWOtG50vfkLR0JG2/uYOlt1WH2bOh\nZ0+cli1jblgYh69c4ZN6yQT0DuDg89JkK4QQxSWBsxJyd4cZM2DyQ0+RPe9XBv30BJO8tqN++w2G\nDqXqokX8Fh7Oj2fO8M8LHiSvT+b8b+dtnWwhRD6JiYn07t0bLy8vQkJCmD9/foHjLliwgCZNmuDr\n60uNGjV48MEHOXnyZO7vXl5eeHt75/65uLgwcuRIAI4ePYqTk1Oe3999990bnj9RuZS6D8eKZudO\npepFHleBr9+qHvixj0rfuE6pWrWUmjtX7UlLU4Hr1qm/lySof2r/o66eu2rr5ApxXezh2M3MLH6f\n0QMGDFADBgxQ6enpat26dcrX11fFxsZaHTchIUGdOXNGKaXfrDJo0CDVv39/q+OmpaUpLy+v3A7h\njxw5ogwGQ973ABeioPWMg/RVKzXOSi4iAnasrUu7/atZu9yH1v8+w6lFP8CYMTSZN4//NmvGw9US\ncOrjx4HhB+T6kBA3QEhICFOmTCEyMhJvb2+ys7OLnCY9PZ2FCxcyYcIEPDw8uOOOO+jVqxdz5861\nOn5QUBCBgYEAKKVwdnamdu3aVsf95ZdfqFmzJu3bt88zPCcnp4Q5c0wSOB2Ajw8s/K87rzWdxfHf\nHyFy5aPs+ukLmDSJTnPm8HGDBjzSJ4nk2DTOzDtj6+QKUSktWLCApUuXkpSURK9evfDz87P617Nn\nTwD279+Pi4sLDRs2zJ1H8+bNiY2NLXAZ69ato1q1avj4+JCQkMDkyfnfmKjNmTOHIUOGXDM8ODiY\noKAgHn/8cS5cuHCdOa68XGydAFE+DAZ4+WUDzZuPou+bDWiX+R9+mfUuXZ7+gMHp6Rx5+GEmv3GW\nV148RLWO1XC/2d3WSRaizBmio8tkPioqqmTLNRgYOXIkdevWBWDJkiVFTpOWloaPj0+eYd7e3qSm\nphY4Tfv27bl48SInT55k6NChvPLKK3z22Wd5xomPj2fNmjV89913ucMCAgLYsmULLVq04Pz584wY\nMYJBgwaxbNmykmTTYUjgdDCdO8Pm4N7cOzSIPlm9eH/KMEa8OY8309MZOngwax5OxXPoXlosb47B\nqdLfVS4cTEkDXlkKCgoq0fheXl6kpKTkGZacnIy3t3eR09apU4cJEybQtWvXawLn3Llz6dChA8HB\nwbnDPD09adWqFQCBgYFMnTqV2rVrk56ejqenZ4nS7QjstanWFegOTAZ+AhYYP3dHCgNFatQIdvzR\nhtt2/8uY9b/x3Eut4Y/f+WbWLJYPduFI8iWOf37c1skUolIxPuMIQLdu3fLcwWr51717dwBCQ0PJ\nysri4EHz42IxMTGEh4cXa3mZmZl4eHhcM/z777/n0UcfLdY85Jpn5fEWsAP4CngM6AJ0Ax4Hpht/\ne/M6l1GsO8vsXVaWUi+MTlFVn7hP3fNhJ5XZqqW6MGqUuuOX9epv/zUqbXearZMoRIlU1GM3JCRE\nrVixosTTDRgwQA0cOFClp6ertWvXKl9fXxUXF2d13Hnz5qmEhASllFJHjx5VHTt2VM8991yecf75\n5x/l6emp0tLyHtsbN25Ue/fuVdnZ2er8+fPqoYceUnfddVeB6SpoPSN31VZYMUBLYDjwHfAnsBT4\nFngaaAXstFnq7IizM3zyvjfTO/3G2vURtLr/Cl6rljNn0yK+fQI2DtxFToaUOIWwlWnTpnH58mUC\nAwMZPHgw06dPJywsDICEhAS8vb05fly3DsXFxdGuXTu8vLyIiori9ttvZ8qUKXnm9/3339OnT59r\nml8PHz5Mt27d8PHxISIigqpVqxb6zKijs8eLWO8Br93gZRgLT45j40bFPeM+wq/Vp+z5qzrbuvZk\n46rO3NGuJm0/aGLr5AlRLNLlXvlw9C737DGD29E1zut1FEgBsoFM4FaL3xwucALEx8MdT/9IZvPn\n2be8Fn91HkyVmbcR8Us4DaJq2Dp5QhRJAmf5kMBpf3YCUYX8Xtw3NB8BWhcwvkMGTtDvwL77iZUc\nrtefuOUBLGr+MjWWN+TeXW3xqeZm6+QJUSgJnOVDAqf9yQBOFPCbAuoXcz5HgDaAtad8HTZwAmRm\nwoDnd7LCrRvbVlZlhfdHZFQP4OlFt+NssMddRjgKCZzlQwKn/SmrptrDQDK6qfZr4BuL3xw6cIJ+\nv+cbUxKYmnAv0dGKw0lTOfxSAK+83DzPbfVCVCQSOMuHowdOR37m8Q7gFBAA/A3sBdaafhw/fnzu\niFFRUUTZ8MFpWzAYYNLom2n83w1EXe7B/62biNuEcXzV9jDPtG9g6+QJISqA6OhoosuoNyZ7Yo8l\ng6HA7DKe5zggDfjI+N3ha5yWVq+/zAPT+vHD2ps55d6H6iua0fumWrZOlhDXkBpn+XD0Gqc9PsfZ\nEbilkN9vQz/fWRgPwNRvlSdwL7Dr+pNWOXVqV5X1by3i8dvTqX1+H9Ev7WJjUpKtkyWEEDZhjyWD\nCOAVoC2wD93cagBqAY2B9cCHwO5C5lEP+NX42QWYh34+1ERqnFacOaPo8vSbTF52Gx+86cqM5ztQ\n38vL1skSIpfUOMuHo9c47TmDbuibhILRd9PGo3sVulIG85bAWYD0dHii99cM+acur0/NYMXA+/B3\nlzepiIpBAmf5cPTAaY9NtSZXgX/Rnbz/F9hI2QRNUQhPT5j7x1PsbJLN8+9epftPP3E1M9PWyRKi\nUkpMTKR37954eXkREhJSaDd4s2fPxtnZOU+H8WvWrCnH1DoOew6cwkZcXGDU+vvxvhxA+4VZ9Pl6\nOjlZWbZOlhB2IasEx8qIESNwd3fn7NmzzJs3j+HDhxMXF1fg+HfccQepqam5fx07diyLJIt8JHCK\nUnF2c6Lb6nbcs7IB2aeq8vj774EETyGsCgkJYcqUKURGRuLt7U12dnaR06Snp7Nw4UImTJiAh4cH\nd9xxB7169WLu3LkFTiPN1OVDAqcoNY+GHrT4tikvzGzEvzVDeOmVURI8hSjAggULWLp0KUlJSfTq\n1Qs/Pz+rfz179gRg//79uLi40LBhw9x5NG/enNjYWKvzNxgMbN++nYCAABo3bszEiROLFaBFydlj\nBwiLLT4r8l6IVkDP8k2OYwvsF0j9f5L5aJYLj42qiu+woYyd+R0GV1dbJ02Ia0QbostkPlEqqkTj\nGwwGRo4cSd26dQFYsmRJkdOkpaXh4+OTZ5i3tzepqalWx+/YsSOxsbEEBweze/du+vfvj4uLC2PG\njClRWkXR7DFwmjop6I1+BOUHdPAcCJyxVaIcWYMpDUjtlMo3q+rxaJ++ePXpyfM/L8LFTTqFFxVL\nSQNeWQoKCirR+F5eXqSkpOQZlpycjLe3t9Xx69Wrl/s5PDycsWPH8sEHH0jgvAHssak22vjXHuiP\nroH+HzpwdrBZqhyYUxUnmv63KTX+d4XpF0KZOOwpZnTtxKX0S7ZOmhAVhmUfz926dctz96vlX/fu\n3QEIDQ0lKyuLgwcP5k4XExNDeHh4sZcp1zxvDHsMnCYegGWnqfWNw4QNuAe5EzYnjJvfvMh7/s2Y\n8MxLzI9qzdnzF22dNCEqnKVLl+a5+9Xy7/fffwfA09OTBx98kLFjx3Lp0iXWrVvH4sWLeeSRRwqc\n55kzutFt7969TJw4kQceeKDc8uRI7DlwvgisAlYb/1YBL9g0RQ7Ov4s/tZ+szW1vpfF00+a8/+xo\n/rw7gv1HTts6aULYpWnTpnH58mUCAwMZPHgw06dPJywsDICEhAS8vb05fvw4ACtXrqR58+Z4eXnR\nvXt3+vTpw+uvv27L5Fda9t7DgzvQBH1T0F50pwhlQXoOKiWVrdjZbSderbz4eEgG69eu5rVP3+Dm\n+Ztp26K4r0oVonSk56Dy4eg9B9ljBvtgvpvW8q5a01ZcWAbLkMB5HTLOZbC19VYaTm3Ic/VOc3rF\nCp6f9iauX/9LjzuLf31GiJKSwFk+JHDan9mYg6Q1j5XBMiRwXqfk9cnsfmA34Wua89CVg3gs+5Nh\n34zj9JSVPNGnna2TJyopCZzlQwKnsEYCZxk4OeMkxz85Tui6SLoc2U3zxUvoPXcSW15bzFtPdrF1\n8kQlJIGzfDh64LTH5zhNagHvAnWBrkBT4HZgli0TJczq/KcOaTFpJDy6nyU/R9AxO5uAjKtETbqf\n4Rfm8NWYgbZOohBClJg931U7G/gLqGP8fgB9p62oQBp+2pDstGxS3znBn82bM7dnT+L6jKTfV0Pp\n9cpUcnJsnUIhhCgZe65x1kC/UszULUYmIB2lVjBOrk40+7kZ227dRr1IT5b1jOSunBw+VopXF7xC\nh9TTrPxsAm5ulb51RwhRSdhz4EwDqlt8bwsk2ygtohBVAqoQviicmM4xRDaO5LeICO4HvnV15fM5\nH9Pm8hnWffE1vj723AAiKgI/P788PfSIG8PPz8/WSbApe97DWgNfAM2AWCAA6AvElMG85eagG+Ds\nL2c59PIhWm9qzT9V0ukfF8fPfy6jxtef0OuezqyY/BPBdaV/WyHslaPcHGTvGXQFGhs/70M315YF\nCZw3yJGxR0hamUSLlS1YlprEY3v3siR6FX6fTeGeLi34ZfTvtA633om1EKJik8BZcd0NrCBvRwhQ\n8g4QnIEtwHHg/ny/SeC8QVSOYveDu3Gt4Urjbxqz8Px5nj1wgOXr/8Fn8kQ6dgvhy2HLua9TgK2T\nKoQoIUcJnPZ4jbMjOnDej/WOEIobOJ8H4gCp3pQjg5OBsLlh7Oi0g4T3EujzejCXsrPpAkSPncjG\nt9+incutxJ9awfAB0kWfEKLiscfAmWT8PxNYV8p53ATch34O9KWySJQoPhdvFyKWRLDt9m24B7vz\nyKBapGdnc4+TE2ve+4CtY16lPbdx+NQyPnixta2TK4QQedjjbYymLvW+uI55fAK8AshThDbiVseN\nyD8iOfjiQZJWJfF03bo8W7cunSMjufLFl2z8LYu1MZ3p8+qf8qynEKJCsccaZxy6s4O6wK58vykg\nsojpewBnge1AVEEjjR8/PvdzVFQUUVEFjipKybOZJ00XNCVuQBwtVrXg5aZBpGdnc5fBwKrZ37N6\n6BC6dx1I26c+Zc0XQ3B3t3WKhRCWoqOjiY6OtnUyyp29XsSthe416H6uzcPRIqadBDyC7izBHfAB\n/gcMsRhHbg4qR6fnnubo2KO0XN8St9pujD9yhJ/PnWNVejr+ffsw4G4XtlR5kS2fjqFGDXvdZYWo\n/Bzl5qBKn8EidAJGIXfV2tzRiUc5/+t5WqxugYuXizl4KkX1nvfz7B3uzK96P5vf/pxGDZ1tnVwh\nhBWOEjjt8RpnWZMIWQEEvxGMV0sv4vrHkZOVw/h69egXEMCdBgMXlq/gy43ZvJi6nIiJfVi17pKt\nkyuEcGCVvmRQSlLjtIGczBx23b8Lt5vcaPxNYwwGg7nm6edHQNcuzA7z5T9BLkxtv4SnBtW0dZKF\nEBakxilEOXNydaLZL81I353OoVcOoZQy1zyTkjgXvZqhxxXLDxt4bmtbXnh3D1K+EUKUN3sMnAHA\neGAkuvOCr9B91f4GNLRdskRZcPFyIfKPSJL+SiL+3XgAc/A8dYqzy5fTKdOL2K01mJnciW7PRJOR\nYeNECyEcij0Gzh+BKkAosBE4gu7cfQm6UwRh51z9XYn8K5Izc85w/IvjgA6eDwUG0unQIY4tWkSj\nWvWJj67Dds9+tBjyA0lJRcxUCCHKiD22RccAzdFpjwdutvhtB9CiDJYh1zgrgCvxV9jeYTv1Jtaj\n1pBaAHx07BhTT5xgeUQEDV57jcvLl9Gi6yUuxD/FhvffpFEje9ylhagc5BpnxWXqR0YBF/L9JtGu\nEnEPdifyr0gOjz7MuV/PAfByUBCv3XwznWJiiJ00iaqPPEbc/wxEBv1E5LhH+XPFVRunWghR2dlj\nySAZWI1OewdgrcVvHYBqZbAMqXFWIKnbUtnZdSdh88Lwv8cfgHlnzvDywYP8HhlJ6//9DzVmNCMG\nNWVmeibvRv7KK8/I21WEKG+OUuO0xwxGFfKbQgfV6yWBs4K5uO4isQ/G0mxhM6q112WjRefO8Z/9\n+1nYrBnt//0XNWQIsx7pwDNO2+mb+X98/2E4LvbYqaQQdkoCp2OTwFkBJf6dyJ5Be2j2v2ZU66CD\n59+JiQzas4d5YWHcc+wY9OjBpp530KHaCpoemMPKr+/Dz8/GCRfCQUjgdGwSOCuopBVJxA2Mo+l/\nm+IXpSPiP8nJPLh7N1MbNaJfRgb06MHppsE0qb8J15jRrP3geZo0kV1diBvNUQKnPd4cJByY391+\nNP2pKXEPxZG0Uj+DcoevL381b86LBw/qd82tXUuti5mc2tCI6i2/oeXYp/m/3+VhTyFE2ZDAKeyO\n351+NPu5GXED4khcnghAcy8v1rVsyZcnTjDm7FnUb79RNbQZsb8auC/yCP0Wd+b1d89IT0NCiOtm\nj1XqxYX8poCeZbAMaaq1AxfXXiS2TyxhP4Thf6++2/ZCZiY9du2iUdWqzAoNxfWTT1CffsqnL3Rl\nzPm/aX98Ib9Nb42Xl40TL0Ql5ChNtfaYwagifo8ug2VI4LQTyf8ks7v3bprMaUL1btUBuJSdzYC4\nOK7m5PBLs2Z4//47PPEEG14ezF2X5lF9yydEfz6IhtJBoxBlSgKnY5PAaUeSNySzu9duQr8OJaC3\nfn4zKyeHZw4cYGtqKn9ERlJz3z7o1Yuz999NRPWVpG5/gP8+OZke98nzKkKUFQmcFV8oMAloBrgb\nhymgfhnMWwKnnUndlsquHrsIeSeEOk/UAUApxTvx8Xx/+jS/R0TQ5NIl6NuXDC8P7o3KYMN+J14J\nWcA7r1XHSa72C3HdHCVw2vPp4jtgOpCJbr6dA8yzZYKE7Xi38qbF6hYkTEog/r14lFIYDAbGhYTw\nVnAwnXbsYLmzM/z9N1WCglk15wyvtAzhw5RbuHPgdukkXghRbPYcOKsCyzF39j4e6G7LBAnb8mjk\nQct1LTk7/yyHXjqEytGtBkNr1+bnZs0YvGcP08+dg6++wjB8OBPfWcySRo+wucm9hPafxbZtNs6A\nEMIu2HOVej26b9pfgBXASeA9oHEZzFuaau1YZlImu+7fhXuIO02+a4KTqy4fHrp8mR67dnGvnx8f\nNWiAS3Q0PPwwZ0YMpbXzb5yPaceHd01lxH+qYrDnI0MIG3GUplp7zuCtwB50p+4TAB9gCvBvGcxb\nAqedy76UTVz/OFS2otnPzXD2dAbgYmYmD8XF4WIwML9pU3yPH4e+fcmsF8zAu5z4fd9BuqX+wg9f\nNMDDw8aZEMLOOErgtOem2k1AKnAMGAo8SPGDpjv6Jdg7gDh0TVVUIs4ezjRb2AzXQFdiOseQcU73\nHFTN1ZXfIyIIdnfnjm3bOFKzJqxbh6uvHz9PjePLW3rwR53badr7N/bvt3EmhBAVkj2WDD4Dnsd6\nRwgl6QDBA7gEuADrgFHG/yA1zkpDKcWRN49wdsFZIhZH4NnUM3f4FydOMCk+nh+bNuUuPz+YORNe\nf519777E7aencWXzQKb1m8jQR1xtnAsh7IOj1DjtMYOtga1Y7wihNK8V8zBO8yi69gkSOCud09+f\n5tCoQ3ne6QmwIimJQXFxjAoK4uWgIAxbtkC/flzq05Nu9fezaW8y3S/PZ/anIdLbkBBFkMBZ8QUC\nZ/MNawzsK+b0TsA2oAHwFfCqxW8SOCuhi2svEtsvlpBxIdQdXjd3ePyVK/TZvZsGVasyq3FjvC5e\nhIcfRmVl8cWIDoyO+Qq/9V/xx4d9aNHChhkQooKTwFnx7QPGAj+h8/ES8AQQVsL5+AJ/AmMwd9en\nxo0blztCVFQUUVFR15daUSFcPnSZXT124dfFj4YfNcTgrA+By9nZPHPgAFtSU1nYrBmN3Nzg3Xfh\nq6/Y9+FrdDz6GSnbu/Bup4948Vm561YIgOjoaKKjo3O/v/3222DfcaVY7DmDtYEZwBWgJrAXHTzT\nSjGvt4DLwIfG71LjrMQyL2YS1y8OQxUDTec3xcVHd7unlGL6yZOMO3qUbxs3pkeNGrB6NQwezJX+\nfXmo8XGW79nP7ScW8N9pYVSvbuOMCFHBOEqN057vqj2Frim2A0KA2RQ/aNZAP8YCuiOFe4DtZZs8\nUVG5VnMl4o8I3ILc2NZuG5cOXAL0QT+8bl0WhYfz9P79jD1yhOyOHWHbNtzj9vHbdyeY0elhNjTp\nSKP+M/nrLylcCeGI7LlksBwdPJ8DgoBZwBr03bFFiUB30edk/JsLfGDxu9Q4HYBSipNfn+To2KM0\nntmYGj1r5P52+upVBu3ZQ7ZSzGvalLqurvDxx/DBByRMfoO7zn/HybhgHvaewRfvB1K1qg0zIkQF\n4Sg1TnvOYG/gV4vvLsBr6M4QrpcETgeSsjGF2H6x1BxSk3pv18u97pmtFJPi4/nyxAm+a9KEbtWr\nw8aNMGAA2V27MOZuT6bumE+N9d/w24fdadXKxhkRwsYkcNqfDsBA4JkymJcETgeTcTaDuAFxGFwM\nhP0YRpUaVXJ/W3PxIoP27GFgYCDv1quHa0oKPPssbNnCtg9fpmvMJFJ3dGF0i494a4wnzs42zIgQ\nNuQogdOer3ECtEI3scaja5p7bJscYa+qBFYh8q9IvFp5sbXNVlK2pOT+1rFaNba3bk1cejodtm/n\nqJsb/PADvP02rR5/g4TMQfS8/xJTUlvQ8v6NHDpkw4wIIW44eywZNEbXLPsD54CfgVeAm8twGVLj\ndGDnFp5j/9P7qTexHrWfrG0qRZOjFJ8eP877CQl82agR/QID4fhxGDoULl3ij7cG0X/zO2RvepIJ\nnd/ixZFu8p5P4VAcpcZpjxnMAZYAzwIJxmFHgHpluAwJnA7u0r5LxPaPxaORB6EzQnH1M3e7tzkl\nhfaWOoMAAB4kSURBVMF79nCLtzdTGzWimrMzfP45vPsuF8ePoZ/bWtbvO0jD2O/4+dNbCA21YUaE\nKEeOEjjtsTz8IPqZyzXoF1nfjQNsKFG+PBp70OrfVlSpW4UtLbZwce3F3N9u8fFhW5s2+Lq4ELll\nCyuSk+GFF2DVKqp9M5e/FmXxw73DOdK2B81HjeG9D66QnW3DzAghypQ9BxwvoBe62fZO4Hv0XbZ/\nlcG8pcYpcl344wL7hu2j9n9qE/xWME4u5vLmn4mJDNu7l74BAbxXvz5Vs7Phvfdg6lSSx7/OwKr/\nsHpvLCE7v+WXT24nrKT9WglhRxylxllZMugP9AUGAHeVwfwkcIo8rp66yt5H95Kdnk3YvDCqhpgf\n3EzMzOSZ/fvZmZ7O3LAwWnt7w86d8Pjj4OfHklG9GbRpAhlbH2ZUq3d4c7Qnbm42zIwQN4ijBE57\nbKq1JhHd/V5ZBE0hruFW243IZZHU6F2Dbbdu48yPZzAVrvxdXVnQrBlvBQfTbedOxh05wtXwcPj3\nX7j7bnoMGssJrxfo2vsUH10Jp1G3paxZY+MMCSFKrdKXDEpJapyiQKlbU9nz6B48GnnQ6KtGuNUy\nVx9PXL3KM/v3c/DyZWY1bkxbX1/Ys0fXPqtUYe0bQ+i3dRIpe9rwgPunTH2/Nv7+hSxMCDsiNU4h\nhFXerb1ps7UNHmEebGm+hTPzzbXPum5uLAoPZ1xICL1jY3nhwAHSGjWCdevgwQfp8PBojqX3Z2Sf\nEH6tHUlIv6/4fm4OUk4Twn5U+pJBKUmNUxRLyuYU9g7di0fotbXPC5mZvHTwIGuSk/k6NJR7/f31\nc58vvAA7dnB00qv0Ov09Bw9lEX70a+ZMbk6TJjbMjBDXyVFqnJU+g6UkgVMUW87VHI6+fZRTs07R\n8NOGBA4IzO00AfSdt0/v308nX18+bNCAGlWqwO+/w7PPotrexg9D2vDM5ilk7RjIsPrjmTTWDx8f\nG2ZIiFJylMApTbVCXCcnNyfqT6pPxJII4ifGs+v+XVw+ejn39y7+/uxq0wY/V1eabd7MjJMnyb7v\nPoiNxRBSj0eGTOaU98v073+Zbz3CuPmBmcyek01Oju3yJIQoWKUvGZSS1DhFqeRk5HDsw2Mc++gY\nQa8EEfRSEE5VzOXTmLQ0RuzfT4ZSfNmoEbf4+EBsLDzzDFy8yP6xI+h7fA6Hjl6l/t4vmPPu7fLW\nFWE3HKXGWekzWEoSOMV1uXz4MgdGHODKsSuEfhVKtQ7Vcn9TSvH9mTOMOXyYXtWr8279+lR3cYFf\nfoFRo1C33srCx9rxxNYPubKnM3183uejt2tTs6YNMyREMThK4JSmWiFugKr1qxLxRwQh40OIGxjH\n3mF7yTifAeiTy6O1arHnlltwdXKi2aZNzDx1iuy+fWHPHgwREfR5ZCKnLw/muQer87+a4dR7dAJj\nJ6Rz6ZKNMyaEqPwlg1KSGqcoM1kpWRwZe4Sz888S8nYItZ+onafbvu2pqTx74ACXcnL4qEED7vLz\ng4QEGD0a1q3jzFsvMcxlAysPr8dt/QQ+emQIjw5xlvd+igrHUWqclT6DpSSBU5S51B2pHHzhIFkX\nsmjwSQP8O5t7PlBK8cu5c4w+fJgIT0+mNGhAYw8PWLsWXnwRgLhXhjLw9AIOHkuh1q4PmPFqF+6+\n21a5+f/27jy+6TrP4/grTdP7SI+kbdrScB/lkBsRsILIAIrgtegMqLPuOKPO7LqjO+qgiKKzs87q\n7MrOul7jCDOOoIMKDKADVpgBRSj3UaAX0DNt0zZJkzTHb//4BagdjhYLocnn+Xjk0eR35fv98SPv\nfH+/X75fIf6eBGd4k+AUl4WiKNR/VE/JYyXE58fT9z/7Etc/7sx8t9/Pq6dO8cuTJ7nbaGSx2Uya\nVgurVsFTT6EMGMCmB29i4eH/panczMj6l1i2aAQjRwaxUkIEhEtwhus1zlzgc+AgcAD4SXCLI8KF\nRqPBMM/AuEPjSJ6cTNG1RRz/6XE8TR4AoiMieKxXLw6NHYtfURi0Ywe/OnUK5+nrn7NmceMPf8mp\nw+N5dcYk9o+YwcSX5zPze8UcORLkygkRJkL+m8F5ZAYee1CHJ9sFzAUOB+ZLi1NcEW21bZQ9XUb9\nx/X0+lkvTA+Z0MacvXh52OHgydJSdtntPJ2Xx/2ZmejsdnjpJfjNb2hb+F1+PSmR5w68ju/wLdyc\n+Ay/WmQmLy+IlRJhK1xanCFfwU76CHgV2BR4LcEprij7fjtli8qw77ZjXmwm496Mb9xA9FVLC4vK\nyihzOnmud2/mG41E1NTACy/Ae+/h+v5CfjEmgpcOv4N//3zuzvk5Lz5hIisriJUSYUeCM3yYgS+A\nfMAemCbBKYKieXszpU+W0lbTRu+lvTHcbvhG932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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "axiallimit = 2.0 # meters from center\n", "radiallimit = 0.5 # maximum radius to investigate\n", "curveqty = 5\n", "X = linspace(0,axiallimit)\n", "R = linspace(0, radiallimit, curveqty)\n", "[plot(X, [Bx(1,1,x,r) for x in X], label=\"r={0}\".format(r)) for r in R]\n", "xlabel(\"Axial Position (m)\")\n", "ylabel(\"Axial B field (T)\")\n", "suptitle(\"Axial component of unit coil (1m radius, 1A current) B field for various measurement radii\")\n", "legend()\n", "show()" ] }, { "cell_type": "code", "execution_count": 26, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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yy5w5c4a9e/eybds2XnjhhfO/q1QqXn31Verq6qirq6OgoKDf1yIZ2Ep1PfAD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\nDh4EBzpbDJeG1gbe3P8mr+59FS93L25KuYl1M9cxNWjqmPd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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "[plot(X, [Br(1,1,x,r) for x in X], label=\"r={0}\".format(r)) for r in R]\n", "xlabel(\"Axial Position (m)\")\n", "ylabel(\"Radial B field (T)\")\n", "suptitle(\"Radial component of unit coil (1m radius, 1A current) B field for various measurement radii\")\n", "legend()\n", "show()" ] }, { "cell_type": "code", "execution_count": 27, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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9MHXqVDw9PenSpQvbt28vu5Wr4FoD/wJLgEPA94BdgTR3HE2Lc+iQUmPGKOXu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\n90x22b7Aupemc297O1NnWYgyIUFBiCK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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "[plot(X, [sqrt(Bx(1,1,x,r)**2 + Br(1,1,x,r)**2) for x in X], label=\"r={0}\".format(r)) for r in R]\n", "xlabel(\"Axial Position (m)\")\n", "ylabel(\"B field (T)\")\n", "suptitle(\"Total unit coil (1m radius, 1A current) B field for various measurement radii\")\n", "legend()\n", "show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now re-examine the nature of the Br field by plotting families of curves where the horizontal axis is radial position:" ] }, { "cell_type": "code", "execution_count": 28, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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SzwMXjKjcLfkK9vG/gdhdj2cR+KhjfX09juOocRwWLlyY8zLkS6NloWWhZdFxQ+Kr5gUl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\nrBGm4JZbI9xmPfbZnBeA84C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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "R = linspace(0, radiallimit)\n", "X = linspace(0, axiallimit, curveqty)\n", "[plot(R, [Bx(1,1,x,r) for r in R], label=\"x={0}\".format(x)) for x in X]\n", "xlabel(\"Radial Position (m)\")\n", "ylabel(\"Axial B field (T)\")\n", "suptitle(\"Axial component of unit coil (1m radius, 1A current) B field for various axial positions\")\n", "legend()\n", "show()" ] }, { "cell_type": "code", "execution_count": 29, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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4mse3ALgH1WLzNGpixED92MeoyTHnoGYC9gdeBK4430xBEATBXfE04RtYzPE/gfudYYgg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\nqIBK+CggCNgLNLMK0w9Yoa93BLY5yzhBEARBKA/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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "[plot(R, [Br(1,1,x,r) for r in R], label=\"x={0}\".format(x)) for x in X]\n", "xlabel(\"Radial Position (m)\")\n", "ylabel(\"Radial B field (T)\")\n", "suptitle(\"Radial component of unit coil (1m radius, 1A current) B field for various axial positions\")\n", "legend()\n", "show()" ] }, { "cell_type": "code", "execution_count": 30, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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6x7v5e6Mo28LL9yfgd8BnirVwRRZlW8SB/4k6wWK8SyfKA1jnAQvd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\niIiIiIiIiIiIiIiIiADw/wF8ZzuNt8miaAAAAABJRU5ErkJggg==\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "[plot(R, [sqrt(Bx(1,1,x,r)**2+Br(1,1,x,r)**2) for r in R], label=\"x={0}\".format(x)) for x in X]\n", "xlabel(\"Radial Position (m)\")\n", "ylabel(\"B field (T)\")\n", "suptitle(\"Total unit coil (1m radius, 1A current) B field for various axial positions\")\n", "legend()\n", "show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "---\n", "[Magnet Formulas](../index.html), © 2018 by Eric Dennison. Source code and License on [Github](https://github.com/tiggerntatie/emagnet.py)" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.5.2" } }, "nbformat": 4, "nbformat_minor": 2 }