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{
"metadata": {
"name": "",
"signature": "sha256:23fe0a698ddd73a9b73b082e06aebc62f797877523bf19c5324fc5a8330a2aa8"
},
"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",
"#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",
"\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",
"#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",
"#importing modules\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",
"\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": {}
}
]
}
|
