{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "f4419154",
   "metadata": {},
   "source": [
    "# Magnetic field of a charged wire\n",
    "- Börge Göbel"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "id": "9342fb0f",
   "metadata": {},
   "source": [
    "![hand](figure_05_hand.svg)\n",
    "\n",
    "https://upload.wikimedia.org/wikipedia/commons/3/3e/Manoderecha.svg"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f402257f",
   "metadata": {},
   "source": [
    "Using the Maxwell equations of magnetostatics (in their integral form) one can derive the vector potential of a current density distribution \\\\( \\vec{j}(\\vec{r}) \\\\)\n",
    "\n",
    "\\\\( \n",
    "\\vec{A}(\\vec{r})=\\frac{\\mu_0}{4\\pi}\\int\\frac{\\vec{j}(\\vec{r}')}{|\\vec{r}-\\vec{r}'|}\\,\\mathrm{d}V'\\\\\n",
    "\\\\)\n",
    "\n",
    "from which we can calculate the magnetic field \n",
    "\n",
    "\\\\( \n",
    "\\vec{B}(\\vec{r})=\\nabla\\times\\vec{A}(\\vec{r})\\\\\n",
    "\\\\)\n",
    "\n",
    "For more details on these equations, please consider my course: \"Electrodynamics based on Maxwell equations\" https://www.udemy.com/course/electrodynamics/"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "ce2064a4",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "73703056",
   "metadata": {},
   "source": [
    "### Straight wire\n",
    "\n",
    "- along z axis\n",
    "- very long: length \\\\( [-l_0,l_0]\\\\) (we will only consider the xy plane, because all other planes will behave equally)\n",
    "- very thin: radius \\\\(r_0\\\\) (basically non-zero only for x = 0, y = 0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "5274b866",
   "metadata": {},
   "outputs": [],
   "source": [
    "mu0 = 1\n",
    "\n",
    "# straight wire\n",
    "j0 = 1 # Ampere / meter^2\n",
    "r0 = 0.001 # m\n",
    "l0 = 1000 # m\n",
    "\n",
    "def j(r):\n",
    "    #if np.sqrt(r[0]**2 +r[1]**2) > r0:\n",
    "    #    return np.array([0.0, 0.0, 0.0])\n",
    "    #else:\n",
    "        return np.array([0.0, 0.0, j0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "220ccbac",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0., 0., 1.])"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "j(np.array([0,0,5]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "ef52f0b0",
   "metadata": {},
   "outputs": [],
   "source": [
    "coordMax = 4.9\n",
    "numpoints = 50\n",
    "d = 2*coordMax / (numpoints-1)\n",
    "\n",
    "# coordinates: standard indexing is yxz, fix by using \"indexing='ij'\"\n",
    "coords = np.array(np.meshgrid(np.linspace(-coordMax, coordMax, numpoints),\n",
    "                              np.linspace(-coordMax, coordMax, numpoints),\n",
    "                              np.zeros(1),\n",
    "                              indexing='ij'\n",
    "                             ))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "744e4b0a",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[-0.1  0.1  0. ]\n",
      "[0.1 0.1 0. ]\n"
     ]
    }
   ],
   "source": [
    "print(coords[:,numpoints//2-1, numpoints//2,0])\n",
    "print(coords[:,numpoints//2, numpoints//2,0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "9ac5f263",
   "metadata": {},
   "outputs": [],
   "source": [
    "# vector potential\n",
    "\n",
    "A = np.array(np.meshgrid(np.zeros(numpoints),\n",
    "                         np.zeros(numpoints),\n",
    "                         np.zeros(1),\n",
    "                         indexing='ij'\n",
    "                        ))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "1998f029",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0. 0. 0.]\n",
      "[0. 0. 0.]\n"
     ]
    }
   ],
   "source": [
    "print(A[:,numpoints//2-1, numpoints//2,0])\n",
    "print(A[:,numpoints//2, numpoints//2,0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "940ee78a",
   "metadata": {},
   "outputs": [],
   "source": [
    "numint = 5001\n",
    "\n",
    "for ix in np.arange(numpoints):\n",
    "    for iy in np.arange(numpoints):\n",
    "        # position r for which we are currently calculating A\n",
    "        r = np.array([-coordMax+ix*d, -coordMax+iy*d, 0.0])\n",
    "        for zj in np.linspace(-l0,l0,numint):\n",
    "            # we integrate of all rj in the wire\n",
    "            rj = np.array([ 0.0, 0.0, zj ])\n",
    "            A[:,ix,iy,0] = A[:,ix,iy,0] + j(rj) / np.sqrt( r[0]**2 + r[1]**2 + rj[2]**2 )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "cb6c4661",
   "metadata": {},
   "outputs": [],
   "source": [
    "dz = (2*l0) / (numint-1)\n",
    "#dx = (2*coordMax) / (numpoints-1)\n",
    "#dy = (2*coordMax) / (numpoints-1)\n",
    "#A = A * mu0 / (4*np.pi) * dx * dy *dz\n",
    "df = np.pi * r0**2\n",
    "A = A * mu0 / (4*np.pi) * df * dz"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "0c0341ed",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure()\n",
    "ax = fig.add_subplot(1,1,1)\n",
    "ax.set_aspect(1)\n",
    "plt.xlabel('x coordinate')\n",
    "plt.ylabel('y coordinate')\n",
    "\n",
    "plt.contourf( coords[0,:,:,0], coords[1,:,:,0], A[2,:,:,0] )\n",
    "cbar = plt.colorbar()\n",
    "cbar.set_label('Vectorpotential Az')"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "id": "4794fa59",
   "metadata": {},
   "source": [
    "__Analytical solution:__\n",
    "\n",
    "\\\\( \\vec{A}(\\vec{r}) = \\frac{\\mu_0}{2\\pi}jF\\log\\frac{2l_0}{\\sqrt{x^2+y^2}}\\vec{e}_z\\\\)\n",
    "\n",
    "For more details on these equations, please consider my course: \"Electrodynamics based on Maxwell equations\" https://www.udemy.com/course/electrodynamics/\n",
    "\n",
    "![derivation_wire](figure_05_derivation_wire.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "c72a1b3f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x1ba2e06ac70>]"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.xlabel('x coordinate')\n",
    "plt.ylabel('Az')\n",
    "\n",
    "plt.scatter(coords[0,:,numpoints//2,0],A[2,:,numpoints//2,0])\n",
    "\n",
    "xlist = np.linspace(-coordMax,coordMax,10001)\n",
    "plt.plot(\n",
    "    xlist,\n",
    "    mu0/(2*np.pi) * j0 * df * np.log( 2*l0/ np.sqrt( xlist**2 + coords[1,0,numpoints//2,0]**2 ) ),\n",
    "    'red')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bc0da924",
   "metadata": {},
   "source": [
    "__We can calculate the magnetic field__\n",
    "\n",
    "\\\\( \n",
    "\\vec{B}(\\vec{r})=\\nabla\\times\\vec{A}(\\vec{r})=\\begin{pmatrix}\n",
    "\\frac{\\partial}{\\partial y}A_z(\\vec{r}) - \\frac{\\partial}{\\partial z}A_y(\\vec{r})\\\\\n",
    "\\frac{\\partial}{\\partial z}A_x(\\vec{r}) - \\frac{\\partial}{\\partial x}A_z(\\vec{r})\\\\\n",
    "\\frac{\\partial}{\\partial x}A_y(\\vec{r}) - \\frac{\\partial}{\\partial y}A_x(\\vec{r})\\\\\n",
    "\\end{pmatrix}=\\begin{pmatrix}\n",
    "\\frac{\\partial}{\\partial y}A_z(\\vec{r})\\\\\n",
    " - \\frac{\\partial}{\\partial x}A_z(\\vec{r})\\\\\n",
    "\\frac{\\partial}{\\partial x}A_y(\\vec{r}) - \\frac{\\partial}{\\partial y}A_x(\\vec{r})\\\\\n",
    "\\end{pmatrix}\\\\\n",
    "\\\\)\n",
    "\n",
    "Since the vector potential only changes in the xy plane and is considered to be constant along z (for infinite \\\\(l_0\\\\)), we know\n",
    "\\\\( \n",
    "\\frac{\\partial }{\\partial z} A_x(\\vec{r}) = \\frac{\\partial }{\\partial z} A_y(\\vec{r}) = 0\n",
    "\\\\)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "af452e7c",
   "metadata": {},
   "outputs": [],
   "source": [
    "# create empty array for magnetic field\n",
    "\n",
    "B = np.array(np.meshgrid(np.zeros(numpoints),\n",
    "                         np.zeros(numpoints),\n",
    "                         np.zeros(1),\n",
    "                         indexing='ij'\n",
    "                        ))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "1918677a",
   "metadata": {},
   "outputs": [],
   "source": [
    "B[0,1:-1,1:-1,0] = (A[2,1:-1,2:,0] - A[2,1:-1,:-2,0]) / (2*d)\n",
    "B[1,1:-1,1:-1,0] =-(A[2,2:,1:-1,0] - A[2,:-2,1:-1,0]) / (2*d)\n",
    "B[2,1:-1,1:-1,0] = (A[1,2:,1:-1,0] - A[1,:-2,1:-1,0]) / (2*d) - (A[0,1:-1,2:,0] - A[0,1:-1,:-2,0]) / (2*d)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "d2f5680a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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P8PSgVbYv6rTSVrbXSDoeuAKYBJxle9Fojhlj6+HtN3jW+6f9WsN56bJpXMWzX4saGKJ5BzWGMlROSDq2XH8mxWjMc4ElFJ05HTWK890J7CFpY0C2H+lk/yqBuiXF+Cr7tJ4XGFWgAtieR/EvI3rAI9uq4/dRq3whBc+E5sD3TUcSpmmdTiyD5UQZpP3TpoNOoAcj6TDb35T0gQHL+8/x2SrHqdI5yojTPiaWKrcN0hqNHjWl/HOwd+wrtzKqDIEyA/gisFd54OuAE20vr3qSGD/6Q7HTlupwYdrfoqzj66a0TqMbbH+5nPyx7Z+3rpO0V9XjVHmx/+sUN323pni364flsliHdfKQquq2ow3DhGmMgS9WXDaoKvdQp9luDdCzJZ1U9QQxfo3knmo7S5dN67ilmiCNbpO0J8UL/dMG3EfdlOJhWCVVAnWlpMOA88v5QykeUsUEMJIxo9rpJFQTpjFG1gc2psjE1vuoq4CDqx6kSqAeDZwGfK6c/3m5LGLEEpTRS2z/FPippLNt3y1piu3H2u44QJWn/PcAB7bbLiJiHbC1pB9RtFa3kbQz8B7b76uyc9uHUpJmSLpY0gOSfifpwvLJf0TEuubzwBsob2vaXgi8uurOecofEdHC9rIBiyr3rlclUKfZ/rrtNeXvbCA3wCJiXbRM0qsAS1pf0snA4qo7VwnUlZIOkzSp/B1GnvJHxLrpWIrPWKdT9GL1Cjr4rLXTp/wGfkGe8kfEOsj2SophnkYkT/kjIkqSpgF/D8yiJR9tV2pEVnnKf46kzVvmt5B0VseVRkT0vh8AmwE/Bi5r+VVS5ZL/5bb/2D9j+yFJu3RYZETEeLCR7Q+PdOcqD6WeJ+np0fEkbUm1II6IGG8ulTR3pDtXCcb/BH4h6QKKh1JvA/5tpCeMiOhhJ1IMgfIk8GeKAQBte9MqO1d5KHVuOczrPuXB32L79lEUHBHRk2wP1sF0ZZUu3csATYhGRM8obz9+h+KJ/FLgbbYfGmS7pcAjFF88rRlu2GpJg40a+TBwt+017Wqqcg81IqIXfQS42vYOwNXl/FBeY/sVw4Vp6XTgeuAr5e964NvAbyS9vl1BCdSIGK8OAs4pp88B3lTDMZcCu9jezfZuFF9K3Qa8Djil3c5VxpQ6HjhvsKZ0RMRAk1Z3NCbZ1PIZTb8+230V932h7fsAbN8n6QVDbGfgSkkGvtzm+Du2Dmdv+3ZJu9i+q38E1OFUuYf6IuAGSQuAs4ArymFbIyJGa2Wbe5o/psiggT7ewTn2sr2iDNyrJP3a9rVDbHuHpDMoLvMB3k5xub8BxVP/YVV5yv9/JP0j8HrgKOA0Sd8Fvmb7zir/NBERI2H7dUOtK/tn3qpsnW4FPDDEMVaUfz4g6WJgDjBUoL4LeB9wEsVbTdcBJ1OE6Wva1VvpHmrZIr2//K0BtgAukNT2nkJERJdcAhxZTh9J8dnos0iaImmT/mmKhuFtQx3Q9p9s/6ftN9t+k+3/sP247adsP9quoCr3UE8oi10JfBX4B9t/lvQ84LfAh9odIyKiC/4d+K6kdwP3AG8FkLQ18FXbc4EXAheX9z8nA9+yfflQB5S0A/B/gZ2ADfuX235xlYKq3EOdSvEy/92tC20/JemAKieJiKib7T8Arx1k+Qpgbjl9F7BzB4f9OvBJiu5KX0Nxm7Py0L9tL/ltf2JgmLasq9yTdUTEOPB821cDsn237X+i+Eq0knRyEhHxjCf6b2eWr4zeCwz1OtZz5MX+iIhnnARsBJwA7AYczjMPvtpKCzUiomT7hnLyUYr7px1JoEbEhCfpkuHW2640DFQCNSIC9gSWAecDv6KDJ/utEqgREcXnrfsChwLvoBhH6vzW7/qryEOpiJjwbK+1fbntI4E9gCXATyS9v5PjNNJClfQZ4O+A1cCdwFGtAwFGRIy1sgOUN1K0UmcBpwIXdXKMplqoVwEvs/1y4DfARxuqIyICSecAvwB2Bf7Z9itt/4vtezs5TiMtVNtXtsxeDxzcRB0REaXDgceAlwAntPR9Wu8gfWPgaIpxYQYl6RjgGIDJm20x1GYRESNmu5ar9a4F6nAdw9r+QbnNxym6AzxvqOOUvWv3AWw4fWY6to6IntW1QB2uY1gASUcCBwCvzQgAEbEuaOop/37Ah4G/tf14EzVERNStqaf8pwGbUIzvcrOkMxuqIyKiNk095f+LJs4bEdFN+VIqIqImCdSIGJckvVXSIklPSRpuKOr9JN0haYmkj3SzpgRqRIxXtwFvYeghoZE0CfgSsD/FwHuHStqpWwX1wov9EREd6x/TruWrpsHMAZaUg/Uh6dvAQcDt3agpgRoRtZr0hNnszierbj5V0vyW+b7yY566TKfo57TfcmD3Go//LAnUiGjSStvD3f9s+8VlG4M1X7v2IVECNSJ6VrsvLitYDsxsmZ8BrBjlMYeUh1IRsS67AdhB0naS1gcOAYYdP2o0EqgRMS5JerOk5RTjQV0m6Ypy+daS5gHYXgMcD1wBLAa+2+mwJp3IJX9EjEu2LwYuHmT5CmBuy/w8YN5Y1JQWakRETRKoERE1SaBGRNQkgRoRUZMEakRETRKoERE1SaBGRNQkgRoRUZMEakRETRKoERE1SaBGRNQkgRoRUZMEakRETRKoERE1SaBGRNQkgRoRUZMEakRETRKoERE1SaBGxLgk6a2SFkl6StJwQ1EvlXSrpJslze9mTRlTKiLGq9uAtwBfrrDta2yv7HI9CdSIGJ9sLwaQ1HQpT8slf0Ss6wxcKelGScd080RpoUZErfTEatZfvKzq5lMH3Nfss9339LGkHwMvGmS/j9v+QcVz7GV7haQXAFdJ+rXta6sW2IkEakQ0aaXtIR8o2X7daE9ge0X55wOSLgbmAF0J1FzyR8Q6S9IUSZv0TwOvp3iY1RUJ1IgYlyS9WdJyYE/gMklXlMu3ljSv3OyFwHWSFgL/DVxm+/Ju1dToJb+kk4HPANPG4pWGiFh32L4YuHiQ5SuAueX0XcDOY1VTYy1USTOBfYF7mqohIqJOTV7yfw74EMUrDRER414jgSrpQOBe2wsrbHuMpPmS5q997LExqC4iYmS6dg91uPfHgI9RPG1rq3wnrQ9gw+kz05qNiJ7VtUAd6v0xSX8NbAcsLD8ZmwEskDTH9v3dqiciotvG/Cm/7VuBF/TPS1oKzM5T/ogY7/IeakRETRr/9NT2rKZriIioQ1qoERE1SaBGRNQkgRoRUZMEakRETRKoERE1SaBGRNQkgRoRUZMEakRETRKoERE1SaBGRNQkgRoRUZMEanTNBsvWb7qE6MB4++8l6TOSfi3pFkkXS9p8iO32k3SHpCWSPtLNmhKoETHuwrR0FfAy2y8HfgN8dOAGkiYBXwL2B3YCDpW0U7cKSqBGV43T/1EnlPH638j2lbbXlLPXU3RWP9AcYIntu2yvBr4NHNStmmSPn1FFJP0euLvGQ04FxlPH1uOtXhh/NU/0ere1PW00B5B0OUVdVWwIPNEy31cOe9TpOX8IfMf2NwcsPxjYz/b/LucPB3a3fXyn56ii8f5QOzHa/9ADSZpve3adx+ym8VYvjL+aU+/o2d6vrmMNNzad7R+U23wcWAOcN9ghBiuxrvoGGleBGhETy1Bj0/WTdCRwAPBaD365vRyY2TI/A1hRX4XPlnuoETEuSdoP+DBwoO3Hh9jsBmAHSdtJWh84BLikWzVN9EDt+F5Nw8ZbvTD+ak6948dpwCbAVZJulnQmgKStJc0DKB9aHQ9cASwGvmt7UbcKGlcPpSIietlEb6FGRNQmgRoRUZMEaknSyZIsqer7c42o+rld08byc786SJop6RpJiyUtknRi0zVVIWmSpJskXdp0LZFABYr/mYB9gXuarqWCtp/bNW2sP/eryRrgg7ZfCuwBHDcOagY4keJhS/SABGrhc8CH6OILv3Wp+Lld08b0c7862L7P9oJy+hGKkJrebFXDkzQDeCPw1aZricKED1RJBwL32l7YdC0jcDTwo6aLGMR0YFnL/HJ6PJxaSZoF7AL8quFS2vk8RUPgqYbriNKE+FJquM/XgI8Brx/bioZXw+d2TRvTz/3qJGlj4ELgJNurmq5nKJIOAB6wfaOkvRsuJ0oTIlCH+nxN0l8D2wELJUFx+bxA0hzb949hic9Sw+d2TRvTz/3qImk9ijA9z/ZFTdfTxl7AgZLmUnQwsqmkb9o+rOG6JrS82N9C0lJgtu2e7W2o/Nzus8Df2v590/UMRtJkigdmrwXupfj87x3d/EJltFT8jXoO8KDtkxoupyNlC/Vk2wc0XMqEN+HvoY5Dg35u10vG+nO/muwFHA7sU/57vbls/UVUlhZqRERN0kKNiKhJAjUioiYJ1IiImiRQIyJqkkCNiKhJAjXGlKRHyz+3lnTBKI5zkqSN6qssYvTy2lR0jaTJLR259C971PbGNRx7KT3+EUZMPGmhTgCSXln2n7qhpCllf58vG2S7I8rtFkr6RrlsW0lXl8uvlrRNm+VnS/qspGuAT5eDo/1S0g2S/qXlXLMk3VZOv0vSRZIul/RbSae0bHeGpPllzf9cLjsB2Bq4pjwPkl5fnmeBpO+V3+RHjC3b+U2AH/CvwH9Q9FP60UHW/xVwBzC1nN+y/POHwJHl9NHA99ssPxu4FJhUzl8CHFFOHwc8Wk7PAm4rp98F3AVsRvFd+t3AzAF1TAJ+Ary8nF/aUutU4FpgSjn/YeATTf87z2/i/dJCnTg+RdGJ9mzglEHW7wNc4PIS2vaD5fI9gW+V098A/meb5QDfs722nN4LOL9lu6Fcbfth208AtwPblsvfJmkBcBNF6A/W6fMe5fKfS7oZOLJl/4gxMyF6mwoAtgQ2BtajaAU+NmC9qNbF3lDbtC4feOwqx32yZXotMFnSdsDJwCttPyTpbIraBxJwle1DK5wnomvSQp04+oB/pOg/9dODrL+aojX4PwAkbVku/wVwSDn9TuC6NssH+vmA7TqxKUU4PyzphRRDqvR7hKKTGChGLthL0l+UtW8k6SUdniti1BKoE4CkI4A1tr8F/DvwSkn7tG7jojeofwN+KmkhRReBACcAR0m6haI3phPbLB/oRIrxmW6guEdamYtRFG4CFgFnUYRzvz7gR5KucdGN4buA88t6rgd27ORcEXXIa1MRETVJCzUioiYJ1IiImiRQIyJqkkCNiKhJAjUioiYJ1IiImiRQIyJq8v8Bq1FjWcBrGcEAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure()\n",
    "ax = fig.add_subplot(1,1,1)\n",
    "ax.set_aspect(1)\n",
    "plt.xlabel('x coordinate')\n",
    "plt.ylabel('y coordinate')\n",
    "plt.contourf( coords[0,:,:,0], coords[1,:,:,0], B[0,:,:,0] )\n",
    "cbar = plt.colorbar()\n",
    "cbar.set_label('Magnetic field Bx')\n",
    "plt.show()\n",
    "\n",
    "fig = plt.figure()\n",
    "ax = fig.add_subplot(1,1,1)\n",
    "ax.set_aspect(1)\n",
    "plt.xlabel('x coordinate')\n",
    "plt.ylabel('y coordinate')\n",
    "plt.contourf( coords[0,:,:,0], coords[1,:,:,0], B[1,:,:,0] )\n",
    "cbar = plt.colorbar()\n",
    "cbar.set_label('Magnetic field By')\n",
    "plt.show()\n",
    "\n",
    "fig = plt.figure()\n",
    "ax = fig.add_subplot(1,1,1)\n",
    "ax.set_aspect(1)\n",
    "plt.xlabel('x coordinate')\n",
    "plt.ylabel('y coordinate')\n",
    "plt.contourf( coords[0,:,:,0], coords[1,:,:,0], B[2,:,:,0] )\n",
    "cbar = plt.colorbar()\n",
    "cbar.set_label('Magnetic field Bz')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "111fd383",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure()\n",
    "ax = fig.add_subplot(1,1,1)\n",
    "ax.set_aspect(1)\n",
    "plt.xlabel('x coordinate')\n",
    "plt.ylabel('y coordinate')\n",
    "plt.contourf( coords[0,:,:,0], coords[1,:,:,0], np.sqrt( B[0,:,:,0]**2 + B[1,:,:,0]**2 + B[2,:,:,0]**2 ) )\n",
    "cbar = plt.colorbar()\n",
    "cbar.set_label('Magnetic field |B|')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "baf9bf8f",
   "metadata": {},
   "source": [
    "__Analytical solution:__\n",
    "\n",
    "\\\\( \\vec{B}(\\vec{r}) = \\frac{\\mu_0}{2\\pi}jF\\frac{1}{\\sqrt{x^2+y^2}}\\begin{pmatrix}-y\\\\x\\\\0\\end{pmatrix}\\\\)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "52c3c95b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x1ba2e331c10>]"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.xlabel('x coordinate')\n",
    "plt.ylabel('By')\n",
    "\n",
    "plt.scatter(coords[0,:,numpoints//2,0],B[1,:,numpoints//2,0])\n",
    "\n",
    "xlist = np.linspace(-coordMax,coordMax,10001)\n",
    "plt.plot(\n",
    "    xlist,\n",
    "    mu0/(2*np.pi) * j0 * df / np.sqrt( xlist**2 + coords[1,0,numpoints//2,0]**2 )**2 * xlist,\n",
    "    'red')"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "id": "c501d3d6",
   "metadata": {},
   "source": [
    "![hand](figure_05_hand.svg)\n",
    "\n",
    "https://upload.wikimedia.org/wikipedia/commons/3/3e/Manoderecha.svg"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "a7611de8",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Change standard size of all figures in this notebook\n",
    "plt.rcParams['figure.figsize'] = [40, 15]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "ff34d5c6",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<mpl_toolkits.mplot3d.art3d.Line3DCollection at 0x1ba2e2ea760>"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 2880x1080 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "arrowplot = plt.axes(projection='3d')\n",
    "arrowplot.set_zlim([-1,1])\n",
    "\n",
    "# background invisible\n",
    "arrowplot.axis(False)\n",
    "\n",
    "scale = 0.2e6\n",
    "arrowplot.quiver(\n",
    "    coords[0],coords[1],coords[2],\n",
    "    B[0]*scale,B[1]*scale,B[2]*scale,\n",
    ")"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "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": "3.9.7"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}
