{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Prøve-eksamen i Fys1120 H2022 - oppgave 1\n",
    "\n",
    "Dette oppgavesettet tilsvarer en av to oppgaver som dere vil få til eksamen. (Denne oppgaven er stor, så den andre oppgaven vil være mindre). Hver oppgave på eksamen vil bestå av en Jupyter-notebook som dette. Dere arbeider med oppgaven i notebook'en og leverer notebook'en som en pdf file ved å lagre notebook'en og så laste den opp i inspera.\n",
    "\n",
    "Dere vil kunne får både teori-oppgaver, programmerings-oppgaver og diskusjons-oppgaver som del av eksamen. Alle svarene skal dere skrive i den samme notebook'en."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Elektrisk potensial og felt rundt en ringladning\n",
    "Vi skal i denne oppgaven studere det elektriske potensialet rundt en ringformet ladning med radius $a$ som ligger i $xy$-planet. Ringen har en total ladning $q$ som er uniformt fordelt på ringen."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Oppgave (a) \n",
    "Vis at det elektriske potensialet $V(z)$ langs $z$-aksen er gitt som\n",
    "$$V(z) = \\frac{q}{4 \\pi \\epsilon_0 (a^2 + z^2)^{1/2}}$$\n",
    "(Du kan ikke levere en figur, så du må forklare hva du gjør med ord og matematiske uttrykk.)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "(*Svar ved å trykke i denne cellen og skriv svaret her*)\n",
    "\n",
    "(__Tips__ Du kan trykke på oppgave-cellene også og kopiere LaTeX koden derfra hvis du trenger den)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Eksempel\n",
    "Som en hjelp til å løse oppgaven, kan du ta utgangspunkt i dette eksempelet.\n",
    "\n",
    "Det elektriske potensialet fra en dipol langs $z$-aksen kan beregnes og visualiseres ved hjelp av følgende program."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "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\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 findpot(R,Q,x0,x1,z0,z1,Nx,Nz): \n",
    "    x = np.linspace(x0,x1,Nx)\n",
    "    z = np.linspace(z0,z1,Nz)\n",
    "    rx,rz = np.meshgrid(x,z)\n",
    "    V = np.zeros((Nx,Nz),float)\n",
    "    for i in range(len(rx.flat)):\n",
    "        r = np.array([rx.flat[i],0,rz.flat[i]])\n",
    "        V.flat[i] = epotlist(r,Q,R) \n",
    "    return x,z,rx,rz,V"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "Q = []\n",
    "R = []\n",
    "a = 1.0\n",
    "q = 1.0\n",
    "R.append(np.array([0,0,-a/2]))\n",
    "Q.append(-q)\n",
    "R.append(np.array([0,0,a/2]))\n",
    "Q.append(q)\n",
    "x,z,rx,rz,V = findpot(R,Q,-1*a,1*a,-1*a,1*a,30,30)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(-1.1, 1.1, -1.1, 1.1)"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x432 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(12,6))\n",
    "plt.subplot(1,2,1)\n",
    "plt.contourf(rx,rz,V)\n",
    "plt.axis('equal')\n",
    "plt.subplot(1,2,2)\n",
    "Ez,Ex = np.gradient(-V)\n",
    "plt.quiver(rx,rz,Ex,Ez)\n",
    "plt.axis('equal')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Sirkelladning\n",
    "Vi skal nå se på en ladning formet som en sirkel med radius $a = 1 \\text{cm}$ i $xy$-planet. Hele sirkelen har ladningen $q = 1 \\text{mC}$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Oppgave (b)\n",
    "\n",
    "Skriv et program som finner det elektriske potensialet i $xy$-planet og i $xz$-planet og visualiser potensialet og feltet i et område som illustrerer oppførselen godt."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "# (Svar)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Sammenlikning med teori nær $z$-aksen"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Oppgave (c)\n",
    "Vi ønsker å sammenlikne det eksakte resutatet vi fant langs $z$-aksen med resultatet fra programmet ditt nær $z$-aksen for å se hvor stor feil vi får hvis vi bruker det eksakte resultet i et område hvor det ikke er gyldig. Lag et plot av $V(a/2,0,z)$ og sammenlikn med det eksakte resultatet i $(0,0,z)$ for $z = -2a$ til $z=2a$. Kommenter kort resultatet."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "# (Svar)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Sammenlikning med teori langt vekk fra linjestykket i $xy$-planet"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Oppgave (d)\n",
    "Hva forventer du at det elektriske potensialet $V(x,y,0)$ vil være når $r = (x^2+ y^2)^{1/2} r\\gg a$? Du skal komme fram til et enkelt uttrykk for $V(r)$ og gi en kort forklaring for hvorfor dette uttrykket er en god tilnærming i den oppgitte grensen. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "(*Svar*)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Oppgave (e)\n",
    "Sammenlikn resultatet fra programmet ditt med $V(r)$ for eksempel ved å plotte $V(r)$ for $r = a+a/10$ til $r= 10a$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Svar"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "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
}
