{ "metadata": { "name": "", "signature": "sha256:08d693988f55ded7946a3910c4b750b4a1419d79f72e5b56719c0d924a66fd5a" }, "nbformat": 3, "nbformat_minor": 0, "worksheets": [ { "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "

Chapter 5: Electric Fields in Material Space

" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

Example 5.1, Page number: 167

" ] }, { "cell_type": "code", "collapsed": false, "input": [ " \n", "import scipy\n", "import scipy.integrate\n", "\n", "#Variable Declaration\n", "\n", "r1= 0.2 # radius of hemispherical shell in metres\n", "r2= 0.1 # radius of spherical shell in metres\n", "\n", "#Calculations\n", "\n", "#Calculation of current through hemispherical shell \n", "\n", "def J1(phi,theta):\n", "\ts1=(1/r1)*(2* scipy.cos(theta)* scipy.sin(theta))\n", "\treturn s1\n", "\n", "if __name__ == '__main__':\n", "\n", " I1, error = scipy.integrate.dblquad(lambda theta , phi: J1(phi,theta), \n", " 0, 2*scipy.pi, lambda theta: 0, lambda theta: scipy.pi/2) \n", "\t \n", "#Calculation of current through spherical shell \n", "\n", "def J2(phi,theta):\n", "\ts2=(1/r2)*(2* scipy.cos(theta)* scipy.sin(theta))\n", "\treturn s2\n", "\n", "if __name__ == '__main__':\n", "\n", " I2, error = scipy.integrate.dblquad(lambda theta , phi: J1(phi,theta), \n", " 0, 2*scipy.pi, lambda theta: 0, lambda theta: scipy.pi) \n", "\t \n", "#Results\n", "\n", "print 'Current through hemispherical shell=',round(I1,1),'A' \n", "print 'Current through spherical shell=',round(I2,0),'A'\n", "\t" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Current through hemispherical shell= 31.4 A\n", "Current through spherical shell= 0.0 A\n" ] } ], "prompt_number": 1 }, { "cell_type": "markdown", "metadata": {}, "source": [ "

Example 5.2, Page number: 168

" ] }, { "cell_type": "code", "collapsed": false, "input": [ " \n", "#Variable Declaration\n", "\n", "ps=10**-7 #Surface charge density of the belt in Couloumb/metre^2\n", "u=2 #Speed of the belt in metres/sec\n", "w=0.1 #Width of the belt in metres\n", "t=5 #Time taken in seconds \n", "\n", "#Calculations\n", "\n", "I=ps*u*w #Current in amperes\n", "Q=I*t*10**9 #Charge collected in 5 seconds in nano Coloumbs\n", "\n", "#Result\n", "\n", "print \"The charge collected in 5 seconds is \",Q,\"nC\" " ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "The charge collected in 5 seconds is 100.0 nC\n" ] } ], "prompt_number": 2 }, { "cell_type": "markdown", "metadata": {}, "source": [ "

Example 5.3, Page number: 169

" ] }, { "cell_type": "code", "collapsed": false, "input": [ " \n", "#Variable Declaration\n", "\n", "n=10**29 #Number density of electrons in m^-3\n", "e=-1.6*10**-19 #Electronic charge in Coloumbs\n", "sigma=5*10**7 #Current density in S/m\n", "E=10**-2 #Electric Field in V/m\n", "S=(3.14*10**-6)/4 #Cross sectional area of the wire in m^2\n", "\n", "#Calculations\n", "\n", "pv=n*e #Charge density of free electrons in C/m^3\n", "J=sigma*E*10**-3 #Current density in kA/m^2\n", "I=J*S*10**3 #Current in amperes\n", "u=J*10**3/pv #Drift velocity in m/s\n", "\n", "#Results\n", "\n", "print \"The charge density is \",pv,\"C/m^3\" \n", "print \"The current density is \",J,\"kA/m^2\" \n", "print \"The current is \",round(I,3), \"A\"\n", "print \"The drift velocity is \",-u,\"m/s\" " ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "The charge density is -16000000000.0 C/m^3\n", "The current density is 500.0 kA/m^2\n", "The current is 0.393 A\n", "The drift velocity is 3.125e-05 m/s\n" ] } ], "prompt_number": 3 }, { "cell_type": "markdown", "metadata": {}, "source": [ "

Example 5.4, Page number: 170

" ] }, { "cell_type": "code", "collapsed": false, "input": [ " \n", "import scipy\n", "\n", "#Variable Declaration\n", "\n", "l=4 #Length of the lead bar in m\n", "d=3 #Width of the lead bar in cm\n", "r=0.5 #Radius of the hole drilled in cm\n", "sigma=5*10**6 #Conductivity of the bar in S/m\n", "\n", "#Calculation\n", "\n", "S=(d**2-(scipy.pi*r**2)) #Cross sectional area in cm^2\n", "R=l/(S*sigma*10**-4) #Resistance in ohms\n", "\n", "#Result\n", "\n", "print 'The resistance between the square ends is',round(R*10**6),'micro ohms'\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "The resistance between the square ends is 974.0 micro ohms\n" ] } ], "prompt_number": 4 }, { "cell_type": "markdown", "metadata": {}, "source": [ "

Example 5.6, Page number: 177

" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "import scipy\n", "\n", "#Variable Declaration\n", "\n", "e0=10**-9/(36*scipy.pi) #permittivity of free space in Farad/m\n", "er=2.55 #relative permittivity (dimensionless)\n", "E=10*10**3 #Electric field in V/m\n", "chi=er-1.0 #Electric susceptibility (dimensionless)\n", "d=1.5 #Distance between plates in mm\n", "\n", "#Calculations\n", "\n", "D=e0*er*E*10**9 #D in nC/m^2\n", "\n", "P=chi*e0*E*10**9 #P in nC/m^2\n", "\n", "ps=D #The surface charge density of \n", " #free charge in nC/m^2\n", " \n", "pps =P #The surface charge density of\n", " #polarization charge in nC/m^2\n", " \n", "V=E*d*10**-3 #The potential difference between \n", " #the plates in volts\n", "\n", "#Results\n", "\n", "print 'D =',round(D,2),'nC/m^2'\n", "print 'P =',round(P,0),'nC/m^2'\n", "print 'Surface charge density of free charge =',round(ps,2),'nC/m^2'\n", "print 'Surface charge density of polarization charge =',round(pps,0),'nC/m^2'\n", "print 'The potential difference between the plates =',V,'V'" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "D = 225.47 nC/m^2\n", "P = 137.0 nC/m^2\n", "Surface charge density of free charge = 225.47 nC/m^2\n", "Surface charge density of polarization charge = 137.0 nC/m^2\n", "The potential difference between the plates = 15.0 V\n" ] } ], "prompt_number": 5 }, { "cell_type": "markdown", "metadata": {}, "source": [ "

Example 5.7, Page number: 178

" ] }, { "cell_type": "code", "collapsed": false, "input": [ " \n", "\n", "import scipy\n", "\n", "#Variable Declaration\n", "\n", "e0=10**-9/(36*scipy.pi) #permittivity of free space\n", " #in Farad/m\n", " \n", "er=5.7 #relative permittivity\n", " #(dimensionless)\n", " \n", "chi=er-1 #Electric susceptibility\n", " #(dimensionless)\n", " \n", "r=0.1 #radius of sphere in m\n", "\n", "q1=2 #charge on sphere in pC\n", "\n", "q2=-4 #value of point charge in pC\n", "\n", "#Calculations\n", "\n", "E=q1/(4*scipy.pi*e0*er*r**2) #Electric field on the\n", " #sphere in pV/m\n", " \n", "P=chi*e0*E #Polarisation in pC/m^2\n", "\n", "pps=P #The surface density of polarization \n", " #charge in pC/m^2\n", " \n", "F=(q1*q2*10**-12)/(4*scipy.pi*e0*er*r**2) #Force exerted on point charge in pN\n", "\n", "#Results\n", "\n", "print 'The surface density of polarization'\n", "print 'charge on the surface of the sphere =',round(pps,2),'pC/m^2'\n", "print 'Force exerted on -4 pC charge =',round(F,3),'pN in the radial direction'" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "The surface density of polarization\n", "charge on the surface of the sphere = 13.12 pC/m^2\n", "Force exerted on -4 pC charge = -1.263 pN in the radial direction\n" ] } ], "prompt_number": 6 }, { "cell_type": "markdown", "metadata": {}, "source": [ "

Example 5.9, Page number: 188

" ] }, { "cell_type": "code", "collapsed": false, "input": [ " \n", "#Variable Declarartion\n", "\n", "import scipy\n", "from numpy import *\n", "\n", "an=array([0,0,1]) #Unit vector normal to the interface\n", "E1=array([5,-2,3]) #Electric field for z >=0 in kV/m\n", "e_r1=4 #Relative permittivity for z >=0 (dimensionless)\n", "e_r2=3 #Relative permittivity for z <=0 (dimensionless)\n", "e0=(10**-9)/(36*scipy.pi) #Permittivity of free space in Farad/m\n", "V=2*2*2 #Volume of cube placed in region 2 in m^3\n", "\n", "#Calculations\n", "\n", "E1n=array([0,0,dot(E1,an)]) #The normal component of E1 in kV/m\n", "E1t=E1-E1n #Transverse component of E1 in kV/m\n", "E2t=E1t #Transverse component of E2 in kV/m\n", "E2n=e_r1*E1n/e_r2 #Normal Component of E2 in kV/m\n", "E2=E2n+E2t #The total field E2 in kV/m\n", "\n", "theta1= 90- 180*scipy.arccos(dot(E1,an)/ #Angle between E1 and \n", " scipy.sqrt(dot(E1,E1)))/scipy.pi #interface in degrees\n", " \n", "theta2= 90- 180*scipy.arccos(dot(E2,an)/ #Angle between E2 and \n", " scipy.sqrt(dot(E2,E2)))/scipy.pi #interface in degrees\n", "\n", "\n", "We1= 0.5*e0*e_r1*dot(E1,E1)*10**6 # The energy density of E1 in J/m^3\n", "We2= 0.5*e0*e_r2*dot(E2,E2)*10**6 # The energy density of E2 in J/m^3\n", "W= We2*V # The energy within the cube in J\n", "\n", "#Results\n", "\n", "print 'The electric field for the region z <=0 is',E2,'kV/m'\n", "print 'The angle E1 makes with the boundary is',round(theta1,1),'degrees'\n", "print 'The angle E2 makes with the boundary is',round(theta2,1),'degrees'\n", "print 'The energy density in dielectric 1 is',round(We1*10**6,0),'J/m^3'\n", "print 'The energy density in dielectric 2 is',round(We2*10**6,0),'J/m^3'\n", "print 'The energy within the cube is',round(W*1000,3),'mJ'" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "The electric field for the region z <=0 is [ 5 -2 4] kV/m\n", "The angle E1 makes with the boundary is 29.1 degrees\n", "The angle E2 makes with the boundary is 36.6 degrees\n", "The energy density in dielectric 1 is 672.0 J/m^3\n", "The energy density in dielectric 2 is 597.0 J/m^3\n", "The energy within the cube is 4.775 mJ\n" ] } ], "prompt_number": 7 }, { "cell_type": "markdown", "metadata": {}, "source": [ "

Example 5.10, Page number: 190

" ] }, { "cell_type": "code", "collapsed": false, "input": [ " \n", "import scipy\n", "\n", "#Variable Declaration\n", "\n", "e=(10**-9)/(36*scipy.pi) #Permittivity of free space in Farad/m\n", "er=2 #Relative permittivity (dimensionless)\n", "ps=2 #Surface charge in nC/m^2\n", "\n", "#Calculations\n", "\n", "#Point A is in the region y <=0. Hence E=D=0\n", "#For point B which is in the region y >=0,\n", "\n", "Dn=ps #Displacement current in nC/m^2\n", "En=Dn*10**-9/(e*er) #Electric Field\n", "\n", "#Result\n", "\n", "print 'E at point A= 0'\n", "print 'D at point A= 0'\n", "print 'E at point B=',round(En,2),'V/m along positive y direction'\n", "print 'D at point B=',Dn,'nC/m^2 along positive y direction'" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "E at point A= 0\n", "D at point A= 0\n", "E at point B= 113.1 V/m along positive y direction\n", "D at point B= 2 nC/m^2 along positive y direction\n" ] } ], "prompt_number": 8 } ], "metadata": {} } ] }