{
 "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": [
    "(*Løsning*) Vi bruker superposisjonsprinsippet og uttrykket for det elektriske potensialet fra en punktladning. \n",
    "\n",
    "En ladning $dq$ i posisjonen $\\phi$ langs sirkelen, hvor vinkelen måles fra $x$-aksen, gir opphav til et elektrisk potensial\n",
    "$$dV = \\frac{d q}{4 \\pi \\epsilon_0 R}$$\n",
    "i et punkt $\\vec{r}$. Her er $\\vec{R} = \\vec{r} - \\vec{r}'$ hvor $\\vec{r}' = (a\\cos \\phi, a\\sin \\phi, 0)$. For et punkt langs $z$-aksen er derfor $\\vec{R} = (0,0,z) - (a\\cos \\phi, a\\sin \\phi, 0)$ slik at $R = (a^2 + z^2)^{1/2}$. Dermed er\n",
    "$$dV = \\frac{d q}{4 \\pi \\epsilon_0 (a^2 + z^2)^{1/2}}$$\n",
    "Dette uttrykket er ikke avhengig av vinkelen $\\phi$. Vi integrerer (summerer) over alle bidragene $dq$ og finner da\n",
    "$$V = \\int d V = \\frac{q}{4 \\pi \\epsilon_0 (a^2 + z^2)^{1/2}}$$"
   ]
  },
  {
   "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": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [],
   "source": [
    "# (Løsning)\n",
    "Q = []\n",
    "R = []\n",
    "a = 1.0e-2\n",
    "q = 1.0e-3\n",
    "N = 200 # Antall punkter\n",
    "for iz in range(N+1):\n",
    "    z = 0\n",
    "    phi_i = iz/(N+1)*(2*np.pi)\n",
    "    x = a*np.cos(phi_i)\n",
    "    y = a*np.sin(phi_i)\n",
    "    R.append(np.array([x,y,z]))\n",
    "    Q.append(q/(N+1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [],
   "source": [
    "def findpot_xz(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\n",
    "def findpot_xy(R,Q,x0,x1,y0,y1,Nx,Ny): \n",
    "    x = np.linspace(x0,x1,Nx)\n",
    "    y = np.linspace(y0,y1,Ny)\n",
    "    rx,ry = np.meshgrid(x,y)\n",
    "    V = np.zeros((Nx,Ny),float)\n",
    "    for i in range(len(rx.flat)):\n",
    "        r = np.array([rx.flat[i],ry.flat[i],0])\n",
    "        V.flat[i] = epotlist(r,Q,R) \n",
    "    return x,y,rx,ry,V"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(-0.010998717497876858,\n",
       " 0.010999938928470327,\n",
       " -0.01099966410145826,\n",
       " 0.01099966410145826)"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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MRsV735uf7hlXnSkieDwBrJG0WtK5ZAPge+vy7AWm0uPrgEcjIlL6pjQbazWwBng8jYd8EfheRPyP2oIkXVjz9MPAMwXUoVSazbRq9MEyGxWecVWMroNHGsO4BXiYbGD7/og4IOkOSdekbF8ExiTNAn8AbEn7HgDuB74LfAO4OSJOAr8CfAT4jZwpuXdJelrSU8AHgd/vtg5l45lWVmZeLFgMRaO/4gipVCoxMzPT78MYGI1aHdD4Q2U2SiYm8gOFBLt2ecZhlaT9EVHJ2+YV5iXjxYFm7roqgoNHybjLysyLBYvg4FEyXhxolvFiwe44eJSMFweaWREcPMyslLxYsDsOHiXjxYFmGS8W7I6DR4l4caDZaZ5x1R0HjxLxTCuz0zzjqjsOHiXimVZmZ/KMq/lz8CgRz7Qys6I4eJhZaTWaKOIJJK05eJSIPyhmZ2rUGne3VWsOHiXiD4qZFcXBw8xKywsF58/Bo0TcbWV2Ji8UnD8HjxJp9EHxAkErKy8UnL9CgoekDZIOSpqVtCVn+3mS7kvbH5M0UbPttpR+UNKVrcpMl7t9TNKhVOa5RdShDK6+urN0s1HnhYLz13XwkLQI+BxwFbAWuF7S2rpsHwNejYj3A3cDd6Z915Jd8/xiYAPweUmLWpR5J3B3RKwBXk1lWxseeqizdLMy8ELB+Smi5bEemI2I5yLiJ8AeYGNdno3AzvT4AeAySUrpeyLirYh4HphN5eWWmfb5jVQGqcxrC6hDKTT6JeVfWGbWqSKCx0rgxZrnR1Jabp6IeBt4DRhrsm+j9DHg/6UyGr0WAJI2S5qRNDM3NzePao0eT9U1O5snksxPEcEj7zyt9b2IjfIUlX52YsSOiKhERGXFihV5WczM/KNqnooIHkeAi2qerwJeapRH0mLgfOBEk30bpb8C/Fwqo9FrWQP+hWVmRSkieDwBrEmzoM4lGwDfW5dnLzCVHl8HPBoRkdI3pdlYq4E1wOONykz7fCuVQSrzwQLqUAr+hWV2Nl8gbX4Wt87SXES8LekW4GFgEfCliDgg6Q5gJiL2Al8EdkmaJWtxbEr7HpB0P/Bd4G3g5og4CZBXZnrJPwL2SPqvwN+nss3MOla9QFredF2vf2pO0WiS8wipVCoxMzPT78Pou3POaXwxqFOnFv54zPptYgIOHz47XYJdu3ydG0n7I6KSt80rzEvE3VZmZ/IF0ubPwcPMSssXSJs/B48S8WwrMyuKg0eJuNvK7Ez+QTV/Dh5mVlr+QTV/Dh4l4gvfmFlRHDxKxBe+MTuTFwjOn4NHifjCN2anVRcI5vECwdYcPErEF74xO23r1saLZrdtW/jjGTYOHiXjC9+YZbxAsDsOHmZWSo26psbHF/Y4hpWDR8l4xpVZ5uqrO0u3Mzl4lIxnXJllHnqos3Q7k4NHyXjGlVkm72y64Mkj7XLwKJlmM64afZjMRo2n6XbPwaOEGg0IuuvKysLTdLvXVfCQtEzSPkmH0v3SBvmmUp5DkqZq0tdJelrSrKTPSNlvAUn/XdI/SHpK0tck/VxKn5D0T5KeTLc/6eb4y8pdV1Z2jVrZnqbbvm5bHluARyJiDfBIen4GScuATwC/DKwHPlETZO4BNpNdu3wNsCGl7wM+EBG/BPwjcFtNkc9GxCXpdmOXx19KXixoZdasy8rTdNvXbfDYCOxMj3cC1+bkuRLYFxEnIuJVssCwQdKFwLsj4tuRXQv3y9X9I+IvI+LttP/fAqu6PE6r48WCVlbusipGt8Hjgog4CpDu35OTZyXwYs3zIyltZXpcn17vd4Cv1zxfLenvJf21pF9tdGCSNkuakTQzNzfXXm3MbOR5ZXkxFrfKIOmbwM/nbGq3dzyvgRhN0mtfeyvwNlAdxj0KvDcijktaB/yFpIsj4odnFRSxA9gBUKlUGnTSlJcXC1pZLVuW/z73pWc707LlEREfiogP5NweBI6l7ifS/cs5RRwBLqp5vgp4KaWvykknlTcF/CYwmbq1iIi3IuJ4erwfeBb4xfara1VeLGhl9eMf9/sIRkO33VZ7gersqSngwZw8DwNXSFqaBsqvAB5O3VyvS7o0zbL6aHV/SRuAPwKuiYg3qwVJWiFpUXr8PrJB9ue6rEMpecaVldH0NPzoR/nbfA2PznQbPD4FXC7pEHB5eo6kiqR7ASLiBPBJ4Il0uyOlAdwE3AvMkrUiqmMbnwV+FthXNyX314CnJH0HeAC4saYs64AXC1oZNfth5MWBnVE0+gYZIZVKJWZmZvp9GANnYiI/UEiwa5cHD230NJqiC7B7t9/z9STtj4hK3javMC8xd11ZmTRb3zE25sDRKQePEnPXlZVJs/Ud27cv/PEMOwePkvN5rqwsfEqSYjl4lJy7rqwMfEqS4jl4lJy7rqwMfEqS4jl4mLuubOS5y6p4Dh7mrisbae6y6g0HD2vZdeXWhw0zd1n1hoOHAc1/gW3e7ABiw2l62l1WveLgYUD2C2zJkvxtb74Jt966sMdj1q3p6eyHTyPusuqOg4cB2S+wHTsabz9+3K0PGy5bt2Y/fPIsWeIuq245eNg7Jieb/xrz4LkNk2ZTzXfscJdVtxw87AzNfo153YcNi1YzrBw4uufgYWeYnGx8RTWv+7BhMD0NU1OeYdVrDh52lu3bve7DhlN1kPzkyfztnmFVnK6Ch6RlkvZJOpTulzbIN5XyHEqXl62mr5P0tKRZSZ9JVxRE0u2SfpAuBPWkpKtr9rkt5T8o6cpujt/yed2HDatmg+TgGVZF6rblsQV4JCLWAI+k52eQtAz4BPDLwHrgEzVB5h5gM9nlZNcAG2p2vTsiLkm3h1JZa4FNwMUp7+erl6W1Ynndhw2jZuNynmFVrG6Dx0ZgZ3q8E7g2J8+VwL6IOBERrwL7gA2SLgTeHRHfjuxyhl9usH/96+2JiLci4nmyy9eu77IOlsPrPmzYNBskX7TIM6yK1m3wuCAijgKk+/fk5FkJvFjz/EhKW5ke16dX3SLpKUlfqmmpNCrrLJI2S5qRNDM3N9dJnQyv+7Dh0+w0JDt3OnAUrWXwkPRNSc/k3Da2+Rp5vwWiSTpk3Vm/AFwCHAU+3aKssxMjdkREJSIqK1asaPNQrZbXfdiw8GlIFl7L4BERH4qID+TcHgSOpe4n0v3LOUUcAS6qeb4KeCmlr8pJJyKORcTJiDgFfIHTXVONyrIeabXuw60P6zefhqQ/uu222gtUZ09NAQ/m5HkYuELS0tT9dAXwcOrmel3SpWmW1Uer+1cDUvJh4Jma19sk6TxJq8kG2R/vsg7WRLN1H+DBc+u/W2/1aUj6odvg8SngckmHgMvTcyRVJN0LEBEngE8CT6TbHSkN4CbgXrKB72eBr6f0u9IU3qeADwK/n8o6ANwPfBf4BnBzRDSY0W1F2b69+eC5u6+sX6ans/G3RjxI3juKRhP6R0ilUomZmZl+H8ZQm56GG25ovH33bn9IbeFNTDQe6xgfhxdeWMijGT2S9kdEJW+bV5hbW1oNnrv7yhZas0FycHdVrzl4WNu89sMGRatB8rExt4R7zcHD2ua1HzYIqic+bDZIvn37wh5TGTl4WEe89sP6qdWJD8GD5AvFwcM65rUf1i/tnPjQgWNhOHhYx7z2w/qh1QC513QsLAcPm5dWaz+mphxArDitBsh94sOFt7jfB2DDqfohbbT24+TJ0x92f6CtG9UB8kbjHEuWOHD0g1seNm+tBs/dArFueYB8cDl4WFearf2A0y0QBxDrVKspueAB8n5y8LCuVNd+LGpyPUef/8o61U6LwwPk/eXgYV2bnMwuttOsBeIpvNaJVlNyPUDefw4eVoh2WiDuvrJ2tDMl11cG7D8HDytMqxbIm29ms7MmJhxELJ+n5A4PT9W1QrWawgvZr0pP47V6npI7XNzysMK1msILnsZrZ/KU3OHTVfCQtEzSPkmH0v3SBvmmUp5DkqZq0telKwbOSvpMuhwtku6T9GS6vSDpyZQ+Iemfarb9STfHb73TagoveBqvZf/7iYmspeopucOl25bHFuCRiFgDPJKen0HSMuATwC8D64FP1ASZe4DNZNciXwNsAIiI34qISyLiEuArwFdriny2ui0ibuzy+K1HqgPoboFYI9XWRrPBcfCU3EHVbfDYCOxMj3cC1+bkuRLYFxEnIuJVYB+wQdKFwLsj4tuRXQv3y/X7p5bIfwT+rMvjtD6YnMwuA7p7txcS2pnaWQAIHiAfZN0Gjwsi4ihAun9PTp6VwIs1z4+ktJXpcX16rV8FjkXEoZq01ZL+XtJfS/rVRgcmabOkGUkzc3Nz7dfICtfuQkLPxCqHdsY3wFNyB13L2VaSvgn8fM6mdtcMKyctmqTXup4zWx1HgfdGxHFJ64C/kHRxRPzwrIIidgA7ACqVSn25tsCqXwCbNzf/temZWKOt1YyqqvHxrKvK74HB1TJ4RMSHGm2TdEzShRFxNHVDvZyT7Qjw6zXPVwF/ldJX1aW/VFP2YuDfAetqjuUt4K30eL+kZ4FfBGZa1cP6r/pF0OrLozoOUruPDb92Tznibqrh0G231V6gOntqCngwJ8/DwBWSlqaB8iuAh1M31+uSLk1jGx+t2/9DwD9ExDtdW5JWSFqUHr+PbJD9uS7rYAuonVOZgMdBRkm7M6o8vjFcug0enwIul3QIuDw9R1JF0r0AEXEC+CTwRLrdkdIAbgLuBWaBZ4Gv15S9ibMHyn8NeErSd4AHgBtryrIh0clMLI+DDLdOZlR5fGO4KJvoNNoqlUrMzLhnaxBVv1xazbqB7NK327f7C2ZYtDu+sWiRA8egkrQ/Iip527zC3PqqnZlYVcePuytr0FW7qCT4yEc8o2qUOXhY37U7DgLuyhpk9V1UrTo1xsc9xjHMHDxsILQ7DlJVndLrANJ/7Q6IVy1Zki0cfeEFB45h5uBhA6PdFelVPrVJf01Pw/LlWdBoNSBe5RlVo8PBwwZOtRUyNtY678mTWd+65K6shVTtojp+vP19PL4xWhw8bCBNTsIrr2StkFZdWdW+dXdl9V6nXVRK55Hw+MbocfCwgTafriwPqBerfgZVu11U4+Owa1cW3D2+MXocPGwodDKlF7IvOHdnda/TGVTgAfGycPCwodHJlF44szvrhhuywV0HkfZ02j1VNTbm7qmycPCwoVI/pbfap96O48fdGmllPjOoIPt/7N6djVM5cJSDg4cNneo4SETWp97u2hA4szXiQJKpH9PodAaVu6jKycHDhlqnA+q1yhxIGg2CtzOm4RlUBg4eNiK66c6CcgSSbgJGlWdQWZWDh42M+u6sdhYZ5hn2QFINEueck41fLF/eXcAAd0/Z2Rw8bCTlLTLstDUC+YGk+oV8zjmDE1TyWhUR2fhFdQxjvldf8Awqy+PgYSOt0eB6N4Gk+oUcsTBBJa8lUWSrol7tmIZnUFkjXQUPScsk7ZN0KN0vbZBvKuU5JGmqJn2bpBclvVGX/zxJ90malfSYpImabbel9IOSruzm+K1cigwktToJKo0eT0zAxz/evLuptiVRVKuiqjZgeEzD2tHVlQQl3QWciIhPSdoCLI2IP6rLswyYASpAAPuBdRHxqqRLgcPAoYj4mZp9Pg78UkTcKGkT8OGI+C1Ja8kuTbse+GfAN4FfjIiml5zxlQStmelp2Lo1+4KWuv8iHhbVuo6Pw7ZtDhR2tl5eSXAjsDM93glcm5PnSmBfRJyIiFeBfcAGgIj424g42qLcB4DLJCml74mItyLiebJrn6/vsg5Wcr1qkQwitzCsKN0GjwuqX/7p/j05eVYCL9Y8P5LSmnlnn4h4G3gNGOukLEmbJc1Impmbm2ujKmajE0iqxzs2lt0kBwwrVsvgIembkp7JuW1s8zXyPnatOgYa7dN2WRGxIyIqEVFZsWJFi5czO1teIJFOfyHDYAWVvFbFK69kt1OnHDCsWC2DR0R8KCI+kHN7EDgm6UKAdP9yThFHgItqnq8CXmrxsu/sI2kxcD5wYp5lmXWtGkhOnTr9hbyQQSWvJeFWhfVTt91We4Hq7Kkp4MGcPA8DV0hammZjXZHS2i33OuDRyEb29wKb0mys1cAa4PEu62A2b50ElWaPx8fhppvy92nUknCrwvppcZf7fwq4X9LHgPJIGnYAAAVwSURBVO8D/wFAUgW4MSJ+NyJOSPok8ETa546IOJHy3QX8J2CJpCPAvRFxO/BFYJekWbIWxyaAiDgg6X7gu8DbwM2tZlqZ9cPkpL/MbbR1NVV3WHiqrplZ53o5VdfMzErIwcPMzDrm4GFmZh1z8DAzs46VYsBc0hzZObSKsBx4paCy+mkU6jEKdYDRqMco1AFGox5F1mE8InJXWZcieBRJ0kyj2QfDZBTqMQp1gNGoxyjUAUajHgtVB3dbmZlZxxw8zMysYw4endvR7wMoyCjUYxTqAKNRj1GoA4xGPRakDh7zMDOzjrnlYWZmHXPwMDOzjjl4JJKWSdon6VC6X9og31TKc0jSVE36NkkvSnqjLv9vS5qT9GS6/e6Q1uM8SfdJmpX0mKSJAa7DOklPp2P9TLqEMZJul/SDmv/F1T049g2SDqbX3pKzveHfUdJtKf2gpCvbLbMXelSPF9L/5UlJPT9T6XzrIGlM0rckvSHps3X75L63hqwOf5XKrH4O8q4A21pE+JaN+9wFbEmPtwB35uRZBjyX7pemx0vTtkuBC4E36vb5beCzI1CPjwN/kh5vAu4b4Do8DvwbsitPfh24KqXfDvxhD497EfAs8D7gXOA7wNp2/o7A2pT/PGB1KmdRO2UOQz3StheA5Qv0OeimDu8C/i1wY/1nt9F7a8jq8FdApdvjc8vjtI3AzvR4J3BtTp4rgX0RcSIiXgX2ARsAIuJvI13Pvc96VY/ach8ALuvhr65510HZFS3fHRHfjuyT8uUG+/fCemA2Ip6LiJ8Ae8jqUqvR33EjsCci3oqI54HZVF47ZQ5DPRbavOsQET+KiL8BflybuQ/vrcLrUCQHj9MuqH5ppvu8ptxK4MWa50dSWiv/XtJTkh6QdFHr7F3pVT3e2Sci3gZeA8a6Ptp83dRhZXpcn151S/pffKlRd1gX2vm7Nvo7NqvPfN5z3ehFPQAC+EtJ+yVt7sFx5x5fznGclafN93Sr91bRelGHqj9NXVZ/PN8fgd1eSXCoSPom8PM5m7a2W0ROWqu5zv8L+LOIeEvSjWS/En6jzdfLP4j+1GM++zQurHd1aHac9wCfTM8/CXwa+J02X6+bY2onT6P0vB94vZ5f34t6APxKRLyU+tj3SfqHiPi/XRxnM93UoZsyi9SLOgBMRsQPJP0s8BXgI2StqI6UKnhExIcabZN0TNKFEXE0NU9fzsl2BPj1mueryPoPm73m8ZqnXwDubPuAG5e54PVI+1wEHJG0GDif7BLB89LDOhxJj2vTX0qveazmNb4A/O/5Hn8D1b/RWa+dk6f+79hs31ZlFq0n9YiI6v3Lkr5G1i3Tq+DRTR2alZn73uqRXtSBiPhBun9d0v8k+z90HDzcbXXaXqA6Y2cKeDAnz8PAFZKWpi6PK1JaQ+nLr+oa4HsFHGszPalHXbnXAY+mft9emHcdUjfX65IuTc3xj1b3r/tffBh4puDjfgJYI2m1pHPJBjD31uVp9HfcC2xKs2dWA2vIBmfbKbNohddD0rvSL10kvYvs/1X037+oOuRq9t7qkcLrIGmxpOXp8U8Bv8l8/w+9mikwbDeyfsJHgEPpfllKrwD31uT7HbJBwFngP9ek30X2K+BUur89pf834ADZTIlvAf9iSOvx08Cfp/yPA+8b4DpU0gfiWeCznD6Twi7gaeApsg/dhT049quBf0yvvTWl3QFc0+rvSNZl9yxwkJpZPHllLsDnodB6kM0Y+k66HViIenRZhxfIfsG/kT4Ha5u9t4alDmSzsPanz8ABYDtpNlynN5+exMzMOuZuKzMz65iDh5mZdczBw8zMOubgYWZmHXPwMDOzjjl4mJlZxxw8zMysY/8fPMrQ2p9ORroAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Vi sjekker at vi har fått riktige punkter ved å plotte dem i xy-planet\n",
    "for i in range(len(R)):\n",
    "    ri = R[i]\n",
    "    plt.plot(ri[0],ri[1],'ob')\n",
    "plt.axis('equal')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Vi finner potensialet i xy planet\n",
    "x,y,rx,ry,V_xy = findpot_xy(R,Q,-1.5*a,1.5*a,-1.5*a,1.5*a,30,30)\n",
    "Ey,Ex = np.gradient(-V_xy)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "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": [
    "# Vi plotter potensialet og feltet i xy planet\n",
    "plt.figure(figsize=(12,6))\n",
    "plt.subplot(1,2,1)\n",
    "plt.contourf(rx,ry,V_xy)\n",
    "plt.axis('equal')\n",
    "for i in range(len(R)):\n",
    "    ri = R[i]\n",
    "    plt.plot(ri[0],ri[1],'.r')\n",
    "plt.subplot(1,2,2)\n",
    "plt.quiver(rx,ry,Ex,Ey)\n",
    "plt.axis('equal')\n",
    "for i in range(len(R)):\n",
    "    ri = R[i]\n",
    "    plt.plot(ri[0],ri[1],'.r')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Vi finner potensialet i xz planet\n",
    "x,z,rx,rz,V_xz = findpot_xz(R,Q,-1.5*a,1.5*a,-1.5*a,1.5*a,30,30)\n",
    "Ez,Ex = np.gradient(-V_xz)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(-0.0165, 0.0165, -0.0165, 0.0165)"
      ]
     },
     "execution_count": 39,
     "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": [
    "# Vi plotter potensialet og feltet i xz planet\n",
    "plt.figure(figsize=(12,6))\n",
    "plt.subplot(1,2,1)\n",
    "plt.contourf(rx,rz,V_xz)\n",
    "plt.axis('equal')\n",
    "plt.subplot(1,2,2)\n",
    "plt.quiver(rx,rz,Ex,Ez)\n",
    "plt.axis('equal')"
   ]
  },
  {
   "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": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, '$V$ (V)')"
      ]
     },
     "execution_count": 43,
     "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",
    "# Først finner vi den numeriske løsningen\n",
    "xi = a/2\n",
    "yi = 0\n",
    "Nz = 1000\n",
    "z = np.zeros(Nz+1)\n",
    "V = np.zeros(Nz+1)\n",
    "for iz in range(Nz+1):\n",
    "    zi = -2*a + (iz/Nz)*(4*a)\n",
    "    z[iz] = zi\n",
    "    ri = np.array([xi,yi,zi])\n",
    "    Vi = epotlist(ri,Q,R)\n",
    "    V[iz] = Vi\n",
    "plt.plot(z,V)\n",
    "# Så sammenlikner vi med det eksakte resultatet i x=0\n",
    "epsilon0 = 8.854e-12\n",
    "V_teori = q/(4*np.pi*epsilon0*np.sqrt(a*a+z*z))\n",
    "plt.plot(z,V_teori)#[-a/2,a/2],[Ez_teori,Ez_teori])\n",
    "plt.xlabel('$z$ (m)')\n",
    "plt.ylabel('$V$ (V)')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "(*Løsning til kommentar*) Vi ser at forskjellen er størst for $z=0$ og at den blir mindre jo større $z$ er. Det kan vi forstå, fordi etterhvert som $z$ blir stor, så vil ringen fremtre mer og mer som en punktladning i origo. Forskjellen i avstand til punktladningen fra punktet $(0,0,z)$ og $(a/5,0,z)$ blir mindre og mindre jo større $z$ er slik at potensialene i disse punktene vil bli mer og mer like jo større $z$ er. (Vi ser også at potensialet er symmetrisk om $z=0$ slik vi forventer fordi ladningsfordelingen er symmetrisk om $xy$-planet, men det vil ikke bli gitt noe ekstra poeng for en slik kommentar om symmetri - det er tilstrekkelig med en kommentar til hvorfor forskjellen blir mindre når $z$ blir større)."
   ]
  },
  {
   "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": [
    "(*Løsning*) Langt vekk fra ringladningen forventer vi at den vil oppføre seg som en punktladning med ladning $q$ i origo. Potensialet fra en punktladning vil være\n",
    "$$V(r) = \\frac{q}{4 \\pi \\epsilon_0 r}$$"
   ]
  },
  {
   "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": 47,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/malthe/opt/anaconda3/lib/python3.7/site-packages/ipykernel_launcher.py:22: MatplotlibDeprecationWarning: Adding an axes using the same arguments as a previous axes currently reuses the earlier instance.  In a future version, a new instance will always be created and returned.  Meanwhile, this warning can be suppressed, and the future behavior ensured, by passing a unique label to each axes instance.\n",
      "/Users/malthe/opt/anaconda3/lib/python3.7/site-packages/ipykernel_launcher.py:27: MatplotlibDeprecationWarning: Adding an axes using the same arguments as a previous axes currently reuses the earlier instance.  In a future version, a new instance will always be created and returned.  Meanwhile, this warning can be suppressed, and the future behavior ensured, by passing a unique label to each axes instance.\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7fda3a610b10>"
      ]
     },
     "execution_count": 47,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 864x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Løsning\n",
    "plt.figure(figsize=(12,4))\n",
    "Nx = 1000\n",
    "dx = 10*a\n",
    "x = np.zeros(Nx+1)\n",
    "Vr = np.zeros(Nx+1)\n",
    "yi = 0\n",
    "zi = 0\n",
    "for ix in range(Nx+1):\n",
    "    xi = a+0.1*a+(ix/Nx)*dx\n",
    "    x[ix] = xi\n",
    "    ri = np.array([xi,0,zi])\n",
    "    Vi = epotlist(ri,Q,R)\n",
    "    Vr[ix] = Vi\n",
    "plt.subplot(1,2,1)\n",
    "plt.plot(x,Vr,label=\"Numerisk\")\n",
    "plt.subplot(1,2,2)\n",
    "plt.loglog(x,Vr,label=\"Numerisk\")\n",
    "# Så sammenlikner vi med en punktladning\n",
    "epsilon0 = 8.854e-12\n",
    "Vr_teori = q/(4*np.pi*epsilon0*x)\n",
    "plt.subplot(1,2,1)\n",
    "plt.plot(x,Vr_teori,label=\"Teori\")\n",
    "plt.xlabel('$x$ (m)')\n",
    "plt.ylabel('$V$ (V)')\n",
    "plt.legend()\n",
    "plt.subplot(1,2,2)\n",
    "plt.loglog(x,Vr_teori,label=\"Teori\")\n",
    "plt.xlabel('$x$ (m)')\n",
    "plt.ylabel('$V$ (V)')\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "(*Løsning: Kommentar til plot*) (Vi forventer at du kort kommenterer et slikt plot) Vi ser at den numeriske løsningen for en ring går mot den eksakte løsningen for en punktladning når avstanden blir stor. Vi ser at forskjellen blir ganske liten allerede i en avstand $r = 4a$ fra sentrum av ringen."
   ]
  },
  {
   "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
}
