Helmholtz coil modelling (2D graph ver).ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Consider a current $I$ flowing counterclockwise in a circle in the xy-plane. Parameterise this loop in terms of t:\n",
    "$$ x = cos(t), y = sin(t), z = z_0$$ \n",
    "\n",
    "\n",
    "where $0 \\leq t \\leq 2\\pi$ and $z_0$ is the position of the circle in the z axis. The Biot-Savard Law tells us\n",
    "\n",
    "$$\\vec{B}(\\vec{r}) =  \\frac{\\mu_0 I}{4 \\pi} \\int_C \\frac{d\\vec{l} \\times (\\vec{r}-\\vec{l})}{|\\vec{r}-\\vec{l}|^3} = \\int_0^{2 \\pi} \\frac{d\\vec{l}/dt \\times (\\vec{r} - \\vec{l})}{|\\vec{r}-\\vec{l}|^3} dt$$\n",
    "\n",
    "Putting this in dimensionless form \n",
    "\n",
    "* $\\vec{l} \\to \\vec{l}/R$\n",
    "* $\\vec{r} \\to \\vec{r}/R$\n",
    "\n",
    "we get\n",
    "\n",
    "$$\\frac{4 \\pi R}{\\mu_0 I} \\vec{B}(\\vec{r}) = \\int_0^{2 \\pi} \\frac{d\\vec{l}/dt \\times (\\vec{r} - \\vec{l})}{|\\vec{r}-\\vec{l}|^3} dt$$\n",
    "\n",
    "So basically the value of $B$ we get here is actually scaled in terms of the other constant. If we want to compare with the magnet mapper then we can mutiply by reciprocal of the constants on the LHS"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from scipy.integrate import quad\n",
    "import plotly.graph_objects as go\n",
    "from IPython.display import HTML\n",
    "import sympy as smp\n",
    "from sympy.vector import cross\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Start by looking at curve"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'\\ndef l(phi):\\n    return np.array([np.cos(phi), np.sin(phi), (phi-np.pi)/np.pi])\\n    '"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "phi = np.linspace(0, 2*np.pi, 100)\n",
    "\n",
    "def l(phi):\n",
    "    return np.array([np.cos(phi), np.sin(phi), np.zeros(len(phi))+0.5])\n",
    "\n",
    "'''\n",
    "def l(phi):\n",
    "    return np.array([np.cos(phi), np.sin(phi), (phi-np.pi)/np.pi])\n",
    "    '''"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "lx, ly, lz = l(phi)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 504x504 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(7,7))\n",
    "plt.plot(lx, ly)\n",
    "plt.xlabel('$x/R$', fontsize=25)\n",
    "plt.ylabel('$y/R$', fontsize=25)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Lets solve for the integrand using sympy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "t, x, y, z = smp.symbols('t, x, y, z') #x,y,z are the x y z of the position vector"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Get $l$, $r$, and the seperation vector $\\vec{r} - \\vec{l}$ for each coil (at z = ±0.5R)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "l = smp.Matrix([smp.cos(t), smp.sin(t), 0.5]) #symbolic \n",
    "#l = smp.Matrix([smp.cos(t), smp.sin(t), (t-smp.pi)/smp.pi])\n",
    "r = smp.Matrix([x, y, z])\n",
    "sep = r-l #separation vector"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}x - \\cos{\\left(t \\right)}\\\\y - \\sin{\\left(t \\right)}\\\\z - 0.5\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "Matrix([\n",
       "[x - cos(t)],\n",
       "[y - sin(t)],\n",
       "[   z - 0.5]])"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "r-l"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Coil 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "l_2 = smp.Matrix([smp.cos(t), smp.sin(t), -0.5]) #symbolic \n",
    "sep_2 = r-l_2 #separation vector"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}x - \\cos{\\left(t \\right)}\\\\y - \\sin{\\left(t \\right)}\\\\z + 0.5\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "Matrix([\n",
       "[x - cos(t)],\n",
       "[y - sin(t)],\n",
       "[   z + 0.5]])"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "r-l_2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Other coils (close together)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "l_3 = smp.Matrix([smp.cos(t), smp.sin(t), 0.508]) #symbolic \n",
    "sep_3 = r-l_3 #separation vector"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "l_4 = smp.Matrix([smp.cos(t), smp.sin(t), -0.508]) #symbolic \n",
    "sep_4 = r-l_4 #separation vector"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Define the integrand for each coil"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "integrand = smp.diff(l, t).cross(sep) / sep.norm()**3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "integrand_2 =  smp.diff(l_2, t).cross(sep_2) / sep_2.norm()**3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "integrand_3 =  smp.diff(l_3, t).cross(sep_3) / sep_3.norm()**3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "integrand_4 =  smp.diff(l_4, t).cross(sep_4) / sep_4.norm()**3"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Get the $x$, $y$, and $z$ components of the integrand for each coil"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "dBxdt = smp.lambdify([t, x, y, z], integrand[0]) #integrand[0] = x component\n",
    "dBydt = smp.lambdify([t, x, y, z], integrand[1])\n",
    "dBzdt = smp.lambdify([t, x, y, z], integrand[2])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "dBxdt_2 = smp.lambdify([t, x, y, z], integrand_2[0]) #integrand[0] = x component\n",
    "dBydt_2 = smp.lambdify([t, x, y, z], integrand_2[1])\n",
    "dBzdt_2 = smp.lambdify([t, x, y, z], integrand_2[2])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "dBxdt_3 = smp.lambdify([t, x, y, z], integrand_3[0]) #integrand[0] = x component\n",
    "dBydt_3 = smp.lambdify([t, x, y, z], integrand_3[1])\n",
    "dBzdt_3 = smp.lambdify([t, x, y, z], integrand_3[2])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "dBxdt_4 = smp.lambdify([t, x, y, z], integrand_4[0]) #integrand[0] = x component\n",
    "dBydt_4 = smp.lambdify([t, x, y, z], integrand_4[1])\n",
    "dBzdt_4 = smp.lambdify([t, x, y, z], integrand_4[2])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Get the magnetic field by performing the integral over each component for each coil"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "def B(x, y, z):\n",
    "    return np.array([quad(dBxdt, 0, 2*np.pi, args=(x, y, z))[0],\n",
    "                     quad(dBydt, 0, 2*np.pi, args=(x, y, z))[0],\n",
    "                     quad(dBzdt, 0, 2*np.pi, args=(x, y, z))[0]]) #[0] is the integral, [1] is uncer\n",
    "\n",
    "#need to add up contribution due to all different t "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "def B_2(x, y, z):\n",
    "    return np.array([quad(dBxdt_2, 0, 2*np.pi, args=(x, y, z))[0],\n",
    "                     quad(dBydt_2, 0, 2*np.pi, args=(x, y, z))[0],\n",
    "                     quad(dBzdt_2, 0, 2*np.pi, args=(x, y, z))[0]]) #[0] is the integral, [1] is uncer\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "def B_3(x, y, z):\n",
    "    return np.array([quad(dBxdt_3, 0, 2*np.pi, args=(x, y, z))[0],\n",
    "                     quad(dBydt_3, 0, 2*np.pi, args=(x, y, z))[0],\n",
    "                     quad(dBzdt_3, 0, 2*np.pi, args=(x, y, z))[0]]) #[0] is the integral, [1] is uncer\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "def B_4(x, y, z):\n",
    "    return np.array([quad(dBxdt_4, 0, 2*np.pi, args=(x, y, z))[0],\n",
    "                     quad(dBydt_4, 0, 2*np.pi, args=(x, y, z))[0],\n",
    "                     quad(dBzdt_4, 0, 2*np.pi, args=(x, y, z))[0]]) #[0] is the integral, [1] is uncer\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Plotting B_z vs z for x=y=0. Make more coils using the same method above then use superposition. Since coils are tightly packed, we can just mutiply it by the number of turns."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [],
   "source": [
    "#scaling for unit here. Mutiply magnetic field by scale to obtain value in tesla \n",
    "u_0 = 4*np.pi*10**(-7)\n",
    "I = 1\n",
    "R = 12.5/1000\n",
    "scale =u_0*I/(4*np.pi*R)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'I = 1 A, radius = 12.5 mm, 14 turns each side')"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 504x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "z_coordinate=np.linspace(-3,3,100)\n",
    "magnetic_field_1 =[] #we will append to this empty list\n",
    "magnetic_field_2=[]\n",
    "magnetic_field_3=[]\n",
    "magnetic_field_4=[]\n",
    "\n",
    "for i in range(len(z_coordinate)):\n",
    "    magnetic_field_1.append(B(0,0,z_coordinate[i])[2]*scale)\n",
    "    magnetic_field_2.append(B_2(0,0,z_coordinate[i])[2]*scale)\n",
    "    magnetic_field_3.append(B_3(0,0,z_coordinate[i])[2]*scale)\n",
    "    magnetic_field_4.append(B_4(0,0,z_coordinate[i])[2]*scale)\n",
    "\n",
    "\n",
    "\n",
    "plt.figure(figsize=(7,5))\n",
    "plt.plot(z_coordinate,magnetic_field_1,label='single coil at z = 0.5R',linestyle='dashed')\n",
    "plt.plot(z_coordinate,magnetic_field_2,label='single coil at z = -0.5R',linestyle='dashed')\n",
    "#plt.plot(z_coordinate,magnetic_field_3,label='coil centered at z = 0.505R',linestyle='dashed')\n",
    "#plt.plot(z_coordinate,magnetic_field_4,label='coil centered at z = -0.505R',linestyle='dashed')\n",
    "\n",
    "\n",
    "\n",
    "magnetic_field_net_1=[]\n",
    "magnetic_field_net_2=[]\n",
    "\n",
    "for j in range(len(magnetic_field_1)):\n",
    "    magnetic_field_net_1.append((magnetic_field_1[j]+magnetic_field_2[j])*14)\n",
    "    #magnetic_field_net_2.append(magnetic_field_1[j]+magnetic_field_2[j]+magnetic_field_3[j]+magnetic_field_4[j])\n",
    "\n",
    "\n",
    "plt.plot(z_coordinate,magnetic_field_net_1,label='14 turns on each side')\n",
    "#plt.plot(z_coordinate,magnetic_field_net_2,label='4 coils. each side slightly separated')\n",
    "\n",
    "#superposition \n",
    "plt.xlabel('z / R',fontsize=25)\n",
    "plt.ylabel(' B_z (T)',fontsize=25)\n",
    "plt.grid()\n",
    "plt.legend()\n",
    "plt.title('I = 1 A, radius = 12.5 mm, 14 turns each side',fontsize=25)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Define the function to calculate field strength"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [],
   "source": [
    "def field_strength(B_x,B_y,B_z):\n",
    "    return np.sqrt(B_x**2+B_y**2+B_z**2)\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [],
   "source": [
    "x = np.linspace(-1, 1, 20) \n",
    "xv, yv= np.meshgrid(x, x) \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Obtaining the component of the field and finding the field strength on z =0"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To change which plane you want to look at, change the '0' to whatever number you want in args part of the next cell"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Defining the integral for each plane \n",
    "def B_zplane(x,y):\n",
    "    return np.array([quad(dBxdt, 0, 2*np.pi, args=(x, y, 0))[0],\n",
    "                     quad(dBydt, 0, 2*np.pi, args=(x, y, 0))[0],\n",
    "                     quad(dBzdt, 0, 2*np.pi, args=(x, y, 0))[0]]) #for example change 0 --> 1 for z = 1\n",
    "\n",
    "def B_zplane_2(x,y):\n",
    "    return np.array([quad(dBxdt_2, 0, 2*np.pi, args=(x, y, 0))[0],\n",
    "                     quad(dBydt_2, 0, 2*np.pi, args=(x, y, 0))[0],\n",
    "                     quad(dBzdt_2, 0, 2*np.pi, args=(x, y, 0))[0]]) #same here"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[5.79516267e-06 3.80244079e-06 7.27249179e-07 3.41648062e-06\n",
      "  8.36193975e-06 1.36129848e-05 1.85741234e-05 2.27095494e-05\n",
      "  2.56396520e-05 2.71496046e-05 2.71496046e-05 2.56396520e-05\n",
      "  2.27095494e-05 1.85741234e-05 1.36129848e-05 8.36193975e-06\n",
      "  3.41648062e-06 7.27249179e-07 3.80244079e-06 5.79516267e-06]\n",
      " [3.80244079e-06 2.28836409e-07 4.90920212e-06 1.13848929e-05\n",
      "  1.85741234e-05 2.56396520e-05 3.18230524e-05 3.66365163e-05\n",
      "  3.98690908e-05 4.14792621e-05 4.14792621e-05 3.98690908e-05\n",
      "  3.66365163e-05 3.18230524e-05 2.56396520e-05 1.85741234e-05\n",
      "  1.13848929e-05 4.90920212e-06 2.28836409e-07 3.80244079e-06]\n",
      " [7.27249179e-07 4.90920212e-06 1.24775919e-05 2.12943924e-05\n",
      "  3.02446508e-05 3.82533434e-05 4.46647318e-05 4.92887070e-05\n",
      "  5.22190776e-05 5.36269847e-05 5.36269847e-05 5.22190776e-05\n",
      "  4.92887070e-05 4.46647318e-05 3.82533434e-05 3.02446508e-05\n",
      "  2.12943924e-05 1.24775919e-05 4.90920212e-06 7.27249179e-07]\n",
      " [3.41648062e-06 1.13848929e-05 2.12943924e-05 3.18230524e-05\n",
      "  4.14792621e-05 4.92887070e-05 5.49921375e-05 5.88021243e-05\n",
      "  6.10811275e-05 6.21372284e-05 6.21372284e-05 6.10811275e-05\n",
      "  5.88021243e-05 5.49921375e-05 4.92887070e-05 4.14792621e-05\n",
      "  3.18230524e-05 2.12943924e-05 1.13848929e-05 3.41648062e-06]\n",
      " [8.36193975e-06 1.85741234e-05 3.02446508e-05 4.14792621e-05\n",
      "  5.07717740e-05 5.75822745e-05 6.21372284e-05 6.49608461e-05\n",
      "  6.65532814e-05 6.72632345e-05 6.72632345e-05 6.65532814e-05\n",
      "  6.49608461e-05 6.21372284e-05 5.75822745e-05 5.07717740e-05\n",
      "  4.14792621e-05 3.02446508e-05 1.85741234e-05 8.36193975e-06]\n",
      " [1.36129848e-05 2.56396520e-05 3.82533434e-05 4.92887070e-05\n",
      "  5.75822745e-05 6.31362735e-05 6.65532814e-05 6.85144047e-05\n",
      "  6.95481173e-05 6.99868963e-05 6.99868963e-05 6.95481173e-05\n",
      "  6.85144047e-05 6.65532814e-05 6.31362735e-05 5.75822745e-05\n",
      "  4.92887070e-05 3.82533434e-05 2.56396520e-05 1.36129848e-05]\n",
      " [1.85741234e-05 3.18230524e-05 4.46647318e-05 5.49921375e-05\n",
      "  6.21372284e-05 6.65532814e-05 6.90577877e-05 7.03757530e-05\n",
      "  7.10107063e-05 7.12604911e-05 7.12604911e-05 7.10107063e-05\n",
      "  7.03757530e-05 6.90577877e-05 6.65532814e-05 6.21372284e-05\n",
      "  5.49921375e-05 4.46647318e-05 3.18230524e-05 1.85741234e-05]\n",
      " [2.27095494e-05 3.66365163e-05 4.92887070e-05 5.88021243e-05\n",
      "  6.49608461e-05 6.85144047e-05 7.03757530e-05 7.12604911e-05\n",
      "  7.16342533e-05 7.17621329e-05 7.17621329e-05 7.16342533e-05\n",
      "  7.12604911e-05 7.03757530e-05 6.85144047e-05 6.49608461e-05\n",
      "  5.88021243e-05 4.92887070e-05 3.66365163e-05 2.27095494e-05]\n",
      " [2.56396520e-05 3.98690908e-05 5.22190776e-05 6.10811275e-05\n",
      "  6.65532814e-05 6.95481173e-05 7.10107063e-05 7.16342533e-05\n",
      "  7.18532852e-05 7.19096504e-05 7.19096504e-05 7.18532852e-05\n",
      "  7.16342533e-05 7.10107063e-05 6.95481173e-05 6.65532814e-05\n",
      "  6.10811275e-05 5.22190776e-05 3.98690908e-05 2.56396520e-05]\n",
      " [2.71496046e-05 4.14792621e-05 5.36269847e-05 6.21372284e-05\n",
      "  6.72632345e-05 6.99868963e-05 7.12604911e-05 7.17621329e-05\n",
      "  7.19096504e-05 7.19331442e-05 7.19331442e-05 7.19096504e-05\n",
      "  7.17621329e-05 7.12604911e-05 6.99868963e-05 6.72632345e-05\n",
      "  6.21372284e-05 5.36269847e-05 4.14792621e-05 2.71496046e-05]\n",
      " [2.71496046e-05 4.14792621e-05 5.36269847e-05 6.21372284e-05\n",
      "  6.72632345e-05 6.99868963e-05 7.12604911e-05 7.17621329e-05\n",
      "  7.19096504e-05 7.19331442e-05 7.19331442e-05 7.19096504e-05\n",
      "  7.17621329e-05 7.12604911e-05 6.99868963e-05 6.72632345e-05\n",
      "  6.21372284e-05 5.36269847e-05 4.14792621e-05 2.71496046e-05]\n",
      " [2.56396520e-05 3.98690908e-05 5.22190776e-05 6.10811275e-05\n",
      "  6.65532814e-05 6.95481173e-05 7.10107063e-05 7.16342533e-05\n",
      "  7.18532852e-05 7.19096504e-05 7.19096504e-05 7.18532852e-05\n",
      "  7.16342533e-05 7.10107063e-05 6.95481173e-05 6.65532814e-05\n",
      "  6.10811275e-05 5.22190776e-05 3.98690908e-05 2.56396520e-05]\n",
      " [2.27095494e-05 3.66365163e-05 4.92887070e-05 5.88021243e-05\n",
      "  6.49608461e-05 6.85144047e-05 7.03757530e-05 7.12604911e-05\n",
      "  7.16342533e-05 7.17621329e-05 7.17621329e-05 7.16342533e-05\n",
      "  7.12604911e-05 7.03757530e-05 6.85144047e-05 6.49608461e-05\n",
      "  5.88021243e-05 4.92887070e-05 3.66365163e-05 2.27095494e-05]\n",
      " [1.85741234e-05 3.18230524e-05 4.46647318e-05 5.49921375e-05\n",
      "  6.21372284e-05 6.65532814e-05 6.90577877e-05 7.03757530e-05\n",
      "  7.10107063e-05 7.12604911e-05 7.12604911e-05 7.10107063e-05\n",
      "  7.03757530e-05 6.90577877e-05 6.65532814e-05 6.21372284e-05\n",
      "  5.49921375e-05 4.46647318e-05 3.18230524e-05 1.85741234e-05]\n",
      " [1.36129848e-05 2.56396520e-05 3.82533434e-05 4.92887070e-05\n",
      "  5.75822745e-05 6.31362735e-05 6.65532814e-05 6.85144047e-05\n",
      "  6.95481173e-05 6.99868963e-05 6.99868963e-05 6.95481173e-05\n",
      "  6.85144047e-05 6.65532814e-05 6.31362735e-05 5.75822745e-05\n",
      "  4.92887070e-05 3.82533434e-05 2.56396520e-05 1.36129848e-05]\n",
      " [8.36193975e-06 1.85741234e-05 3.02446508e-05 4.14792621e-05\n",
      "  5.07717740e-05 5.75822745e-05 6.21372284e-05 6.49608461e-05\n",
      "  6.65532814e-05 6.72632345e-05 6.72632345e-05 6.65532814e-05\n",
      "  6.49608461e-05 6.21372284e-05 5.75822745e-05 5.07717740e-05\n",
      "  4.14792621e-05 3.02446508e-05 1.85741234e-05 8.36193975e-06]\n",
      " [3.41648062e-06 1.13848929e-05 2.12943924e-05 3.18230524e-05\n",
      "  4.14792621e-05 4.92887070e-05 5.49921375e-05 5.88021243e-05\n",
      "  6.10811275e-05 6.21372284e-05 6.21372284e-05 6.10811275e-05\n",
      "  5.88021243e-05 5.49921375e-05 4.92887070e-05 4.14792621e-05\n",
      "  3.18230524e-05 2.12943924e-05 1.13848929e-05 3.41648062e-06]\n",
      " [7.27249179e-07 4.90920212e-06 1.24775919e-05 2.12943924e-05\n",
      "  3.02446508e-05 3.82533434e-05 4.46647318e-05 4.92887070e-05\n",
      "  5.22190776e-05 5.36269847e-05 5.36269847e-05 5.22190776e-05\n",
      "  4.92887070e-05 4.46647318e-05 3.82533434e-05 3.02446508e-05\n",
      "  2.12943924e-05 1.24775919e-05 4.90920212e-06 7.27249179e-07]\n",
      " [3.80244079e-06 2.28836409e-07 4.90920212e-06 1.13848929e-05\n",
      "  1.85741234e-05 2.56396520e-05 3.18230524e-05 3.66365163e-05\n",
      "  3.98690908e-05 4.14792621e-05 4.14792621e-05 3.98690908e-05\n",
      "  3.66365163e-05 3.18230524e-05 2.56396520e-05 1.85741234e-05\n",
      "  1.13848929e-05 4.90920212e-06 2.28836409e-07 3.80244079e-06]\n",
      " [5.79516267e-06 3.80244079e-06 7.27249179e-07 3.41648062e-06\n",
      "  8.36193975e-06 1.36129848e-05 1.85741234e-05 2.27095494e-05\n",
      "  2.56396520e-05 2.71496046e-05 2.71496046e-05 2.56396520e-05\n",
      "  2.27095494e-05 1.85741234e-05 1.36129848e-05 8.36193975e-06\n",
      "  3.41648062e-06 7.27249179e-07 3.80244079e-06 5.79516267e-06]]\n"
     ]
    }
   ],
   "source": [
    "B_field = np.vectorize(B_zplane, signature='(),()->(n)')(xv, yv)\n",
    "B_field_2 = np.vectorize(B_zplane_2, signature='(),()->(n)')(xv, yv)\n",
    "\n",
    "Bx =(B_field[:,:,0]+B_field_2[:,:,0])*scale \n",
    "By = (B_field[:,:,1]+B_field_2[:,:,1])*scale\n",
    "Bz = (B_field[:,:,2]+B_field_2[:,:,2])*scale\n",
    "field_magnitude = field_strength(Bx,By,Bz) #unit in tesla\n",
    "print(field_magnitude)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Contour plot using matplotlib"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x432 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from matplotlib import ticker, cm\n",
    "fig, ax = plt.subplots(figsize=(6,6))\n",
    "cs = ax.contourf(xv, yv, field_magnitude*14) #14 turns each side\n",
    "cbar = fig.colorbar(cs)\n",
    "\n",
    "plt.xlabel('x / R',fontsize=13)\n",
    "plt.ylabel('y / R',fontsize=13)\n",
    "plt.title('Magnetic field strength on the plane z =0',fontsize=13)\n",
    "plt.savefig('1.png',dpi=500)\n",
    "\n",
    "#so 1000 A from the disc"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "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": 4
}