{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from matplotlib.patches import Circle"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Primero definimos una función para calcular el campo eléctrico"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def E(xp, yp, xf=0, yf=0, q=1):\n",
    "    \"\"\"Campo Eléctrico en 2 Dimensiones \n",
    "    en un punto de prueba xp, yp\n",
    "    de una carga fuente en un punto xf, yf\n",
    "    de valor q\n",
    "    \"\"\"    \n",
    "    \n",
    "    Dx = xp - xf\n",
    "    Dy = yp - yf\n",
    "    \n",
    "    den = (Dx**2 + Dy**2)**1.5\n",
    "    \n",
    "    # Noten que la respuesta e sun vector (Ex, Ey)\n",
    "    return q * Dx / den, q * Dy / den"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Algunos graficos a lo largo de los ejes cartesianos de una carga en el origen"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Primero definimos un rango para graficar, de 1 a 10 con 100 pasos\n",
    "rango = np.linspace(1, 10, 100)\n",
    "\n",
    "# Campo a lo largo del Eje X \n",
    "Ex, Ey = E(rango, 0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "plt.plot(rango, Ex);\n",
    "plt.xlabel('x');\n",
    "plt.ylabel('Ex');\n",
    "plt.title('Campo sobre el eje x (y=0)');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "plt.plot(rango, Ey);\n",
    "plt.xlabel('y');\n",
    "plt.ylabel('Ey');\n",
    "plt.title('Campo sobre el eje x (y=0)');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Ahora lo mismo sobre el eje y \n",
    "Ex, Ey = E(0, rango)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "plt.plot(rango, Ex);\n",
    "plt.xlabel('x');\n",
    "plt.ylabel('Ex');\n",
    "plt.title('Campo sobre el eje y (x=0)');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "plt.plot(rango, Ey);\n",
    "plt.xlabel('y');\n",
    "plt.ylabel('Ey');\n",
    "plt.title('Campo sobre el eje y (x=0)');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Ahora en la dirección radial, x=y\n",
    "Ex, Ey = E(rango, rango)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# y graficamos todo junto\n",
    "r = (rango**2+rango**2)**0.5\n",
    "plt.plot(rango, Ex, 'rx-', rango, Ey, 'g.-', rango, (Ex**2+Ey**2)**0.5, 'b');\n",
    "plt.xlabel('r');\n",
    "plt.ylabel('E');\n",
    "plt.title('Campo sobre la dirección radial (x=y)');\n",
    "plt.legend(['Ex', 'Ey', 'Etotal']);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Ahora con carga negativa. \n",
    "# Noten que el campo total esta en modulo\n",
    "\n",
    "Ex, Ey = E(rango, rango, q=-1)\n",
    "r = (rango**2+rango**2)**0.5\n",
    "plt.plot(rango, Ex, 'rx-', rango, Ey, 'g.-', rango, (Ex**2+Ey**2)**0.5, 'b');\n",
    "plt.xlabel('r');\n",
    "plt.ylabel('E');\n",
    "plt.title('Campo sobre la dirección radial (x=y)');\n",
    "plt.legend(['Ex', 'Ey', 'Etotal']);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Generamos una grilla donde vamos a calcular el campo eléctrico\n",
    "nx, ny = 64, 64\n",
    "rangoX = np.linspace(-2, 2, nx)*1\n",
    "rangoY = np.linspace(-2, 2, ny)*1\n",
    "grillaX, grillaY = np.meshgrid(rangoX, rangoY)\n",
    "\n",
    "# Y calculamos los campos\n",
    "Ex, Ey = E(grillaX, grillaY)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "fig = plt.figure(figsize=(17,17))\n",
    "ax = fig.add_subplot(111)\n",
    "\n",
    "\n",
    "color = np.log(np.sqrt(Ex**2 + Ey**2))\n",
    "ax.streamplot(grillaX, grillaY, Ex, Ey, color=color, linewidth=1, cmap=plt.cm.inferno,\n",
    "              density=2, arrowstyle='->', arrowsize=1.5)\n",
    "\n",
    "ax.add_artist(Circle([0,0], 0.05, color='#aa0000'))\n",
    "\n",
    "ax.set_xlabel('$x$')\n",
    "ax.set_ylabel('$y$')\n",
    "ax.set_xlim(-2,2)\n",
    "ax.set_ylim(-2,2)\n",
    "ax.set_aspect('equal')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Ahora para una carga negativa\n",
    "Ex, Ey = E(grillaX, grillaY, q=-1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "fig = plt.figure(figsize=(17,17))\n",
    "ax = fig.add_subplot(111)\n",
    "\n",
    "\n",
    "color = np.log(np.sqrt(Ex**2 + Ey**2))\n",
    "ax.streamplot(grillaX, grillaY, Ex, Ey, color=color, linewidth=1, cmap=plt.cm.inferno,\n",
    "              density=2, arrowstyle='->', arrowsize=1.5)\n",
    "\n",
    "ax.add_artist(Circle([0,0], 0.05, color='#0000aa'))\n",
    "\n",
    "ax.set_xlabel('$x$')\n",
    "ax.set_ylabel('$y$')\n",
    "ax.set_xlim(-2,2)\n",
    "ax.set_ylim(-2,2)\n",
    "ax.set_aspect('equal')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
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