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+{
+ "metadata": {
+ "name": "Chapter13"
+ },
+ "nbformat": 3,
+ "nbformat_minor": 0,
+ "worksheets": [
+ {
+ "cells": [
+ {
+ "cell_type": "heading",
+ "level": 1,
+ "metadata": {},
+ "source": "13: Dielectric Properties of Materials"
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": "Example number 13.1, Page number 287"
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": "#To calculate the electronic polarizability \n\n#importing modules\nimport math\n\n#Variable declaration\nepsilon_0 = 8.85*10**-12; #Absolute electrical permittivity of free space(F/m)\nR = 0.52; #Radius of hydrogen atom(A)\nn = 9.7*10**26; #Number density of hydrogen(per metre cube)\n\n#Calculation\nR = R*10**-10; #Radius of hydrogen atom(m)\nalpha_e = 4*math.pi*epsilon_0*R**3; #Electronic polarizability of hydrogen atom(Fm**2)\n\n#Result\nprint \"The electronic polarizability of hydrogen atom is\", alpha_e, \"Fm**2\"",
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": "The electronic polarizability of hydrogen atom is 1.56373503182e-41 Fm**2\n"
+ }
+ ],
+ "prompt_number": 1
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": "Example number 13.2, Page number 287"
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": "#To calculate the capacitance of capacitor and charge on the plates\n\n#importing modules\nimport math\nfrom __future__ import division\n\n#Variable declaration\nepsilon_0 = 8.854*10**-12; #Absolute electrical permittivity of free space(F/m)\nA = 100; #Area of a plate of parallel plate capacitor(cm**2)\nd = 1; #Distance between the plates of the capacitor(cm)\nV = 100; #Potential applied to the plates of the capacitor(V)\n\n#Calculation\nA= A*10**-4; #Area of a plate of parallel plate capacitor(m**2)\nd = d*10**-2; #Distance between the plates of the capacitor(m)\nC = epsilon_0*A/d; #Capacitance of parallel plate capacitor(F)\nQ = C*V; #Charge on the plates of the capacitor(C)\n\n#Result\nprint \"The capacitance of parallel plate capacitor is\",C, \"F\"\nprint \"The charge on the plates of the capacitor is\",Q, \"C\"\n",
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": "The capacitance of parallel plate capacitor is 8.854e-12 F\nThe charge on the plates of the capacitor is 8.854e-10 C\n"
+ }
+ ],
+ "prompt_number": 2
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": "Example number 13.3, Page number 288"
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": "#To calculate the dielectric displacement\n\n#importing modules\nimport math\nfrom __future__ import division\n\n#Variable declaration\nepsilon_0 = 8.854*10**-12; #Absolute electrical permittivity of free space(F/m)\nepsilon_r = 5.0; #Dielectric constant of the material between the plates of capacitor\nV = 15; #Potential difference applied between the plates of the capacitor(V)\nd = 1.5; #Separation between the plates of the capacitor(mm)\n\n#Calculation\nd = d*10**-3; #Separation between the plates of the capacitor(m)\n#Electric displacement, D = epsilon_0*epsilon_r*E, as E = V/d, so \nD = epsilon_0*epsilon_r*V/d; #Dielectric displacement(C/m**2)\n\n#Result\nprint \"The dielectric displacement is\",D, \"C/m**2\"",
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": "The dielectric displacement is 4.427e-07 C/m**2\n"
+ }
+ ],
+ "prompt_number": 3
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": "Example number 13.4, Page number 288"
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": "#To calculate the relative dielectric constant\n\n#importing modules\nimport math\nfrom __future__ import division\n\n#Variable declaration\nepsilon_0 = 8.854*10**-12; #Absolute electrical permittivity of free space(F/m)\nN = 3*10**28; #Number density of solid elemental dielectric(atoms/metre cube)\nalpha_e = 10**-40; #Electronic polarizability(Fm**2)\n\n#Calculation\nepsilon_r = 1 + (N*alpha_e/epsilon_0); #Relative dielectric constant of the material\nepsilon_r = math.ceil(epsilon_r*10**3)/10**3; #rounding off the value of epsilon_r to 3 decimals\n\n#Result\nprint \"The Relative dielectric constant of the material is\",epsilon_r\n",
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": "The Relative dielectric constant of the material is 1.339\n"
+ }
+ ],
+ "prompt_number": 5
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": "Example number 13.5, Page number 288"
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": "#To calculate the electronic polarizability\n\n#importing modules\nimport math\nfrom __future__ import division\n\n#Variable declaration\nN_A = 6.02*10**23; #Avogadro's number(per mole)\nepsilon_0 = 8.854*10**-12; #Absolute electrical permittivity of free space(F/m)\nepsilon_r = 3.75; #Relative dielectric constant\nd = 2050; #Density of sulphur(kg/metre cube)\ny = 1/3; #Internal field constant\nM = 32; #Atomic weight of sulphur(g/mol)\n\n#Calculation\nN = N_A*10**3*d/M; #Number density of atoms of sulphur(per metre cube)\n#Lorentz relation for local fields give E_local = E + P/(3*epsilon_0) which gives\n#(epsilon_r - 1)/(epsilon_r + 2) = N*alpha_e/(3*epsilon_0), solving for alpha_e\nalpha_e = (epsilon_r - 1)/(epsilon_r + 2)*3*epsilon_0/N; #Electronic polarizability of sulphur(Fm**2)\n\n#Result\nprint \"The electronic polarizability of sulphur is\",alpha_e, \"Fm**2\"",
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": "The electronic polarizability of sulphur is 3.2940125351e-40 Fm**2\n"
+ }
+ ],
+ "prompt_number": 6
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": "Example number 13.6, Page number 289"
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": "#To calculate the electronic polarizability\n\n#importing modules\nimport math\nfrom __future__ import division\n\n#Variable declaration\nN = 3*10**28; #Number density of atoms of dielectric material(per metre cube)\nepsilon_0 = 8.854*10**-12; #Absolute electrical permittivity of free space(F/m)\nn = 1.6; #Refractive index of dielectric material\n\n#Calculation\n#As (n^2 - 1)/(n^2 + 2) = N*alpha_e/(3*epsilon_0), solving for alpha_e\nalpha_e = (n**2 - 1)/(n**2 + 2)*3*epsilon_0/N; #Electronic polarizability of dielectric material(Fm**2)\n\n#Result\nprint \"The electronic polarizability of dielectric material is\",alpha_e, \"Fm**2\"",
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": "The electronic polarizability of dielectric material is 3.029e-40 Fm**2\n"
+ }
+ ],
+ "prompt_number": 8
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": "Example number 13.7, Page number 289"
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": "#To calculate the ratio of electronic polarizability to ionic polarizability\n\n#importing modules\nimport math\nfrom __future__ import division\n\n#Variable declaration\nepsilon_r = 4.9; #Absolute relative dielectric constant of material(F/m)\nn = 1.6; #Refractive index of dielectric material\n\n#Calculation\n#As (n^2 - 1)/(n^2 + 2)*(alpha_e + alpha_i)/alpha_e = N*(alpha_e + alpha_i)/(3*epsilon_0) = (epsilon_r - 1)/(epsilon_r + 2)\n#let alpha_ratio = alpha_i/alpha_e\nalpha_ratio = ((epsilon_r - 1)/(epsilon_r + 2)*(n**2 + 2)/(n**2 - 1) - 1)**(-1); #Ratio of electronic polarizability to ionic polarizability\nalpha_ratio = math.ceil(alpha_ratio*10**3)/10**3; #rounding off the value of alpha_ratio to 3 decimals\n\n#Result\nprint \"The ratio of electronic polarizability to ionic polarizability is\",alpha_ratio",
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": "The ratio of electronic polarizability to ionic polarizability is 1.534\n"
+ }
+ ],
+ "prompt_number": 9
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": "",
+ "language": "python",
+ "metadata": {},
+ "outputs": []
+ }
+ ],
+ "metadata": {}
+ }
+ ]
+} \ No newline at end of file
generated by cgit (git 2.34.1) at 2024-12-20 10:38:12 +0000