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-{
- "metadata": {
- "name": "",
- "signature": "sha256:be254bf95838dd01a87a63582117a886c3167a80cf387f9901b2e2de7a990b8e"
- },
- "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": [
- "\n",
- "\n",
- "#importing modules\n",
- "import math\n",
- "\n",
- "#Variable declaration\n",
- "epsilon_0 = 8.85*10**-12; #Absolute electrical permittivity of free space(F/m)\n",
- "R = 0.52; #Radius of hydrogen atom(A)\n",
- "n = 9.7*10**26; #Number density of hydrogen(per metre cube)\n",
- "\n",
- "#Calculation\n",
- "R = R*10**-10; #Radius of hydrogen atom(m)\n",
- "alpha_e = 4*math.pi*epsilon_0*R**3; #Electronic polarizability of hydrogen atom(Fm**2)\n",
- "\n",
- "#Result\n",
- "print \"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": [
- "\n",
- "\n",
- "#importing modules\n",
- "import math\n",
- "from __future__ import division\n",
- "\n",
- "#Variable declaration\n",
- "epsilon_0 = 8.854*10**-12; #Absolute electrical permittivity of free space(F/m)\n",
- "A = 100; #Area of a plate of parallel plate capacitor(cm**2)\n",
- "d = 1; #Distance between the plates of the capacitor(cm)\n",
- "V = 100; #Potential applied to the plates of the capacitor(V)\n",
- "\n",
- "#Calculation\n",
- "A= A*10**-4; #Area of a plate of parallel plate capacitor(m**2)\n",
- "d = d*10**-2; #Distance between the plates of the capacitor(m)\n",
- "C = epsilon_0*A/d; #Capacitance of parallel plate capacitor(F)\n",
- "Q = C*V; #Charge on the plates of the capacitor(C)\n",
- "\n",
- "#Result\n",
- "print \"The capacitance of parallel plate capacitor is\",C, \"F\"\n",
- "print \"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\n",
- "The 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": [
- "\n",
- "\n",
- "#importing modules\n",
- "import math\n",
- "from __future__ import division\n",
- "\n",
- "#Variable declaration\n",
- "epsilon_0 = 8.854*10**-12; #Absolute electrical permittivity of free space(F/m)\n",
- "epsilon_r = 5.0; #Dielectric constant of the material between the plates of capacitor\n",
- "V = 15; #Potential difference applied between the plates of the capacitor(V)\n",
- "d = 1.5; #Separation between the plates of the capacitor(mm)\n",
- "\n",
- "#Calculation\n",
- "d = 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 \n",
- "D = epsilon_0*epsilon_r*V/d; #Dielectric displacement(C/m**2)\n",
- "\n",
- "#Result\n",
- "print \"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": [
- "\n",
- "#importing modules\n",
- "import math\n",
- "from __future__ import division\n",
- "\n",
- "#Variable declaration\n",
- "epsilon_0 = 8.854*10**-12; #Absolute electrical permittivity of free space(F/m)\n",
- "N = 3*10**28; #Number density of solid elemental dielectric(atoms/metre cube)\n",
- "alpha_e = 10**-40; #Electronic polarizability(Fm**2)\n",
- "\n",
- "#Calculation\n",
- "epsilon_r = 1 + (N*alpha_e/epsilon_0); #Relative dielectric constant of the material\n",
- "epsilon_r = math.ceil(epsilon_r*10**3)/10**3; #rounding off the value of epsilon_r to 3 decimals\n",
- "\n",
- "#Result\n",
- "print \"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": [
- "\n",
- "\n",
- "#importing modules\n",
- "import math\n",
- "from __future__ import division\n",
- "\n",
- "#Variable declaration\n",
- "N_A = 6.02*10**23; #Avogadro's number(per mole)\n",
- "epsilon_0 = 8.854*10**-12; #Absolute electrical permittivity of free space(F/m)\n",
- "epsilon_r = 3.75; #Relative dielectric constant\n",
- "d = 2050; #Density of sulphur(kg/metre cube)\n",
- "y = 1/3; #Internal field constant\n",
- "M = 32; #Atomic weight of sulphur(g/mol)\n",
- "\n",
- "#Calculation\n",
- "N = 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\n",
- "alpha_e = (epsilon_r - 1)/(epsilon_r + 2)*3*epsilon_0/N; #Electronic polarizability of sulphur(Fm**2)\n",
- "\n",
- "#Result\n",
- "print \"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": [
- " \n",
- "import math\n",
- "from __future__ import division\n",
- "\n",
- "#Variable declaration\n",
- "N = 3*10**28; #Number density of atoms of dielectric material(per metre cube)\n",
- "epsilon_0 = 8.854*10**-12; #Absolute electrical permittivity of free space(F/m)\n",
- "n = 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\n",
- "alpha_e = (n**2 - 1)/(n**2 + 2)*3*epsilon_0/N; #Electronic polarizability of dielectric material(Fm**2)\n",
- "\n",
- "#Result\n",
- "print \"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": [
- " \n",
- "#importing modules\n",
- "import math\n",
- "from __future__ import division\n",
- "\n",
- "#Variable declaration\n",
- "epsilon_r = 4.9; #Absolute relative dielectric constant of material(F/m)\n",
- "n = 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\n",
- "alpha_ratio = ((epsilon_r - 1)/(epsilon_r + 2)*(n**2 + 2)/(n**2 - 1) - 1)**(-1); #Ratio of electronic polarizability to ionic polarizability\n",
- "alpha_ratio = math.ceil(alpha_ratio*10**3)/10**3; #rounding off the value of alpha_ratio to 3 decimals\n",
- "\n",
- "#Result\n",
- "print \"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 2025-01-23 16:02:00 +0000