{
"metadata": {
"name": "",
"signature": "sha256:dd76b185872085137646ef650e27e3207f4aa1a0d590f7c3a0d53ab66156e953"
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"worksheets": [
{
"cells": [
{
"cell_type": "heading",
"level": 1,
"metadata": {},
"source": [
"21: Dielectric Materials"
]
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example number 21.1, Page number 27"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#importing modules\n",
"import math\n",
"from __future__ import division\n",
"\n",
"#Variable declaration\n",
"a=0.629*10**-9; #lattice parameter(m)\n",
"alphaeK=1.26*10**-40; #electronic polarizability for K+(F/m**2)\n",
"alphaeCl=3.408*10**-40; #electronic polarizability for Cl-(F/m**2)\n",
"n=4; #number of atoms\n",
"epsilon0=8.854*10**-12;\n",
"\n",
"#Calculation\n",
"alphae=alphaeK+alphaeCl; #electronic polarizability for KCl(F/m**2)\n",
"N=n/(a**3); #number of dipoles(atoms/m**3)\n",
"epsilonr=(N*alphae/epsilon0)+1; #dielectric constant of KCl\n",
"\n",
"#Result\n",
"print \"dielectric constant of KCl is\",round(epsilonr,4)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"dielectric constant of KCl is 1.8474\n"
]
}
],
"prompt_number": 8
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example number 21.2, Page number 27"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#importing modules\n",
"import math\n",
"from __future__ import division\n",
"\n",
"#Variable declaration\n",
"R=0.12*10**-9; #atomic radius of Se(m)\n",
"epsilon0=8.854*10**-12;\n",
"\n",
"#Calculation\n",
"alphae=4*math.pi*epsilon0*(R**3); #electronic polarizability of isolated Se(F/m**2)\n",
"\n",
"#Result\n",
"print \"electronic polarizability of isolated Se is\",round(alphae*10**40,4),\"*10**-40 F/m**2\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"electronic polarizability of isolated Se is 1.9226 *10**-40 F/m**2\n"
]
}
],
"prompt_number": 12
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example number 21.3, Page number 28"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#importing modules\n",
"import math\n",
"from __future__ import division\n",
"\n",
"#Variable declaration\n",
"alphae=0.35*10**-40; #electronic polarizability(F/m**2)\n",
"N=2.7*10**25; #number of atoms(atoms/m**3)\n",
"epsilon0=8.854*10**-12;\n",
"\n",
"#Calculation\n",
"a=N*alphae/(3*epsilon0);\n",
"epsilonr=(1+(2*a))/(1-a); #dielectric constant of Ne\n",
"\n",
"#Result\n",
"print \"dielectric constant of Ne is\",round(epsilonr,9)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"dielectric constant of Ne is 1.000106735\n"
]
}
],
"prompt_number": 1
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example number 21.4, Page number 28"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#importing modules\n",
"import math\n",
"from __future__ import division\n",
"\n",
"#Variable declaration\n",
"R=0.384*10**-9; #radius of Ar(m)\n",
"N=2.7*10**25; #number of atoms(atoms/m**3)\n",
"epsilon0=8.854*10**-12;\n",
"\n",
"#Calculation\n",
"alphae=4*math.pi*epsilon0*(R**3); #electronic polarizability of Ar(F/m**2)\n",
"a=N*alphae/(3*epsilon0);\n",
"epsilonr=(1+(2*a))/(1-a); #dielectric constant of Ar\n",
"\n",
"#Result\n",
"print \"dielectric constant of Ar is\",epsilonr\n",
"print \"answer given in the book is wrong\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"dielectric constant of Ar is 1.01933559019\n",
"answer given in the book is wrong\n"
]
}
],
"prompt_number": 2
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example number 21.5, Page number 29"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#importing modules\n",
"import math\n",
"from __future__ import division\n",
"\n",
"#Variable declaration\n",
"C=2*10**-6; #capacitance(F)\n",
"epsilonr=80; #permitivity of dielectric\n",
"V=1*10**3; #applied voltage(V)\n",
"\n",
"#Calculation\n",
"E1=(1/2)*C*V**2; #energy stored in capacitor(J)\n",
"C0=C/epsilonr; #capacitance when dielectric is removed(F)\n",
"E2=(1/2)*C0*V**2; #energy stored in capacitor with vacuum as dielectric(J)\n",
"E=1-E2; #energy stored in capacitor in polarizing the dielectric(J)\n",
"\n",
"#Result\n",
"print \"energy stored in capacitor is\",E1,\"J\"\n",
"print \"energy stored in capacitor in polarizing the dielectric is\",E,\"J\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"energy stored in capacitor is 1.0 J\n",
"energy stored in capacitor in polarizing the dielectric is 0.9875 J\n"
]
}
],
"prompt_number": 3
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example number 21.6, Page number 30"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#importing modules\n",
"import math\n",
"from __future__ import division\n",
"\n",
"#Variable declaration\n",
"N=5*10**28; #number of atoms(per m**3)\n",
"alpha=2*10**-40; #polarizability(Fm**2)\n",
"epsilon0=8.854*10**-12;\n",
"\n",
"#Calculation\n",
"P=N*alpha;\n",
"a=1-(P/(3*epsilon0));\n",
"EibyE=1/a; #ratio of internal field to applied field\n",
"\n",
"#Result\n",
"print \"ratio of internal field to applied field is\",round(EibyE,4)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"ratio of internal field to applied field is 1.6038\n"
]
}
],
"prompt_number": 5
}
],
"metadata": {}
}
]
}