Electrostatic_aug2.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Electrostatic functions "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- Electrostatic force between the charges $q_1$ & $q_2$ separated by distance $r$ is given by\n",
    "## $F=\\frac{Kq_1q_2}{r^2}$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "9000000000.0"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def force(q1,q2,r): \n",
    "    f=k*q1/r\n",
    "    return f\n",
    "k=9*10**9\n",
    "force(1,1,1) #when q1=1C, q2=1C and r=1m the force between q1 and q2 is:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- Electrostatic Potential of charge $q_1$ at distance $r$\n",
    "## $V=\\frac{Kq_1}{r}$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "9000000000.0"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def potential(q1,r):\n",
    "    v=k*q1/r\n",
    "    return v\n",
    "k=9*10**9\n",
    "potential(1,1) # when q1-1c and r=1m the potential is:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- Electric Field Intensity of charge $q_1$ at distance $r$ is:\n",
    "## $V=\\frac{Kq_1}{r^2}$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "9000000000.0"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def intensity(q1,r):\n",
    "    I=k*q1/r**2\n",
    "    return I\n",
    "k=9*10**9\n",
    "intensity(1,1) # when charge q1 = 1C and distance r = 1m, the intensity is:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Now, let us make a class of three functions \"Electrostatic\":"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "class Electrostatic():\n",
    "    def __init__(self,value_k,info,info1,info2):\n",
    "        self.k=value_k\n",
    "        self.info=info\n",
    "        self.info1=info1\n",
    "        self.info2=info2\n",
    "    def force(self,q1,q2,r):\n",
    "        f=self.k*q1*q2/r**2\n",
    "        #print(self.give)\n",
    "        return f\n",
    "    def potential(self,q1,r):\n",
    "        v=self.k*q1/r\n",
    "        #print(self.info1)\n",
    "        return v\n",
    "    def intensity(self,q1,r):\n",
    "        I=self.k*q1/r**2\n",
    "        #print(self.info2)\n",
    "        return I\n",
    "E1=Electrostatic(value_k=9*10**9,info='This is coulomb force',info1='This is coulomb potential',info2='This is intensity' )\n",
    "#E.force(1,1,1),E.potential(1,1),E.intensity(1,1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "q1=3.2*10**-16 #let us fix the charge q1\n",
    "q2=3.2*10**-10 #fix another charge q2 \n",
    "R=[]  #empty list of distance\n",
    "F=[]  #empty list of force\n",
    "V=[]  #empty list of potential\n",
    "E=[]  #empty list of intensity\n",
    "for r in range(1,10000): #taking the calue of distance from 1 to 1000\n",
    "    ff=E1.force(q1,q2,r) \n",
    "    vv=E1.potential(q1,r)\n",
    "    ee=E1.intensity(q1,r)\n",
    "    R.append(r)\n",
    "    F.append(ff)\n",
    "    V.append(vv)\n",
    "    E.append(ee)\n",
    "#print(R,F,V,E)\n",
    "    "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- Create a dictionary of above created list"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "data={} #create an empty list\n",
    "data.update({\"Distance\":R, \"Force\":F, \"Potential\":V, \"Intensity\":E}) #update above information with Rename\n",
    "#print(data) "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- Convert dictionary to DataFrame"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "DF=pd.DataFrame(data)  \n",
    "#print(DF)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- Save DataFrame in csv (comma separated variable) Excel file"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "DF.to_csv('Electrostatic_variable.csv')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- Read and Open the csv file from computer by jupyter notebook"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Unnamed: 0</th>\n",
       "      <th>Distance</th>\n",
       "      <th>Force</th>\n",
       "      <th>Potential</th>\n",
       "      <th>Intensity</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>9.216000e-16</td>\n",
       "      <td>2.880000e-06</td>\n",
       "      <td>2.880000e-06</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "      <td>2.304000e-16</td>\n",
       "      <td>1.440000e-06</td>\n",
       "      <td>7.200000e-07</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>2</td>\n",
       "      <td>3</td>\n",
       "      <td>1.024000e-16</td>\n",
       "      <td>9.600000e-07</td>\n",
       "      <td>3.200000e-07</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>3</td>\n",
       "      <td>4</td>\n",
       "      <td>5.760000e-17</td>\n",
       "      <td>7.200000e-07</td>\n",
       "      <td>1.800000e-07</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>4</td>\n",
       "      <td>5</td>\n",
       "      <td>3.686400e-17</td>\n",
       "      <td>5.760000e-07</td>\n",
       "      <td>1.152000e-07</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   Unnamed: 0  Distance         Force     Potential     Intensity\n",
       "0           0         1  9.216000e-16  2.880000e-06  2.880000e-06\n",
       "1           1         2  2.304000e-16  1.440000e-06  7.200000e-07\n",
       "2           2         3  1.024000e-16  9.600000e-07  3.200000e-07\n",
       "3           3         4  5.760000e-17  7.200000e-07  1.800000e-07\n",
       "4           4         5  3.686400e-17  5.760000e-07  1.152000e-07"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df=pd.read_csv('Electrostatic_variable.csv')\n",
    "df.head() #head mean title eg; distance, Force, Potential, ..."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- Make a plot between variables in  columns in csv file"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "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": [
    "#plt.figure(figsize=(10,10))\n",
    "plt.plot(df.Distance,df.Force,'o',color='r',label='force',lw=1) #lw= line width\n",
    "plt.plot(df.Distance,df.Potential,'.',color='g',label='potential',lw=1)\n",
    "plt.plot(df.Distance,df.Intensity,'-.',color='b',label='intensity',lw=1)\n",
    "plt.xlabel(\"Distance(m)\")\n",
    "plt.ylabel(\"Force(N), Potential(V), Intensity(N/m^2)\")\n",
    "plt.grid(True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This graph doesnot gives better vizualization for the variation of electrostatic functions with distance. Also, there is no clear difference for variation of force, potential and intensity with distance. For the better vizualization we need semilog or loglog plot. Log - log and semi - log plot are done if the range of variation of data is wide."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Semi - Log Plot\n",
    "In semi - log plot, variable in one axis is in mog scale and variable in other axis is left as it is. In the following semi - log plot, the variable in y axis (i.e., force, potential and intensity) are plotted in log scale and distance is left as it is. Which can be seen in the plot below;"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "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": [
    "plt.semilogy(df.Distance,df.Force,label='force')\n",
    "plt.semilogy(df.Distance,df.Potential,label='potential')\n",
    "plt.semilogy(df.Distance,df.Intensity,label='intensity')\n",
    "plt.xlabel(\"Distance(m)\")\n",
    "plt.ylabel(\"log(F), log(V), log(E)\")\n",
    "plt.legend()\n",
    "plt.grid(True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Log - Log Plot\n",
    "In log - log plot, variable in both axis are in log scale. It helps for better visualization in every point of graph, more than semi - log plot. Which can be seen in the plot below;"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "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": [
    "plt.loglog(df.Distance,df.Force,label='force')\n",
    "plt.loglog(df.Distance,df.Potential,label='potential')\n",
    "plt.loglog(df.Distance,df.Intensity,label='intensity')\n",
    "plt.xlabel(\"log(R)\",fontsize=16)\n",
    "plt.ylabel(\"log(F), log(V), log(E)\",fontsize=16)\n",
    "plt.legend(loc='center',fontsize=16)\n",
    "plt.grid(True)"
   ]
  },
  {
   "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": "3.7.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}