{
"nbformat": 4,
"nbformat_minor": 0,
"metadata": {
"colab": {
"name": "SNOWs_Inductance.ipynb",
"provenance": [],
"collapsed_sections": [],
"include_colab_link": true
},
"kernelspec": {
"name": "python3",
"display_name": "Python 3"
}
},
"cells": [
{
"cell_type": "markdown",
"metadata": {
"id": "view-in-github",
"colab_type": "text"
},
"source": [
"![\"Open](\"https://colab.research.google.com/assets/colab-badge.svg\")
"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "h5yEUkcppbQ8",
"colab_type": "text"
},
"source": [
"# SNOWs formula for inductance of a single layer solenoid\n",
"\n",
"\n",
"This is quite accurate formula for a single layer solenoid. Formula comes from the paper\n",
"http://www.coe.ufrj.br/~acmq/tesla/maxwell.pdf\n",
" and compares well with Kirchoffs and Maxwells formulas. "
]
},
{
"cell_type": "code",
"metadata": {
"id": "IIJIE7k9ph2_",
"colab_type": "code",
"colab": {}
},
"source": [
"import numpy as np\n",
"import math\n",
"import matplotlib.pyplot as plt\n",
"import matplotlib\n",
"import scipy.special as special"
],
"execution_count": 0,
"outputs": []
},
{
"cell_type": "code",
"metadata": {
"id": "cs9s5hH2pxos",
"colab_type": "code",
"colab": {}
},
"source": [
"a=0.486 #5e-2 # coil raduis\n",
"b=0.0921 #4e-2 # coil height\n",
"c=0.0095 #1.88e-3 # coil diameter\n",
"n=5 # number of coils\n",
"pi=np.pi\n",
"mi_0=4*pi*1e-7"
],
"execution_count": 0,
"outputs": []
},
{
"cell_type": "code",
"metadata": {
"id": "btL6wf_uqBdG",
"colab_type": "code",
"colab": {}
},
"source": [
"p=2*a/b\n",
"theta=np.arctan(p)\n",
"k=np.sin(theta)\n",
"k1=np.cos(theta)\n",
"z=pi*n*c/b"
],
"execution_count": 0,
"outputs": []
},
{
"cell_type": "code",
"metadata": {
"id": "6tKvwZKPqaI9",
"colab_type": "code",
"outputId": "c395bdf0-83f5-476a-e60e-19e0149f60b2",
"colab": {
"base_uri": "https://localhost:8080/",
"height": 461
}
},
"source": [
"K=special.ellipk(k) # elliptic integral of a first kind\n",
"E=special.ellipe(k) # elliptic integral of a second kind\n",
"\n",
"\n",
"%whos\n"
],
"execution_count": 0,
"outputs": [
{
"output_type": "stream",
"text": [
"Variable Type Data/Info\n",
"---------------------------------\n",
"E float64 1.008021304684566\n",
"K float64 4.0961576922801575\n",
"L float64 1.98269910975166e-05\n",
"S1 float64 199.84660832730418\n",
"S2 float64 -0.6290450162020763\n",
"S3 float64 0.10305798056070045\n",
"S4 float64 0.31999368858514404\n",
"a float 0.486\n",
"b float 0.0921\n",
"c float 0.0095\n",
"k float64 0.9955409295862284\n",
"k1 float64 0.09433057573548517\n",
"math module \n",
"matplotlib module /matplotlib/__init__.py'>\n",
"mi_0 float 1.2566370614359173e-06\n",
"n int 5\n",
"np module kages/numpy/__init__.py'>\n",
"p float 10.553745928338762\n",
"pi float 3.141592653589793\n",
"plt module es/matplotlib/pyplot.py'>\n",
"special module ipy/special/__init__.py'>\n",
"theta float64 1.4763252916068947\n",
"z float 1.6202567974540192\n"
],
"name": "stdout"
}
]
},
{
"cell_type": "code",
"metadata": {
"id": "2Z3FggTnqcFF",
"colab_type": "code",
"colab": {}
},
"source": [
""
],
"execution_count": 0,
"outputs": []
},
{
"cell_type": "code",
"metadata": {
"id": "bCbSk960rWKA",
"colab_type": "code",
"colab": {}
},
"source": [
"S1=8*n**2*a*pi/3*((K+(p**2-1)*E)/k-p*p)\n",
"S2=2*n*(1/4-np.log(z))+1/3*np.log(2*pi*n*a/b)-4/pi**2*(E/k-1)*(1+z**2/8)\n",
"S3=-2/3*((K-E)/k-k*K/2)-k1/(2*k)*(1-k1*theta/k)\n",
"S4=np.log((1+k1)/(1-k1))+k1*np.log(4)\n"
],
"execution_count": 0,
"outputs": []
},
{
"cell_type": "code",
"metadata": {
"id": "VRalbsL5tTS5",
"colab_type": "code",
"colab": {}
},
"source": [
"L=mi_0/(4*pi)*(S1+2*pi*a*(S2+S3)+b*S4)"
],
"execution_count": 0,
"outputs": []
},
{
"cell_type": "code",
"metadata": {
"id": "fdT9IntArnQA",
"colab_type": "code",
"outputId": "b8b0b46b-d4a5-446d-da0d-17ccf07e6c48",
"colab": {
"base_uri": "https://localhost:8080/",
"height": 461
}
},
"source": [
"%whos"
],
"execution_count": 0,
"outputs": [
{
"output_type": "stream",
"text": [
"Variable Type Data/Info\n",
"---------------------------------\n",
"E float64 1.008021304684566\n",
"K float64 4.0961576922801575\n",
"L float64 4.5368905947438836e-05\n",
"S1 float64 457.86893963105894\n",
"S2 float64 -0.6290450162020763\n",
"S3 float64 -0.7494305196721343\n",
"S4 float64 0.31999368858514404\n",
"a float 0.486\n",
"b float 0.0921\n",
"c float 0.0095\n",
"k float64 0.9955409295862284\n",
"k1 float64 0.09433057573548517\n",
"math module \n",
"matplotlib module /matplotlib/__init__.py'>\n",
"mi_0 float 1.2566370614359173e-06\n",
"n int 5\n",
"np module kages/numpy/__init__.py'>\n",
"p float 10.553745928338762\n",
"pi float 3.141592653589793\n",
"plt module es/matplotlib/pyplot.py'>\n",
"special module ipy/special/__init__.py'>\n",
"theta float64 1.4763252916068947\n",
"z float 1.6202567974540192\n"
],
"name": "stdout"
}
]
},
{
"cell_type": "code",
"metadata": {
"id": "mvlvlQGHroBM",
"colab_type": "code",
"outputId": "69c770ee-ef6e-4930-9c10-5aeb2c8330fa",
"colab": {
"base_uri": "https://localhost:8080/",
"height": 35
}
},
"source": [
"4**2/2"
],
"execution_count": 0,
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": [
"8.0"
]
},
"metadata": {
"tags": []
},
"execution_count": 9
}
]
}
]
}