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diff --git a/Applied_Physics_for_Engineers/Chapter_13.ipynb b/Applied_Physics_for_Engineers/Chapter_13.ipynb new file mode 100755 index 00000000..0622b390 --- /dev/null +++ b/Applied_Physics_for_Engineers/Chapter_13.ipynb @@ -0,0 +1,492 @@ +{ + "metadata": { + "name": "" + }, + "nbformat": 3, + "nbformat_minor": 0, + "worksheets": [ + { + "cells": [ + { + "cell_type": "heading", + "level": 1, + "metadata": {}, + "source": [ + "Chapter 13: Dielectric Properties of Materials" + ] + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 13.1, Page 648" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import *\n", + "from scipy import integrate\n", + "\n", + "#Variable declaration\n", + "q = 1e-006; # Electric charge on either side of the dipole, C\n", + "l = 2e-02; # Dipole length, m\n", + "p = q*l; # Dipole moment for the pair of opposite charges, C-m\n", + "E = 1e+005; # External electric field, N/C\n", + "theta = 90; # Angle which the dipole makes with the external field, degrees\n", + "\n", + "#Calculations&Results\n", + "tau = p*E*sin(theta); # The maximum torque on dipole placed in external electric field, Nm\n", + "print \"The maximum torque = %1.0e N-m\"%tau\n", + "W = p*E*(cos(0)-cos(180*pi/180))\n", + "#W = integrate('p*E*sin(thet)', 'thet', 0, pi); # The work done in rotating the dipole direction = %1.0e J\", W\n", + "print \"The work done in rotating the dipole direction = %1.0e J\"%W\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The maximum torque = 2e-03 N-m\n", + "The work done in rotating the dipole direction = 4e-03 J\n" + ] + } + ], + "prompt_number": 30 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 13.2, Page 648" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import *\n", + "\n", + "#Variable declaration\n", + "Q = 8e-019; # Charge of the nucleus, C\n", + "p = 3.2e-029; # Electric dipole moment, C-m\n", + "r = 1e-10; # Distance of dipole relative to the nucleus, m\n", + "k = 9e+9; # Coulomb constant, N-meter-square/C-square\n", + "theta = 0; # Angle for radial direction, radian \n", + "\n", + "#Calculations&Results\n", + "F = k*p*Q*sqrt(3*cos(theta**2)+1)/r**3; # The force acting on the dipole in the radial direction, N\n", + "print \"The force acting on the dipole in the radial direction = %3.1e N\"%F\n", + "theta = pi/2; # Angle for perpendicular direction, radian\n", + "F = k*p*Q*sqrt(3*cos(theta)**2+1)/r**3;\n", + "print \"The force acting on the dipole in the direction perpendicular to radial direction = %3.1e N\"%F\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The force acting on the dipole in the radial direction = 4.6e-07 N\n", + "The force acting on the dipole in the direction perpendicular to radial direction = 2.3e-07 N\n" + ] + } + ], + "prompt_number": 2 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 13.3, Page 649" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#Variable declaration\n", + "chi_e = 35.4e-12; # Susceptability of the material, C-square/N-meter-square\n", + "eps_0 = 8.85e-12; # Electric permittivity in free space, C-squre/N-meter-square\n", + "\n", + "#Calculations&Results\n", + "K = 1 + (chi_e/eps_0);\n", + "print \"The dielectric constant = %d \"%K\n", + "eps = (eps_0*K); \n", + "print \"The electric permittivity = %5.3e C-square/N-meter square \"%eps\n", + "\n", + " " + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The dielectric constant = 5 \n", + "The electric permittivity = 4.425e-11 C-square/N-meter square \n" + ] + } + ], + "prompt_number": 3 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 13.4, Page 649" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#Variable declaration\n", + "eps = 1.46e-10; # Electric permittivity, C-square/n-meter-square\n", + "eps_0 = 8.85e-12; # Permittivity in free space, C-squre/N-meter-square\n", + "\n", + "#Calculations&Results\n", + "K = (eps/eps_0);\n", + "print \"The dielectric constant = %4.1f \"%K\n", + "chi_e = eps_0*(K-1); # Susceptability,in C-square/N-meter-square\n", + "print \"The electric susceptability = %4.2e C-square/N-meter square \"%chi_e\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The dielectric constant = 16.5 \n", + "The electric susceptability = 1.37e-10 C-square/N-meter square \n" + ] + } + ], + "prompt_number": 4 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 13.5, Page 650" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#Variable declaration\n", + "K = 7.0; # Dielectric constant of the slab\n", + "d = 0.01; # Distance between the two parallel plates, m\n", + "V_0 = 100; # Potential difference across the plates, V\n", + "eps_0 = 8.85e-12; # Electric permability of the free space, C-square/N-meter-square\n", + "\n", + "#Calculations&Results\n", + "E_0 = V_0/d; # Electric intensity in the absence of dielectric slab, V/m\n", + "E = E_0/K; # Electric intensity with dielectric slab introduced between the plates, V/m\n", + "print \"The electric field intensity in the presence of the dielectric slab = %4.2e V/m \"%E\n", + "D = (eps_0*K*E); # Electric displacement, C-square/m-square\n", + "print \"The electric displacement in the dielectric slab = %4.2e C-square/meter-square \"%D\n", + "P = eps_0*(K-1)*E; # Electric polarization in the dielectric slab, C-square/m-square\n", + "print \"The electric polarization in the dielectric slab = %3.1e C-square/meter-square \"%P\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The electric field intensity in the presence of the dielectric slab = 1.43e+03 V/m \n", + "The electric displacement in the dielectric slab = 8.85e-08 C-square/meter-square \n", + "The electric polarization in the dielectric slab = 7.6e-08 C-square/meter-square \n" + ] + } + ], + "prompt_number": 5 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 13.6, Page 650" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#Variable declaration\n", + "K = 1.000074; # Dielectric constant of the He\n", + "n = 2.69e+025; # Atomic density of He, atoms/meter-cube\n", + "eps_0 = 8.85e-012; # Electric permability of the free space, C-square/N-meter-square\n", + "E = 1; # Electric field strength, V/m\n", + "\n", + "#Calculations\n", + "p = (eps_0*(K-1)*E)/n; # Dipole moment induced in He, C-m\n", + "\n", + "#Result\n", + "print \"The dipole moment induced in each He atom = %4.2e C-m \"%p\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The dipole moment induced in each He atom = 2.43e-41 C-m \n" + ] + } + ], + "prompt_number": 6 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 13.7, Page 650" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#Variable declaration\n", + "K = 1.000134; # Dielectric constant of the neon\n", + "n = 2.69e+25; # Atomic density of argon,atoms/meter-cube\n", + "eps_0 = 8.85e-12; # Electric Permability in the free space, C-square/N-meter-square\n", + "E = 90e+03; # External electric field, V/m\n", + "\n", + "#Calculations\n", + "p = eps_0*(K-1)*E/n; # Dipole moment induced in each neon atom, C-m\n", + "alpha = p/E; # Atomic polarizability of neon gas, C-metre-square/V\n", + "\n", + "#Results\n", + "print \"The induced dipole moment of noen atom = %4.2e C-m\"%p\n", + "print \"The electronic polarizability of neon gas = %3.1e C-m-square/V \"%alpha\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The induced dipole moment of noen atom = 3.97e-36 C-m\n", + "The electronic polarizability of neon gas = 4.4e-41 C-m-square/V \n" + ] + } + ], + "prompt_number": 7 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 13.8, Page 651" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#Variable declaration\n", + "K = 1.0024; # Dielectric constant of the argon\n", + "n = 2.7e+25; # Atomic density of argon,atoms/meter-cube\n", + "eps_0 = 8.85e-12; # Electric Permability in the free space, C-square/N-meter-square\n", + "\n", + "#Calculations\n", + "alpha = eps_0*(K-1)/n;\n", + "\n", + "#Result\n", + "print \"The electronic polarizability of argon atom = %4.1e C-m-square/V \"%alpha\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The electronic polarizability of argon atom = 7.9e-40 C-m-square/V \n" + ] + } + ], + "prompt_number": 8 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 13.9, Page 651" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#Variable declaration\n", + "K = 2.24; # Dielectric constant \n", + "eps_0 = 8.85e-12; # Electric permability in the free space, C-square/N-meter-square\n", + "rho = 1.6e+003; # Density of CCl4, kg/meter-cube\n", + "M = 156; # Molecular weight of CCl4\n", + "E = 1e+007; # External electric field strength, V/m\n", + "N_A = 6.02e+26; # Avogadro's number, per kmol\n", + "\n", + "#Calculations\n", + "rho_M = rho*N_A/M; # Molecular density of CCl4\n", + "p = eps_0*(K-1)*E/rho_M; # Individual dipole moment of CCL4 molecule, C-m\n", + "\n", + "#Result\n", + "print \"Individual dipole moment of CCL4 molecule = %4.2e C-m \"%p\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Individual dipole moment of CCL4 molecule = 1.78e-32 C-m \n" + ] + } + ], + "prompt_number": 9 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 13.10, Page 652" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import *\n", + "\n", + "#Variable declaration\n", + "K = 1.0000684; # Dielectric constant of He at 1 atm\n", + "n = 2.7e+25; # Density of He at 1 atm and 273 K, atoms/meter-cube\n", + "\n", + "#Calculations\n", + "# The atomic polarizibility, alpha = eps_0*(K-1)/n \n", + "# In terms of atomic radius, alpha = 4*%pi*eps_0*R^3 so, we have\n", + "R = ((K-1)/(4*pi*n))**(1./3); # Radius of He atom, m\n", + "\n", + "#Result\n", + "print \"The atomic radius of He = %4.2e m \"%R\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The atomic radius of He = 5.86e-11 m \n" + ] + } + ], + "prompt_number": 11 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 13.11, Page 652" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#Variable declaration\n", + "mu = 1.5; # Optical index of refraction of NaCl crystal\n", + "K = 5.6; # Static dielectric constant of NaCl crystal\n", + "\n", + "#Calculations\n", + "P_IP = (1-((mu**2-1)*(K+2))/((mu**2+2)*(K-1)))*100;\n", + "\n", + "#Result\n", + "print \"The percentage of ionic polarizibility in NaCl crystal = %4.1f percent \"%P_IP\n", + "\n", + "\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The percentage of ionic polarizibility in NaCl crystal = 51.4 percent \n" + ] + } + ], + "prompt_number": 12 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 13.12, Page 653" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import *\n", + "\n", + "#Variable declaration\n", + "K_B = 1.38e-23; # Boltzmann constant, J/mol/K\n", + "T = 300; # Room temperature, K \n", + "eps_0 = 8.85e-12; # Electric permittivity of free space, F/m\n", + "N_A = 6.0e+23; # Avogadro's number\n", + "\n", + "#Calculations\n", + "n2 = N_A*1000; # Number of molecules of non-polar substance in 1000 cc volume\n", + "p_0 = sqrt((9*K_B*T*eps_0*0.023)/n2); # Dipole moment of polar molecules, C-m\n", + "\n", + "#Result\n", + "print \"The dipole moment of polar molecules = %4.3e C-m\"%p_0\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The dipole moment of polar molecules = 3.555e-30 C-m\n" + ] + } + ], + "prompt_number": 31 + } + ], + "metadata": {} + } + ] +}
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