{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "a511b486",
   "metadata": {},
   "outputs": [],
   "source": [
    "import sympy as sym\n",
    "import matplotlib.pyplot as plt\n",
    "from IPython.display import display\n",
    "from numpy import pi\n",
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "4135d0a2",
   "metadata": {},
   "outputs": [],
   "source": [
    "xs, xi, ys,yi, xj, yj, r, th, q, q1, qi,eps0, U = sym.symbols(\"x x_i  y y_i x_j y_j r theta q q_1 q_i epsilon_0 U\", real=True, positive=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "989d5f25",
   "metadata": {},
   "source": [
    "The value for $\\epsilon_0$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "2b15f7f2",
   "metadata": {},
   "outputs": [],
   "source": [
    "eps0_val = 8.8541878128e-12"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "86ca2ad3",
   "metadata": {},
   "outputs": [],
   "source": [
    "# elementary charge in coulombs\n",
    "elem_charge = 1.60218e-19"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "478e0776",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle - \\frac{q_{i}}{4 \\pi \\epsilon_{0} \\sqrt{\\left(r \\sin{\\left(\\theta \\right)} - y_{i} + y_{j}\\right)^{2} + \\left(r \\cos{\\left(\\theta \\right)} - x_{i} + x_{j}\\right)^{2}}}$"
      ],
      "text/plain": [
       "-q_i/(4*pi*epsilon_0*sqrt((r*sin(theta) - y_i + y_j)**2 + (r*cos(theta) - x_i + x_j)**2))"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "e1 = -qi/(4*sym.pi*eps0 * sym.sqrt((xj-xi+r*sym.cos(th))**2+(yj-yi+r*sym.sin(th))**2))\n",
    "e1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "f8edfba3",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle - \\frac{q_{i}}{4 \\pi \\epsilon_{0} \\sqrt{r^{2} \\sin^{2}{\\left(\\theta \\right)} + r^{2} \\cos^{2}{\\left(\\theta \\right)}}}$"
      ],
      "text/plain": [
       "-q_i/(4*pi*epsilon_0*sqrt(r**2*sin(theta)**2 + r**2*cos(theta)**2))"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "e2 = e1.subs([(xi, xj), (yi,yj)])\n",
    "e2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "4eb9a83f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle - \\frac{q_{i}}{4 \\pi \\epsilon_{0} r}$"
      ],
      "text/plain": [
       "-q_i/(4*pi*epsilon_0*r)"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sym.simplify(e2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 86,
   "id": "3284ebc8",
   "metadata": {},
   "outputs": [],
   "source": [
    "charges =[(-5, 0, elem_charge), (5, 0, -elem_charge) ]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 87,
   "id": "8bb93fa3",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\frac{4.52379154890926 \\cdot 10^{-9}}{\\pi \\sqrt{r^{2} \\sin^{2}{\\left(\\theta \\right)} + \\left(r \\cos{\\left(\\theta \\right)} - 10\\right)^{2}}} - \\frac{4.52379154890926 \\cdot 10^{-9}}{\\pi \\sqrt{r^{2} \\sin^{2}{\\left(\\theta \\right)} + r^{2} \\cos^{2}{\\left(\\theta \\right)}}}$"
      ],
      "text/plain": [
       "4.52379154890926e-9/(pi*sqrt(r**2*sin(theta)**2 + (r*cos(theta) - 10)**2)) - 4.52379154890926e-9/(pi*sqrt(r**2*sin(theta)**2 + r**2*cos(theta)**2))"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "expr = None\n",
    "for charge in charges:\n",
    "    x,y, q = charge \n",
    "    xx, yy, _ = charges[0]\n",
    "    ex = e1.subs([(eps0, eps0_val ), (xi, x), (yi, y), (xj, xx), (yj, yy), (qi, q)])\n",
    "    if expr:\n",
    "        expr = expr + ex\n",
    "    else:\n",
    "        expr = ex\n",
    "display((expr))\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 98,
   "id": "d32b4a8c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[(1.0, -1.2966854442641348e-09),\n",
       " (1.5555555555555556, -7.834078724500479e-10),\n",
       " (2.111111111111111, -5.411985388632747e-10),\n",
       " (2.666666666666667, -4.008531417970741e-10),\n",
       " (3.2222222222222223, -3.098291875021055e-10),\n",
       " (3.7777777777777777, -2.4646293894691007e-10),\n",
       " (4.333333333333334, -2.0017517447414152e-10),\n",
       " (4.888888888888889, -1.6517438697462444e-10),\n",
       " (5.444444444444445, -1.3801606071754804e-10),\n",
       " (6.0, -1.1651839479395206e-10)]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fexpr = sym.lambdify([th, r], expr)\n",
    "potentials = []\n",
    "for rr in np.linspace(1, 6, 10):\n",
    "    potentials.append((rr, fexpr(pi/2, rr)))\n",
    "    #print (rr, f(rr, pi/2 ))\n",
    "display(potentials)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "id": "39f01395",
   "metadata": {},
   "outputs": [],
   "source": [
    "from scipy.optimize import root_scalar\n",
    "from matplotlib.collections import LineCollection"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 90,
   "id": "3da69438",
   "metadata": {},
   "outputs": [],
   "source": [
    "def fn(r, theta, potential_num):\n",
    "    return fexpr(theta, r) - potentials[potential_num][1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "id": "8aab7a25",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.6714268217467587e-11"
      ]
     },
     "execution_count": 91,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "fn(1,0, 0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 99,
   "id": "025cb173",
   "metadata": {},
   "outputs": [],
   "source": [
    "results = []\n",
    "for ellipse in np.arange(0,8):\n",
    "    subresults = []\n",
    "    for theta in np.linspace(0, 2*pi, 36):\n",
    "        res = root_scalar(fn,args=(theta, ellipse), method='secant', x0=.1, x1=.2, rtol=0.01 )\n",
    "        subresults.append((res.root*np.cos(theta)-5, res.root*np.sin(theta)))\n",
    "    results.append(subresults)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "e730e62f",
   "metadata": {},
   "outputs": [],
   "source": [
    "tot = 0\n",
    "for charge in charges:\n",
    "    print (charge)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 100,
   "id": "49ae030a",
   "metadata": {},
   "outputs": [
    {
     "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": [
    "fig, ax = plt.subplots()\n",
    "\n",
    "for charge in charges:\n",
    "    ax.plot(int(charge[0]), int(charge[1]), 'o', ms=15)\n",
    "\n",
    "lines = LineCollection(results)\n",
    "ax.add_collection(lines)\n",
    "ax.set_xlim((-10,10))\n",
    "ax.set_ylim((-10,10))\n",
    "\n",
    "\n",
    "ax.grid()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "f1a7a2bb",
   "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": "3.8.10"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}