{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Eksamen i Fys1120 H2023 - Oppgave 1\n",
    "*Du kan totalt få 100 poeng i denne oppgaven. Maksimal poengsum er oppgitt for hver deloppgave.*\n",
    "\n",
    "Vi skal i denne oppgaven studere det elektriske feltet rundt en dipol som består av to ringformede ladninger.\n",
    "Vi skal først studere en enkelt ringladning og deretter se på to ringladninger med motsatt ladning."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Potensial og felt fra en ringladning\n",
    "Vi ser på en enkelt ringladning med ladning $Q$ som ligger i $xy$-planet. Ringladningen består av en tynn ring med uniform linjeladningstetthet. Den har sentrum i origo og radius $a$. Du kan anta at ringladningen ligger i vakuum."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Oppgave (a) (10 poeng)\n",
    "Vis at det elektriske potensialet langs $z$-aksen er gitt som\n",
    "\n",
    "$$V(z) = \\frac{Q}{4 \\pi \\epsilon_0} \\frac{1}{\\sqrt{z^2 + a^2}}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "*(Svar ved å trykke på cellen under og skriv svaret her. Du kan godt bruke mer enn en celle til å skrive svaret ditt.)*\n",
    "\n",
    "(__Tips__ Du kan trykke på oppgave-cellene også og kopiere LaTeX koden derfra hvis du trenger den)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "__Løsning:__ Vi bruker i denne oppgaven uttrykket for det elektriske potensialet fra en kontinuerlig linjeladningsfordeling med linjeladningstetthet $\\rho_l$:\n",
    "\n",
    "$$V(\\vec{r}) = \\int \\frac{\\rho_l dl }{4 \\pi \\epsilon_0 R}$$\n",
    "\n",
    "hvor $R$ er avstanden fra observasjonspunktet $\\vec{r}$ til linjestykket $dl$. I dette tilfellet er denne avstanden $R^2 = a^2 + z^2$ for alle punkter på linjeladningen. Vi får derfor at $R$ er en konstant i integrasjonen og kan settes utenfor integrasjonen:\n",
    "\n",
    "$$V(z) = \\frac{1}{4 \\pi \\epsilon_0 R} \\int \\rho_l d l$$\n",
    "\n",
    "Hvor integralet blir ladningen til ringen, $Q$. Når vi setter inn $R = \\sqrt{z^2 + a^2}$ blir svaret\n",
    "\n",
    "$$V(z) = \\frac{Q}{4 \\pi \\epsilon_0 \\sqrt{z^2 + a^2}}$$\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Oppgave (b) (10 poeng)\n",
    "Finn $z$-komponenten av det elektriske feltet langs $z$-aksen, $E_z(z)$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "__Løsning:__ Vi finner det elektriske feltet langs $z$-aksen ved\n",
    "\n",
    "$$E_z = - \\frac{\\partial V}{\\partial z}$$\n",
    "\n",
    "Vi setter inn og finner at\n",
    "\n",
    "$$E_z = - \\frac{\\partial }{\\partial z} \\left( \\frac{Q}{4 \\pi \\epsilon_0} (z^2 + a^2)^{-1/2} \\right) = -\\frac{Q}{4 \\pi \\epsilon_0} \\left(-\\frac{1}{2}\\right)2z (z^2 + a^2)^{-3/2}  =\n",
    "\\frac{Q}{4 \\pi \\epsilon_0} \\frac{z}{(z^2 + a^2)^{3/2}} \n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Eksempel\n",
    "Som en hjelp til å løse oppgaven, kan du ta utgangspunkt i dette eksempelet. Merk at dette eksempelet løser et annet problem enn det du skal løse i denne oppgaven, men du kan bruke deler av koden fra dette eksempelet til å løse oppgavene nedenfor hvis du ønsker det.\n",
    "\n",
    "Det elektriske potensialet fra en linje med ladning $q = 1\\text{mC}$ langs $x$-aksen fra $x=-a$ til $x=a$ kan beregnes og visualiseres ved hjelp av følgende program:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "def epotlist(r,Q,R):\n",
    "    epsilon0 = 8.854e-12\n",
    "    K = 1.0/(4.0*np.pi*epsilon0)\n",
    "    V = 0.0\n",
    "    for i in range(len(R)):\n",
    "        Ri = r - R[i]\n",
    "        qi = Q[i]\n",
    "        Rinorm = np.linalg.norm(Ri)\n",
    "        V = V + qi/Rinorm\n",
    "    V = V*K\n",
    "    return V\n",
    "def findpotential(R,Q,y0,y1,z0,z1,Ny,Nz):\n",
    "    y = np.linspace(y0,y1,Ny)\n",
    "    z = np.linspace(z0,z1,Nz)\n",
    "    ry,rz = np.meshgrid(y,z)\n",
    "    V = np.zeros((Ny,Nz),float)\n",
    "    for i in range(len(ry.flat)):\n",
    "        r = np.array([0.0,ry.flat[i],rz.flat[i]])\n",
    "        V.flat[i] = epotlist(r,Q,R)\n",
    "    return y,z,ry,rz,V"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "Q = []\n",
    "R = []\n",
    "a = 1.0\n",
    "q = 1.0e-3\n",
    "nline = 100\n",
    "for i in range(nline):\n",
    "    x = -a + i/nline*(2*a)\n",
    "    y = 0\n",
    "    z = 0\n",
    "    dq = q/nline\n",
    "    R.append(np.array([x,y,z]))\n",
    "    Q.append(dq)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "y,z,ry,rz,V = findpotential(R,Q,-2*a,2*a,-2*a,2*a,30,30)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(-2.0, 2.0, -2.0, 2.0)"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "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": [
    "plt.figure(figsize=(6,6))\n",
    "plt.contourf(ry,rz,V)\n",
    "plt.colorbar()\n",
    "plt.axis('equal')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Oppgave (c) (15 poeng)\n",
    "Skriv et program som finner det elektriske potensialet fra ringladningen i $yz$-planet og visualiserer dette i et passende område slik at potensialets form klart kommer frem."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Vi velger den samme ladningen som tidligere, dvs $q = 1 \\text{mC}$. Vi kan enten velge en radius $a = 1 \\text{m}$ eller vi kan uttrykke alle størrelser i enheter av $a$. Vi velger $a = 1 \\text{m}$ og oppgir størrelsene med disse enhetene."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(-2.0, 2.0, -2.0, 2.0)"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "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": [
    "# Løsning\n",
    "\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "def epotlist(r,Q,R):\n",
    "    epsilon0 = 8.854e-12\n",
    "    K = 1.0/(4.0*np.pi*epsilon0)\n",
    "    V = 0.0\n",
    "    for i in range(len(R)):\n",
    "        Ri = r - R[i]\n",
    "        qi = Q[i]\n",
    "        Rinorm = np.linalg.norm(Ri)\n",
    "        V = V + qi/Rinorm\n",
    "    V = V*K\n",
    "    return V\n",
    "def findpotential(R,Q,y0,y1,z0,z1,Ny,Nz):\n",
    "    y = np.linspace(y0,y1,Ny)\n",
    "    z = np.linspace(z0,z1,Nz)\n",
    "    ry,rz = np.meshgrid(y,z)\n",
    "    V = np.zeros((Ny,Nz),float)\n",
    "    for i in range(len(ry.flat)):\n",
    "        r = np.array([0.0,ry.flat[i],rz.flat[i]])\n",
    "        V.flat[i] = epotlist(r,Q,R)\n",
    "    return y,z,ry,rz,V\n",
    "\n",
    "Q = []\n",
    "R = []\n",
    "a = 1.0\n",
    "q = 1.0e-3\n",
    "nline = 100\n",
    "for i in range(nline):\n",
    "    theta = 2*np.pi/nline*i\n",
    "    x = a*np.cos(theta)\n",
    "    y = a*np.sin(theta)\n",
    "    z = 0\n",
    "    dq = q/nline\n",
    "    R.append(np.array([x,y,z]))\n",
    "    Q.append(dq)\n",
    "    \n",
    "y,z,ry,rz,V = findpotential(R,Q,-2*a,2*a,-2*a,2*a,30,30)\n",
    "\n",
    "plt.figure(figsize=(6,6))\n",
    "plt.contourf(ry,rz,V)\n",
    "plt.colorbar()\n",
    "plt.axis('equal')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Oppgave (d) (15 poeng)\n",
    "\n",
    "Kontroller resultatet fra programmet ditt ved å sammenlikne med den eksakte løsningen du fant i oppgave (a). Vis ved et plot at beregningen fra programmet sammenfaller med det teoretiske resultatet langs $z$-aksen.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7f8250d01790>"
      ]
     },
     "execution_count": 6,
     "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": [
    "# Løsning\n",
    "\n",
    "# Vi beregner potensialet langs z-aksen med programmet\n",
    "# og kaller disse resultatne z_mod,V_mod\n",
    "z_mod = np.linspace(0,3*a,1000)\n",
    "V_mod = np.zeros(z_mod.shape)\n",
    "for i in range(len(z_mod)):\n",
    "    r = np.array([0,0,z_mod[i]])\n",
    "    V_mod[i] = epotlist(r,Q,R)\n",
    "# Vi beregner potensialet langs z-aksen med det teoretiske resultatet\n",
    "epsilon0 = 8.854e-12\n",
    "V_teori = q/(4*np.pi*epsilon0*np.sqrt(z_mod**2+a**2))\n",
    "plt.plot(z_mod,V_mod,'o',label='Program')\n",
    "plt.plot(z_mod,V_teori,'-',label='Teori')\n",
    "plt.xlabel('$z/a$')\n",
    "plt.ylabel('$V$ (V)')\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Vi ser at verdiene fra den numeriske metoden sammenfaller perfekt med det eksakte teoretiske resultatet. I dette tilfellet er dette ikke overraskende fordi svaret fra den numeriske metoden langs $z$-aksen blir det samme uavhengig av hvilken oppløsning man har valgt på ringen.\n",
    "\n",
    "Merk at man her kan plotte $V(z)$ bare for positive $z$ eller for både positive og negative $z$ --- begge alternativer er like riktige."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Dipol av to ringladninger\n",
    "Vi skal nå studere et dipol-aktig system som består av to ringladninger: \n",
    "- En ringladning med ladning $Q = 1\\text{mC}$ og radius $a$ med sentrum i $(0,0,a)$ som ligger i et plan parallellt med $xy$-planet.\n",
    "- En ringladning med ladning $Q = -1\\text{mC}$ og radius $a$ med sentrum i $(0,0,-a)$ som ligger i et plan parallellt med $xy$-planet.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Oppgave (e) (15 poeng)\n",
    "Skriv et program som finner det elektriske potensialet i $yz$-planet for dette systemet og visualiserer det i et passende område så potensialets form klart kommer frem."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, '$z/a$')"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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MDaCdCFyZyiF0Sc1tvE1dL1SnqdtQLuuVSw9FcxC4ULpcGvAg2nB0AtVp0raU09ggbKEOBK6M5dQ0cmnEs2nCOiA9OQWVfnKvH6gCgQuVyXViybVu5CXXbSy3unPaUUWzELgyl2PzyKlB51Qr8pfb9pZbvUCdCFyoRQ6NOoca0Tw5HFHNocZectxBRXMQuBog1yaSasPOdTJBs6S6DaZaF5C6hXUXgHabbt7H77Wx5kqYSJCe7m2SMTI/ue6YojkIXA3xwNSe2n/p1rrLGNmahw+uZULJeQJBu9QdvhgrwPwQuJCMqkIXEwdyV+WR4SaMF45uIQUErgbJ/SiXVF7oasKkAcxU9lEvxg0wPgSuhmlK6JrLIJMLkwXaZNjw1ZbxwdEtpILAhSy1ZbIARsH46CBsISV8LEQD0WQAAEgLgauhCF0A2oweiNQQuBqMhgOgjeh9SBGBq+FoPADahJ6HVBG4WoAGBKAN6HVIGYGrJWhEAJqMHofUEbhahIYEoInobcgBgatlaEwAmoSehlwQuFqIBgWgCehlyAmBCwCQHcIWckPgaimaFYBc0b+QIwJXi9G0AOSGvoVcEbhajuYFIBf0K+SMwAWaGIDk0aeQOwIXJNHMAKSL/oQmIHDhRQ9M7UljA5AUehKagsCFndDgANSNHUA0DYELPdHsANSF3oMmInBhVjQ+AFVhRw9NRuDCnGiCAMpGj0HTLay7AORjuiHuv3RrzZUAaAqCFtqCwIWhEbwAzBdBC23DKUWMjIYJYFhcooC2SiZw2T7B9t22N9k+p8fzp9veavu24uvMOurEjmieAAZBr8C4DZAbzrK9rsgM37G9vI46pyURuGwvkHShpBMlLZd0ap//mMsj4tDi67OVFolZ0UwB9ENvwLgNmBu+GBFviYhDJf2ppE9UXOYOUrmG6whJmyLifkmyfZmkFZLuqrUqDI3ruwBMI2ihRHPmhoh4umv5V0qKSiucIZXAtY+kh7ruT0k6ssdy77H9i5LukfRfI+KhHssgAQQvoJ0IWajIQLnB9gclfVjSIknHVlNab6kELvd4bGYS/VtJl0bE87bPknSx+vzn2V4paaUkLVu2bJx1YkjdzZfwBTQTIavdtm1bWNY2sMT22q77kxExWdweJDcoIi6UdKHtX5P03yWdNv4yB5NK4JqStG/X/aWSNncvEBGPd939jKTz+71Y8YZMStLExESthxDxkpkDkgAG5IuQhQo8FhETfZ6bMzfMcJmkvxpXYaNIJXDdLOkg2wdI+hdJp0j6te4FbO8dEVuKuydL2lBtiRg3jn7VK/cJk22merlvM2iUQXLDQRFxb3H3VyTdqxolEbgiYrvtsyVdK2mBpIsiYr3t8yStjYhVkn7b9smStkt6QtLptRWMsSN8zV/bJsNh15ftajRt266QhwFzw9m23yHpR5KeVI2nE6VEApckRcRqSatnPHZu1+2PSPpI1XWher0afFsnSya78Rn0/7Kt25rE9oa8DJAbfqfyomaRTOACZtNvIsh1cmRiS9cw7w3bH4BBEbiQtbkmjiomRCav9hrlvWebBNqJwIVGY+JBatgmgXZK4k/7AAAANBmBCwAAoGQELgAAgJIRuAAAAEpG4AIAACgZgQsAAKBkBC4AAICSEbgAAABKRuACAAAoGYELAACgZAQuAACAkhG4AAAASkbgAgAAKBmBCwAAoGQELgAAgJIRuAAAAEpG4AIAACgZgQsAAKBkBC4AAICSEbgAAABKRuACAAAoGYELAACgZAQuAACAkhG4AAAASkbgAgAAKBmBCwAAoGQELgAAgJIRuAAAAEpG4AIAACgZgQsAAKBkBC4AAICSEbgAAABKRuACAAAoGYELAACgZAQuAACAkhG4AAAASkbgAgAAKBmBCwAAoGQELgAAgJIRuAAAAEpG4AIAACjZwkEXtL2HpPdLek7SeknrIuLfyioMAACgKYY5wnWlpD0l/S9JH5f0lO2NpVQFAADQIMMErsURcZ6kRyLilySdKumvx1WI7RNs3217k+1zejy/q+3Li+dvsr3/uH42AADIS265YZjA9Vzx7/O2Xx4RX5Z00jiKsL1A0oWSTpS0XNKptpfPWOwMSU9GxE9L+gtJ54/jZwMAgLxUmRtsX2D7bfOpVxoucP2Z7VdLulzSRbY/JGmf+RZQOELSpoi4PyK2SbpM0ooZy6yQdHFx+wpJx9n2mH4+AADIR5W54V5Jf277Advn2z50lILnDFy2j7LtiPhyRDwREZ+Q9DVJ+2rnlRvVPpIe6ro/pZ3D3IvLRMR2SU9J2qNPzSttr7W9duvWrWMqEQAAVGjJ9FxefK3sem6suWE2EfGXEXGUpF+S9ISkv7a9wfa5tt8w6OsM8luKp0m60PY9kq6RdE1EXDJswXPolThjhGU6D0ZMSpqUpImJiZ2W2fX7i4atDwAA9OBtLmtefSwiJvr92B6PjZwbBhERD6pzWvJ824dJukjSH0laMMj3zxm4IuIsSbJ9sDrnSj9vezdJ16sTwP4hIl4YrfwXTalzxGzaUkmb+ywzZXuhpN3USZoAAKBdKs8NtneRdIKkUyQdJ+nvJf3PQb9/mGu43izpf0fECZKOlfQdSe+TdNMQr9HPzZIOsn2A7UXqrMyqGcusUudomyS9V9I3I2LkpAoAALJVWW6wfbzti9QJcCslrZZ0YET8akRcNejrDBO4/p+kL9peEBH/FhGrJd06y+G+gRXnVs+WdK2kDZK+FBHrbZ9n++Risc9J2sP2JkkflrTTr4ACAIDmqzg3/KGk70l6U0T8x4j4QkT867AvMvAnzUvaqM7hsy/bfl9E/EjShzSmz+IqAtzqGY+d23X7OXWOqAEAgJarKjdExNvn+xrScEe4IiI+LekrklbZfrl6X5AGAACALsMc4XpSkiLiEts/lHS1pFeUUhUAAECDDBy4IuK4rttX2H5O0ufLKAoAAKBJhjnCtYOI+DtJS8ZYCwAAQCMNcw0XAAAARkDgAgAAKBmBCwAAoGQELgAAgJIRuAAAAEpG4AIAACgZgQsAAKBkBC4AAICSEbgAAABKRuACAAAoGYELAACgZAQuAACAkhG4AAAASkbgAgAAKBmBCwAAoGQELgAAgJIRuAAAAEpG4AIAACgZgQsAAKBkBC4AAICSEbgAAABKRuACAAAoGYELAACgZAQuAACAkhG4AAAASkbgAgAAKBmBCwAAoGQELgAAgJIRuAAAAEpG4AIAACgZgQsAAKBkBC4AAICSEbgAAABKRuACAAAoGYELAACgZAQuAACAkhG4AAAASkbgAgAAKBmBCwAAoGQL6y4AGLfFD0atP/+Z/Vzrz0c66t4WJbZHIBUELmQrhcmsl2HrYkLMS6rbXT/96mW7A6pVe+Cy/WpJl0vaX9IDkt4fEU/2WO4FSeuKu9+PiJOrqhH1ym2CG9ag68cEWa6mb2czEcTQZINkC9v7SfqKpAWSdpH0fyLi02XVVHvgknSOpOsi4mO2zynu/0GP5f4tIg6ttjTUoW0T36CG+X9h0uxgWxrezP8ztiVkapBssUXS2yLieds/KelO26siYnMZBaUQuFZIOqa4fbGkb6l34EJDMSmO3yj/p6lPrGwn9ej+f099GwG6zJktImJb191dVfIvEqYQuF4bEVskKSK22H5Nn+VeZnutpO2SPhYRV1VWIcaOyTM9vCeYC+ELGRkoW9jeV9LVkn5a0u+XdXRLqihw2f6GpL16PPXRIV5mWURstv16Sd+0vS4i7uvz81ZKWilJy5YtG7pelIMJHWgOwhemLdhWWn9fUhxomTYZEZPTd8aRLSLiIUmH2H6dpKtsXxERj4xc8SwqCVwR8Y5+z9l+xPbeRQLdW9KjfV5jc/Hv/ba/JekwST0DV/GGTErSxMQEs3yNCFlA83HdF0ryWERM9HtyHNmi67U2214v6RckXTFyxbNI4YNPV0k6rbh9mqSvzlzA9u62dy1uL5F0tKS7KqsQQ1v8YBC2gJZi7CMBg2SLpbZfXtzeXZ1scXdZBaUQuD4m6Xjb90o6vrgv2xO2P1ss8yZJa23fLul6da7hInAliKAFQKIXoHaDZoubimzx95L+LCLW9Xy1Maj9ovmIeFzScT0eXyvpzOL2dyW9peLSMAQaK4BepnsDpxlRpQGzxRpJh1RVUwpHuJA5whaAuXDEC21X+xEu5IvmCWBYHPFCW3GEC0NjTxXAfNFD0DYc4cLAaJAAxomjXWgTAhfmRNACUCaCF9qAU4qYFWELQFW4XAFNRuBCXzQ+AHWg96CJCFzYCXuZAOpGD0LTELiwA5ocgFSw84cmIXDhRTQ2ACmiN6EJCFyQREMDkDZ6FHJH4AKNDEAW6FXIGYGr5WhgAHJCz0KuCFwtRuMCkCN6F3JE4GopGhYAANUhcLUQYQtA7uhjyA2Bq2VoUgCagn6GnBC4WoTmBKBp6GvIBYGrJWhKAJqK/oYcELhagGYEoOnoc0gdgavhaEIA2oJ+h5QRuBqM5gOgbeh7SBWBCwDQKIQupIjA1VA0HABtRg9EahbWXQDGr6mNZrf7nh9q+acO3LWkSoC0DTtWJMYLUDYCF5I0yoQx22swmaDp5jtmen1/7uNm8YOhZ/Zz3WUAkghcjdOEo1vjCFuzvWbukwgwrYyxMvP1GS/AeBC4kIyyJ49eP4fJBLmpapx0/7ycxwlHuZAKAleD5Hx0q+pJpNfPzXlSQbPVNT66fz7jA5gffksRtat7Mpm2233PJ1MLMC2VbTLn8ZHzziiag8DVELk2lBQbeIo1oX1SDTgp1jSIXHskmoPA1QA5NpJUJ5NpqdeHZkt920u9PiBFBC5ULqdmnVOtaIZctrkcd0py3DlFcxC4MpdbA8mtQUt51oz85BhgJMYHMCgCFyqTc2POdTJEHnLftnKqP7edVDQHgStjuTSOJoWVpqwH0sDYANqDwIVSNbEJN2mSRH2auA3lMjZy2VlFsxC4MpVDw8ih8c5H09cP5WHbAdqHwIVStGVCact6YjxyOQI0XzmsYw47rWgWAleGaBRpyWFyAQDUi8AFABg7dkSAHRG4AKACBJD0cLYAVSJwYezaOLG0cZ0BAIMjcGWmLXtkizZO1V0CMDZtDeRtXW+gFwIXkpVb6GJyQRMs2jj14heA8ak9cNl+n+31tn9se2KW5U6wfbftTbbPqbJGDG4coaO70efW+AldmCmnbSKnsTYubTlr0Da2X217je17i39377PcMttft73B9l229y+rptoDl6Q7Jb1b0g39FrC9QNKFkk6UtFzSqbaXV1MeUtDGiQD5yyVs9duxYdwhY+dIui4iDpJ0XXG/l0skfTwi3iTpCEmPllVQ7YErIjZExN1zLHaEpE0RcX9EbJN0maQV5VeXljbsic3W4HM52pXLJAtIc4eq+Y45xgNqskLSxcXtiyW9c+YCxYGbhRGxRpIi4tmI+GFZBdUeuAa0j6SHuu5PFY+hQQZt7LkEL7Rb6kGDcYSGe21EbJGk4t/X9FjmDZJ+YPsrtv/J9seLM2qlWFjWC3ez/Q1Je/V46qMR8dVBXqLHY30P99heKWmlJC1btmygGjF/VU8wizZOadvBSyv9mYPa7b7n9dSBu9ZdBrCTUUJWymNtHBY/GHpmv17TDGq2xPbarvuTETE5fWe2bDHg6y+U9AuSDpP0fUmXSzpd0udGqnaAH1a6iHjHPF9iStK+XfeXSto8y8+blDQpSRMTE80/D9cAo+5pT39fipMBoau9Uj26VdcRLcZCsy14Lsra5h+LiL6/TDdbtrD9iO29I2KL7b3V+9qsKUn/FBH3F99zlaS3qqTAlcspxZslHWT7ANuLJJ0iaVXNNVWqyddvjWMS4NQIUpFi2BrH6UPGGDKzStJpxe3TJPU6m3azpN1t71ncP1bSXWUVVHvgsv0u21OSjpJ0te1ri8dfZ3u1JEXEdklnS7pW0gZJX4qI9XXVjJ2lMMmkeE1KCv8vaLdxjonUxtc4NXmntqU+Jul42/dKOr64L9sTtj8rSRHxgqTfk3Sd7XXqXL70mbIKquSU4mwi4kpJV/Z4fLOkk7rur5a0usLSMISnDty19nCR4mlFoG7bDl46tqDEGEMuIuJxScf1eHytpDO77q+RdEgVNdV+hL1s9GwAAA8RSURBVAuYbxPfdvBSJgJgFuMYI4wxYH4IXEjCKM2coAUMp64xwwXzQAKnFNEc8z2tOOipj5xCFhMNUtQ9hpo25oBUcYQrA226mHO2xs4RLWD85hpX8x1z7HQAHQQujNU4muvMBk/QQk5yDRi9xhnjDhgfTikiWTR7oHqMO6AcHOFCkmj6QP5yPdoHlIHAhbGjyXbw/wAAmEbgAgCMXY47HG36BSVUj8CFUuTYbIFxYfsHMBOBCwAAoGQELqAEHOFAm7H9AzsjcKE0NF0AADoIXABQgrbucLR1vYG5ELhQqjY23zauM3pr27bQtvUFhkHgQumeOnDX1jTitqwnBteWbaIt6wmMisCFyjS9ITd9/TC6pm8bTV8/YBwIXKhUExtzm47gYXRN3Uaaul7AuBG4ULkmNegmrQvK17Rw3qR1kaRn9nPdJaDBCFyoRe6NumkTJ6qV+7bD9g8Mj8CF2uTasHOtG2nJNbTkWDOQAgIXapVb886tXqQvp20qp1qB1BC4MtD06wpy2NPPoUbkK4dtK4cagZQRuJCMVBt6qnWhWVIO9anWBeSEwIWkpNTYU54A0VypbXOp1QPkisCF5KTQ4FOoAe2VSthPoQagKRbWXQDQS3ej3+2+52v5uUDdnjpw10q3/+mf2UZNv1YW9SNwIXn9JoD5TkRtnViQl17b6ThCGNs/UC0CF7I16ETExIKmmW2bZgwAaSJwZeKZ/azFD0bdZSSPiQVtxxgA0sRF8wAAACUjcAEAWo0L5lEFAhcAAEDJCFwZYS8MAIA8EbgAAABKRuACALQWZw5QFQJXZmgOAADkh8AFAABQMgIXAKCVOGOAKhG4AAAASkbgyhB7ZQAA5IXABQAAUDICFwCgdThTgKoRuDJFswAAIB8ELgAAgJIRuDLGUS4AGB69E3WoPXDZfp/t9bZ/bHtiluUesL3O9m2211ZZIwAAyIftV9teY/ve4t/d+yx3vu07i69fLbOm2gOXpDslvVvSDQMs+/aIODQi+gaztmFPDQAGR89sjXMkXRcRB0m6rri/A9u/IulwSYdKOlLS79v+qbIKqj1wRcSGiLi77joAAEBjrJB0cXH7Yknv7LHMckl/HxHbI+JfJd0u6YSyCqo9cA0hJH3d9i22V862oO2VttfaXrt169aKyqsPe2wAMDd6ZXaWTM/lxdesc/8Mr42ILZJU/PuaHsvcLulE26+wvUTS2yXtO/+ye1tY1gt3s/0NSXv1eOqjEfHVAV/m6IjYbPs1ktbY3hgRPU9DRsSkpElJmpiYiJGKBgAAc/Jz27Ro41QZL/3YbJcQzZYtBnnxiPi67X8n6buStkr6nqTtoxQ6iEoCV0S8Ywyvsbn491HbV0o6QoNd9wUAaDmObjXPbNnC9iO2946ILbb3lvRon9f4Y0l/XHzPFyXdW0qxyuSUou1X2l48fVvSL6tzsT0KNBMAAF60StJpxe3TJO10Ns32Att7FLcPkXSIpK+XVVDtgcv2u2xPSTpK0tW2ry0ef53t1cVir5X0Hdu3S/pHSVdHxDX1VAwAyAk7pK30MUnH275X0vHFfdmesP3ZYpldJH3b9l3qXIb0nyIi71OKs4mIKyVd2ePxzZJOKm7fL+lnKy4tO8/sZy1+kEvWAADtFhGPSzqux+NrJZ1Z3H5Ond9UrETtR7gAACgLR7eQCgJXw9BcAABID4ELANBI7IAiJQSuBqLJAACQFgJXQxG6ALQZPRCpIXABABqFsIUUEbgajKYDAEAaCFwNR+gC0Cb0PKSKwAUAaATCFlJG4GoBmhAAAPUicLUEoQtAk9HjkDoCFwAga4Qt5IDA1SI0JQBNQ19DLghcLUNzAgCgegSuFiJ0AWgCehlyQuBqKRoVgJzRw5AbAhcAICuELeSIwNViNC0AuaFvIVcErpajeQEAUD4CFwhdALJAr0LOCFyQRCMDkDZ6FHJH4MKLaGgAUkRvQhMQuLADGhuAlNCT0BQELgBAkghbaBICF3ZCkwNQN/oQmobAhZ5odgDqQv9BExG40BdND0DV6DtoKgIXZkXzA1AV+g2ajMCFOdEEAZSNPoOmI3BhIM/sZxoigFLQW9AGBC4MhcYIYJzoKWgLAheGRoMEMA70ErQJgQsjoVECGBWXKKCNCFwYGQ0TwLDoG2grAhfmhT1VAIOiV6DNCFwYCxopgNnQI9B2BC6MDQ0VQC/0BoDAhTGjsQKYxiUHwEsIXBg7GiwA+gCwIwIXSsGeLdBejH1gZwQulIrGC7QHO1pAfwQulI4mDDQfYxyYHYELlaEhA83DDhUwmIV1F4B2mW7Mix+MmisBMB+ELGA4HOFCLdgrBvLF2AWGV3vgsv1x2xtt32H7Stuv6rPcCbbvtr3J9jlV14ly0LiBfLCjhFzYfp/t9bZ/bHuizzL72r7e9oZi2d8ps6baA5ekNZJ+JiIOkXSPpI/MXMD2AkkXSjpR0nJJp9peXmmVKA1NHEgbYxQZulPSuyXdMMsy2yX9t4h4k6S3Svpgmdmi9sAVEV+PiO3F3RslLe2x2BGSNkXE/RGxTdJlklZUVSOqQVMH0sOYRI4iYkNE3D3HMlsi4tbi9jOSNkjap6yaag9cM/ympK/1eHwfSQ913Z9Sif8pqBcNHkgDYxFtYXt/SYdJuqmsn1HJbyna/oakvXo89dGI+GqxzEfVObz3hV4v0eOxvr/mZnulpJXF3Wdtz0y5SyQ9NlfdmWrqurFe+WnqurFe+Wnqui3xuR/utV77VVnE09u3XnvNw59aUsJLv8z22q77kxExOX1nkGwxCNs/KenLkn43Ip4eudo5VBK4IuIdsz1v+zRJ/0HScRHRK0hNSdq36/5SSZtn+XmTkib7PW97bUT0vIgud01dN9YrP01dN9YrP01dt1TWKyJOqOnnzpotBmF7F3XC1hci4ivzr6q/2k8p2j5B0h9IOjkifthnsZslHWT7ANuLJJ0iaVVVNQIAgGaxbUmfk7QhIj5R9s+rPXBJukDSYklrbN9m+9OSZPt1tldLUnFR/dmSrlXnorYvRcT6ugoGAADpsv0u21OSjpJ0te1ri8dfzBaSjpb0G5KOLfLHbbZPKqum2j9pPiJ+us/jmyWd1HV/taTVvZYdQd/TjQ3Q1HVjvfLT1HVjvfLT1HVr6nrNW0RcKenKHo+/mC0i4jvqfY14Kdz7kikAAACMSwqnFAEAABqtFYGryX8+aJA/X1As94DtdcU56rX9lkvFEOuV1Xtm+9W219i+t/h39z7LvdB1TUHSvyAy13tge1fblxfP31R83k3yBliv021v7XqfzqyjzmHZvsj2o7bv7PO8bX+yWO87bB9edY2jGGC9jrH9VNf7dW7VNY5ikD8/k+t71joR0fgvSb8saWFx+3xJ5/dYZoGk+yS9XtIiSbdLWl537QOs25skvVHStyRNzLLcA5KW1F3vONcrx/dM0p9KOqe4fU6vbbF47tm6ax1wfeZ8DyT9lqRPF7dPkXR53XWPab1Ol3RB3bWOsG6/KOlwSXf2ef4kdT6A2ur8uZOb6q55TOt1jKS/q7vOEdZrb0mHF7cXq/Mn8GZui1m+Z237asURrmjwnw+KAf58QY4GXK8c37MVki4ubl8s6Z011jIOg7wH3et8haTjil/HTlmO29ZAIuIGSU/MssgKSZdEx42SXmV772qqG90A65WlGOzPz2T5nrVNKwLXDG3980Eh6eu2byk+ib8JcnzPXhsRW6ROI5X0mj7Lvcz2Wts32k45lA3yHry4TLHj85SkPSqpbnSDblvvKU7hXGF73x7P5yjHcTWoo2zfbvtrtt9cdzHDcv8/P9Pk96wxav9YiHFxxX8+qEqDrNsAjo6IzbZfo85nnm0s9ghrM4b1SvI9m229hniZZcX79XpJ37S9LiLuG0+FYzXIe5Dk+zSHQWr+W0mXRsTzts9S5yjesaVXVr4c369B3Cppv4h4tvispaskHVRzTQPz7H9+pqnvWaM0JnBFxX8+qEpzrduAr7G5+PdR21eqc8qk1sA1hvVK8j2bbb1sP2J774jYUhzyf7TPa0y/X/fb/pY6e7UpBq5B3oPpZaZsL5S0m9I/9TPnekXE4113P6PO9aFNkOS4mq/ukBIRq21/yvaSiEj+byx67j8/08j3rGlacUrRLf/zQbZfaXvx9G11fomg52/yZCbH92yVpNOK26dJ2ulInu3dbe9a3F6izqch31VZhcMZ5D3oXuf3Svpmn52elMy5XjOukTlZnWtrmmCVpA8Uv/n2VklPTZ8Gz5ntvaavHbR9hDrz3+Ozf1f9iprn+vMzjXzPGqfuq/ar+JK0SZ3z27cVX9O/MfU6Sau7ljtJnd8AuU+d01q11z7Aur1Lnb2b5yU9Iunameumzm9a3V58rc9h3QZZrxzfM3WuXbpO0r3Fv68uHp+Q9Nni9tskrSver3WSzqi77jnWaaf3QNJ56uzgSNLLJP1NMQ7/UdLr6655TOv1J8V4ul3S9ZIOrrvmAdfrUklbJP2oGGNnSDpL0lnF85Z0YbHe6zTLbz+n9DXAep3d9X7dKOltddc84Hr9vDqnB+/omsNOasJ71rYvPmkeAACgZK04pQgAAFAnAhcAAEDJCFwAAAAlI3ABAACUjMAFAABQMgIXAABAyQhcAAAAJSNwASiF7f9r++i66wCAFPDBpwBKYfs2ST8XES/UXQsA1I0jXABGYvsttv+h6/7htr9Z3H6TpHsi4gXb77V9o+3bbX/H9p61FQ0ANSFwARjVekkH2l5Q3P9zSb9X3D5R0jXF7esj4q0R8bOS1kh6f7VlAkD9CFwARhIRP1YndL3Z9nskfT8ibi2e/vd6KXCdbvsfbd8u6bckPVd9tQBQr4V1FwAgazdKOlqdIHWCJNl+haRXRcRm2x+QdISkYyPiWds3qBPSAKBVCFwA5uNGSZ+XdGFE/Evx2NslXV/cfouk7xZh6z2S3iZpXeVVAkDNOKUIYD42Snpe0vldj3Vfv3WxpN+2/W1Jb5B0f0T8a7UlAkD9+FgIACOzfYGkmyPi4q7HbpV0ZET8qL7KACAtHOECMDTbB9reKOnl3WFLkiLicMIWAOyII1wAAAAl4wgXAABAyQhcAAAAJSNwAQAAlIzABQAAUDICFwAAQMkIXAAAACUjcAEAAJSMwAUAAFCy/w/NwA/KuVb3QwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 720x576 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Løsning\n",
    "\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "def epotlist(r,Q,R):\n",
    "    epsilon0 = 8.854e-12\n",
    "    K = 1.0/(4.0*np.pi*epsilon0)\n",
    "    V = 0.0\n",
    "    for i in range(len(R)):\n",
    "        Ri = r - R[i]\n",
    "        qi = Q[i]\n",
    "        Rinorm = np.linalg.norm(Ri)\n",
    "        V = V + qi/Rinorm\n",
    "    V = V*K\n",
    "    return V\n",
    "def findpotential(R,Q,y0,y1,z0,z1,Ny,Nz):\n",
    "    y = np.linspace(y0,y1,Ny)\n",
    "    z = np.linspace(z0,z1,Nz)\n",
    "    ry,rz = np.meshgrid(y,z)\n",
    "    V = np.zeros((Ny,Nz),float)\n",
    "    for i in range(len(ry.flat)):\n",
    "        r = np.array([0.0,ry.flat[i],rz.flat[i]])\n",
    "        V.flat[i] = epotlist(r,Q,R)\n",
    "    return y,z,ry,rz,V\n",
    "\n",
    "Q = []\n",
    "R = []\n",
    "a = 1.0\n",
    "q = 1.0e-3\n",
    "\n",
    "# Positivt ladet ring\n",
    "nline = 100\n",
    "for i in range(nline):\n",
    "    theta = 2*np.pi/nline*i\n",
    "    x = a*np.cos(theta)\n",
    "    y = a*np.sin(theta)\n",
    "    z = a\n",
    "    dq = q/nline\n",
    "    R.append(np.array([x,y,z]))\n",
    "    Q.append(dq)\n",
    "\n",
    "# Negativt ladet ring\n",
    "nline = 100\n",
    "for i in range(nline):\n",
    "    theta = 2*np.pi/nline*i\n",
    "    x = a*np.cos(theta)\n",
    "    y = a*np.sin(theta)\n",
    "    z = -a\n",
    "    dq = -q/nline\n",
    "    R.append(np.array([x,y,z]))\n",
    "    Q.append(dq)\n",
    "\n",
    "y,z,ry,rz,V = findpotential(R,Q,-2*a,2*a,-2*a,2*a,30,30)\n",
    "\n",
    "plt.figure(figsize=(10,8))\n",
    "plt.contourf(ry,rz,V)\n",
    "plt.colorbar(label='V')\n",
    "plt.axis('equal')\n",
    "plt.xlabel('$y/a$')\n",
    "plt.ylabel('$z/a$')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Oppgave (f) (15 poeng)\n",
    "Det elektriske potensialet $V(\\vec{r})$ i et punkt $\\vec{r}$ fra en dipol med dipolmoment $\\vec{p} = q \\vec{d}$ med sentrum i origo er tilnærmet lik:\n",
    "\n",
    "$$V(\\vec{r}) = \\frac{1}{4 \\pi \\epsilon_0}\\frac{\\vec{p}\\cdot \\hat{r}}{r^2}$$\n",
    "\n",
    "hvor $\\hat{r} = \\vec{r}/r$, $r = |\\vec{r}|$ og $\\vec{d}$ er en vektor fra den negative ladningen $-q$ til den positive ladningen $q$.\n",
    "\n",
    "Sammenlikn det elektriske potensialet fra programmet med det tilnærmede uttrykket for en dipol langs en linje som er parallell med $z$-aksen og går gjennom $(2a,0,0)$ ved å plotte de to uttrykkene i samme plot."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7f8270ccd290>"
      ]
     },
     "execution_count": 8,
     "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": [
    "# Løsning\n",
    "\n",
    "# Dipolmoment\n",
    "q = 1.0e-3\n",
    "p = np.array([0,0,2*a*q])\n",
    "z_dipol = np.linspace(-5*a,5*a,1000)\n",
    "V_dipol = np.zeros(z_dipol.shape)\n",
    "V_model = np.zeros(z_dipol.shape)\n",
    "for i in range(len(z_dipol)):\n",
    "    ri = np.array([2*a,0,z_dipol[i]])\n",
    "    V_dipol[i] = 1/(4*np.pi*epsilon0)*np.dot(p,ri)/np.linalg.norm(ri)**3\n",
    "    V_model[i] = epotlist(ri,Q,R)\n",
    "plt.plot(z_dipol,V_dipol,'-',label='Dipol')\n",
    "plt.plot(z_dipol,V_model,'-',label='Modell')\n",
    "plt.xlabel('$z/a$')\n",
    "plt.ylabel('$V$ (V)')\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Vi ser at den numeriske løsningen og det tilnærmede uttrykket sammenfaller godt, men at avviket er størst nærmeste ringene som er som forventet, da det tilnærmede uttrykket ikke inkluderer effekten av ringene.\n",
    "\n",
    "(Merk: Hvis du her har lagt dipolen langs linjen gjennom $(2a,0,0)$ er det også en mulig tolkning av oppgaven og du vil få full uttelling hvis dette er korrekt gjort)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Oppgave (g) (10 poeng)\n",
    "Visualiser det elektriske feltet fra de to ringladningene i $yz$-planet. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, '$z/a$')"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Løsning\n",
    "\n",
    "Ez,Ey = np.gradient(-V)\n",
    "\n",
    "plt.figure(figsize=(6,6))\n",
    "plt.contourf(ry,rz,V)\n",
    "plt.quiver(ry,rz,Ey,Ez)\n",
    "plt.axis('equal')\n",
    "plt.xlabel('$y/a$')\n",
    "plt.ylabel('$z/a$')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Oppgave (h) (10 poeng)\n",
    "\n",
    "Bruk modellen til å finne $E_z(x,0,0)$ for systemet som består av de to ringladningene.\n",
    "\n",
    "*(Hint: Finn det elektriske potensialet umiddelbart over og under $xy$-planet langs en linje langs $x$-aksen og bruk dette til å finne $E_z$)*"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, '$E_z$ (V/m)')"
      ]
     },
     "execution_count": 10,
     "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": [
    "# Løsning\n",
    "\n",
    "xm = np.linspace(-5*a,5*a,1000)\n",
    "Ez = np.zeros(xm.shape)\n",
    "dz = 0.01*a\n",
    "for i in range(len(xm)):\n",
    "    # Finner potensialet umiddelbart over og under xy-planet\n",
    "    r1 = np.array([xm[i],0,dz])\n",
    "    V1 = epotlist(r1,Q,R)\n",
    "    r2 = np.array([xm[i],0,-dz])\n",
    "    V2 = epotlist(r2,Q,R)\n",
    "    Ez[i] = -(V1-V2)/(2*dz)\n",
    "plt.plot(xm,Ez)\n",
    "plt.xlabel('$z/a$')\n",
    "plt.ylabel('$E_z$ (V/m)')"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "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": "3.7.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
