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authorTrupti Kini2016-03-17 23:30:24 +0600
committerTrupti Kini2016-03-17 23:30:24 +0600
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+{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# 10: Dielectric Properties"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Example number 10.1, Page number 276"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 1,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "relative permittivity is 5.86\n"
+ ]
+ }
+ ],
+ "source": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration \n",
+ "P=4.3*10**-8; #polarisation(per cm**2)\n",
+ "epsilon0=8.85*10**-12; #relative permeability(F/m)\n",
+ "E=1000; #electric field(V/m)\n",
+ "\n",
+ "#Calculations\n",
+ "epsilonr=1+(P/(epsilon0*E)); #relative permittivity\n",
+ "\n",
+ "#Result\n",
+ "print \"relative permittivity is\",round(epsilonr,2)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Example number 10.2, Page number 276"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 2,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "electric displacement is 36 *10**-6 C/m**2\n",
+ "polarisation is 27 *10**-6 C/m**2\n"
+ ]
+ }
+ ],
+ "source": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration \n",
+ "k=4;\n",
+ "epsilon0=9*10**-12; #relative permeability(F/m)\n",
+ "E=10**6; #electric field(V/m)\n",
+ "\n",
+ "#Calculations\n",
+ "D=k*epsilon0*E; #electric displacement(C/m**2)\n",
+ "P=epsilon0*E*(k-1); #polarisation(C/m**2)\n",
+ "\n",
+ "#Result\n",
+ "print \"electric displacement is\",int(D*10**6),\"*10**-6 C/m**2\"\n",
+ "print \"polarisation is\",int(P*10**6),\"*10**-6 C/m**2\""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Example number 10.3, Page number 277"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 3,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "electric field is 0.113 N/C\n",
+ "polarisation is 4e-12 C/m**2\n",
+ "induced dipole moment is 2e-18 cm\n"
+ ]
+ }
+ ],
+ "source": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration \n",
+ "k=5;\n",
+ "epsilon0=8.86*10**-12; #relative permeability(F/m)\n",
+ "D=5*10**-12; #electric displacement(C/m**2)\n",
+ "V=0.5*10**-6;\n",
+ "\n",
+ "#Calculations\n",
+ "E=D/(k*epsilon0); #electric field(N/C)\n",
+ "P=D*(1-(1/k)); #polarisation(C/m**2)\n",
+ "dm=P*V; #induced dipole moment(cm)\n",
+ "\n",
+ "#Result\n",
+ "print \"electric field is\",round(E,3),\"N/C\"\n",
+ "print \"polarisation is\",P,\"C/m**2\"\n",
+ "print \"induced dipole moment is\",dm,\"cm\""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "collapsed": true
+ },
+ "source": [
+ "# Example number 10.4, Page number 277"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 5,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "dipole moment is 2.43 *10**-41 coul x metre\n"
+ ]
+ }
+ ],
+ "source": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration \n",
+ "k=1.000074;\n",
+ "epsilon0=8.85*10**-12; #relative permeability(F/m)\n",
+ "E=1; #electric field(N/C)\n",
+ "n=2.69*10**25; #molecular density\n",
+ "\n",
+ "#Calculations\n",
+ "p=epsilon0*E*(k-1)/n; #dipole moment(coulx metre)\n",
+ "\n",
+ "#Result\n",
+ "print \"dipole moment is\",round(p*10**41,2),\"*10**-41 coul x metre\""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Example number 10.5, Page number 278"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 6,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "dipole moment is 3.97 *10**-36 coul-metre\n",
+ "atomic polarizability is 4.4 *10**-41 coul-m**2/volt\n"
+ ]
+ }
+ ],
+ "source": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration \n",
+ "k=1.000134;\n",
+ "epsilon0=8.85*10**-12; #relative permeability(F/m)\n",
+ "E=90000; #electric field(N/C)\n",
+ "N=6.023*10**26; #avagadro number\n",
+ "\n",
+ "#Calculations\n",
+ "n=N/22.4;\n",
+ "p=epsilon0*E*(k-1)/n; #dipole moment(coul-metre)\n",
+ "alpha=p/E; #atomic polarizability(coul-m**2/volt)\n",
+ "\n",
+ "#Result\n",
+ "print \"dipole moment is\",round(p*10**36,2),\"*10**-36 coul-metre\"\n",
+ "print \"atomic polarizability is\",round(alpha*10**41,1),\"*10**-41 coul-m**2/volt\""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Example number 10.6, Page number 278"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 7,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "electric field is 1.43 *10**3 volt/m\n",
+ "electric displacement is 8.9e-08 C/m**2\n",
+ "dipole moment is 7.6 *10**-8 C/m**2\n"
+ ]
+ }
+ ],
+ "source": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration \n",
+ "k=7;\n",
+ "epsilon0=8.9*10**-12; #relative permeability(F/m)\n",
+ "V0=100; #potential difference(V)\n",
+ "d=10**-2; #displacement(m)\n",
+ "\n",
+ "#Calculations\n",
+ "E0=V0/d; #electric field intensity(volt/m)\n",
+ "E=E0/k; #electric field(N/C)\n",
+ "D=k*E*epsilon0; #electric displacement(C/m**2)\n",
+ "p=epsilon0*E*(k-1); #dipole moment(coul-metre)\n",
+ "\n",
+ "#Result\n",
+ "print \"electric field is\",round(E/10**3,2),\"*10**3 volt/m\"\n",
+ "print \"electric displacement is\",D,\"C/m**2\"\n",
+ "print \"dipole moment is\",round(p*10**8,1),\"*10**-8 C/m**2\""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Example number 10.7, Page number 279"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 10,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "dielectric constant is 5.0\n",
+ "permittivity is 44.25 *10**-12 coul**2/nt-m**2\n"
+ ]
+ }
+ ],
+ "source": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration \n",
+ "epsilon0=8.85*10**-12; #relative permeability(F/m)\n",
+ "chi=35.4*10**-12; #electric susceptibility(coul**2/nt-m**2)\n",
+ "\n",
+ "#Calculations\n",
+ "k=1+(chi/epsilon0); #dielectric constant\n",
+ "epsilon=epsilon0*k; #permittivity(coul**2/nt-m**2) \n",
+ "\n",
+ "#Result\n",
+ "print \"dielectric constant is\",k\n",
+ "print \"permittivity is\",round(epsilon*10**12,2),\"*10**-12 coul**2/nt-m**2\""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Example number 10.8, Page number 279"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 11,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "dipole moment is 2.4437 *10**-41 C/m**2\n",
+ "answer in the book is wrong\n"
+ ]
+ }
+ ],
+ "source": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration \n",
+ "epsilon0=8.85*10**-12; #relative permeability(F/m)\n",
+ "E=100; #electric field(N/C)\n",
+ "epsilonr=1.000074; #dielectric constant\n",
+ "n=2.68*10**27; #density\n",
+ "\n",
+ "#Calculations\n",
+ "p=epsilon0*E*(epsilonr-1)/n; #dipole moment(coul-metre)\n",
+ "\n",
+ "#Result\n",
+ "print \"dipole moment is\",round(p*10**41,4),\"*10**-41 C/m**2\"\n",
+ "print \"answer in the book is wrong\""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Example number 10.9, Page number 287"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 12,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "electronic polarizability is 1.6557 *10**-41 Fm**2\n",
+ "relative permittivity is 1.0018\n"
+ ]
+ }
+ ],
+ "source": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration \n",
+ "epsilon0=8.85*10**-12; #relative permeability(F/m)\n",
+ "R=0.053*10**-9; #radius(nm)\n",
+ "N=9.8*10**26; #number of atoms\n",
+ "\n",
+ "#Calculations\n",
+ "alphae=4*math.pi*epsilon0*R**3; #electronic polarizability(Fm**2)\n",
+ "epsilonr=1+(4*math.pi*N*R**3); #relative permittivity\n",
+ "\n",
+ "#Result\n",
+ "print \"electronic polarizability is\",round(alphae*10**41,4),\"*10**-41 Fm**2\"\n",
+ "print \"relative permittivity is\",round(epsilonr,4)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Example number 10.10, Page number 288"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 13,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "electronic polarizability is 2.242e-41 Fm**2\n",
+ "answer varies due to rounding off errors\n"
+ ]
+ }
+ ],
+ "source": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration \n",
+ "epsilon0=8.85*10**-12; #relative permeability(F/m)\n",
+ "epsilonr=1.0000684; #dielectric constant\n",
+ "N=2.7*10**25; #number of atoms\n",
+ "\n",
+ "#Calculations\n",
+ "alphae=epsilon0*(epsilonr-1)/N; #electronic polarizability(Fm**2)\n",
+ "\n",
+ "#Result\n",
+ "print \"electronic polarizability is\",alphae,\"Fm**2\"\n",
+ "print \"answer varies due to rounding off errors\""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Example number 10.11, Page number 288"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 14,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "dielectric constant is 1.339\n"
+ ]
+ }
+ ],
+ "source": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration \n",
+ "epsilon0=8.854*10**-12; #relative permeability(F/m)\n",
+ "alphae=10**-40; #dielectric polarizability(Fm**2)\n",
+ "N=3*10**28; #number of atoms\n",
+ "\n",
+ "#Calculations\n",
+ "epsilonr=1+(N*alphae/epsilon0); #dielectric constant\n",
+ "\n",
+ "#Result\n",
+ "print \"dielectric constant is\",round(epsilonr,3)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Example number 10.12, Page number 288"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 15,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "electronic polarizability is 7.9 *10**-40 Fm**2\n",
+ "answer in the book is wrong\n"
+ ]
+ }
+ ],
+ "source": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration \n",
+ "epsilon0=8.85*10**-12; #relative permeability(F/m)\n",
+ "epsilonr=1.0024; #dielectric constant\n",
+ "N=2.7*10**25; #number of atoms\n",
+ "\n",
+ "#Calculations\n",
+ "alphae=epsilon0*(epsilonr-1)/N; #electronic polarizability(Fm**2)\n",
+ "\n",
+ "#Result\n",
+ "print \"electronic polarizability is\",round(alphae*10**40,1),\"*10**-40 Fm**2\"\n",
+ "print \"answer in the book is wrong\""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Example number 10.13, Page number 289"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 16,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "radius of electron cloud is 5.86 *10**-11 m\n",
+ "displacement is 6.99987 *10**-17 m\n"
+ ]
+ }
+ ],
+ "source": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration \n",
+ "epsilonr=1.0000684; #dielectric constant\n",
+ "N=2.7*10**25; #number of atoms\n",
+ "X=1/(9*10**9);\n",
+ "E=10**6; #electric field(V/m)\n",
+ "Z=2; #atomic number\n",
+ "e=1.6*10**-19; #electron charge(coulomb)\n",
+ "\n",
+ "#Calculations\n",
+ "R=((epsilonr-1)/(4*math.pi*N))**(1/3); #radius of electron cloud(m)\n",
+ "x=X*E*R**3/(Z*e); #displacement(m)\n",
+ "\n",
+ "#Result\n",
+ "print \"radius of electron cloud is\",round(R*10**11,2),\"*10**-11 m\"\n",
+ "print \"displacement is\",round(x*10**17,5),\"*10**-17 m\""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Example number 10.14, Page number 293"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 17,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "dielectric constant is 1.38\n"
+ ]
+ }
+ ],
+ "source": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration \n",
+ "epsilon0=8.85*10**-12; #dielectric constant\n",
+ "N=3*10**28; #number of atoms\n",
+ "alphae=10**-40; #dielectric polarizability(Fm**2)\n",
+ "\n",
+ "#Calculations\n",
+ "x=N*alphae/(3*epsilon0);\n",
+ "epsilonr=(1+(2*x))/(1-x); #dielectric constant\n",
+ "\n",
+ "#Result\n",
+ "print \"dielectric constant is\",round(epsilonr,2)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Example number 10.15, Page number 294"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 18,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "dielectric constant is 3.8\n"
+ ]
+ }
+ ],
+ "source": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration \n",
+ "epsilon0=8.85*10**-12; #dielectric constant\n",
+ "Na=6.023*10**26; #number of atoms\n",
+ "M=32; #atomic mass\n",
+ "alphae=3.28*10**-40; #dielectric polarizability(Fm**2)\n",
+ "rho=2.08*10**3; #density(kg/m**3)\n",
+ "\n",
+ "#Calculations\n",
+ "x=Na*rho*alphae/(M*3*epsilon0);\n",
+ "epsilonr=(1+(2*x))/(1-x); #dielectric constant\n",
+ "\n",
+ "#Result\n",
+ "print \"dielectric constant is\",round(epsilonr,1)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Example number 10.16, Page number 294"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 19,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "electronic polarizability is 3.29 *10**-40 Fm**2\n"
+ ]
+ }
+ ],
+ "source": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration \n",
+ "epsilon0=8.85*10**-12; #dielectric constant\n",
+ "Na=6.02*10**26; #number of atoms\n",
+ "epsilonr=3.75; #dielectric constant\n",
+ "M=32; #atomic mass\n",
+ "rho=2050; #density(kg/m**3)\n",
+ "gama=1/3; #internal field constant\n",
+ "\n",
+ "#Calculations\n",
+ "N=Na*rho/M; #number of atoms\n",
+ "alphae=((epsilonr-1)/(epsilonr+2))*(3*epsilon0/N); #electronic polarizability(Fm**2)\n",
+ "\n",
+ "#Result\n",
+ "print \"electronic polarizability is\",round(alphae*10**40,2),\"*10**-40 Fm**2\""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Example number 10.17, Page number 295"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 20,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "ratio between electronic and ionic polarizability is 1.738\n"
+ ]
+ }
+ ],
+ "source": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration \n",
+ "epsilonr=4.94; #dielectric constant\n",
+ "n2=2.69;\n",
+ "\n",
+ "#Calculations\n",
+ "x=(epsilonr-1)/(epsilonr+2);\n",
+ "y=(n2-1)/(n2+2);\n",
+ "alpha=1/((x/y)-1); #ratio between electronic and ionic polarizability\n",
+ "\n",
+ "#Result\n",
+ "print \"ratio between electronic and ionic polarizability is\",round(alpha,3)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Example number 10.18, Page number 296"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 21,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "percentage of ionic polarizability is 51.4 %\n"
+ ]
+ }
+ ],
+ "source": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration \n",
+ "epsilonr=5.6; #dielectric constant\n",
+ "n=1.5;\n",
+ "\n",
+ "#Calculations\n",
+ "x=(epsilonr+2)/(epsilonr-1);\n",
+ "y=(n**2-1)/(n**2+2);\n",
+ "alpha=(1-(x*y))*100; #percentage of ionic polarizability\n",
+ "\n",
+ "#Result\n",
+ "print \"percentage of ionic polarizability is\",round(alpha,1),\"%\""
+ ]
+ }
+ ],
+ "metadata": {
+ "kernelspec": {
+ "display_name": "Python 2",
+ "language": "python",
+ "name": "python2"
+ },
+ "language_info": {
+ "codemirror_mode": {
+ "name": "ipython",
+ "version": 2
+ },
+ "file_extension": ".py",
+ "mimetype": "text/x-python",
+ "name": "python",
+ "nbconvert_exporter": "python",
+ "pygments_lexer": "ipython2",
+ "version": "2.7.11"
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 0
+}