{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"#13: Dielectrics"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"##Example number 13.1, Page number 356"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"The electron polarisation is 3.945 *10**-7 C/m^2\n"
]
}
],
"source": [
"#importing modules\n",
"import math\n",
"from __future__ import division\n",
"\n",
"#Variable declaration\n",
"a=3.61*10**-10; #lattice constant of copper which is Fcc crystal(m)\n",
"x=1*10**-18; #average displacement of the electrons relative to the nucleus(m)\n",
"z=29; #atomic number of copper\n",
"n=4; #number of atoms per unit cell in FCC crystal\n",
"e=1.6*10**-19; #charge of electron(c)\n",
"\n",
"#Calculation\n",
"ne=((n*z)/(a*a*a)); #number of electrons(electrons/m^3) \n",
"P=ne*e*x; #The electron polarisation(C/m^2)\n",
"\n",
"#Result\n",
"print \"The electron polarisation is\",round(P*10**7,3),\"*10**-7 C/m^2\""
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"##Example number 13.2, Page number 356"
]
},
{
"cell_type": "code",
"execution_count": 19,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"The dipole moment of each atom in a field is 1.9646 *10**-35 C m**-3\n",
"The effective distance at this field strength between the centre and the nucleus is 8.77 *10**-18 m\n"
]
}
],
"source": [
"#importing modules\n",
"import math\n",
"from __future__ import division\n",
"\n",
"#Variable declaration\n",
"rp=11.7; #relative permittivity of silicon\n",
"N=4.82*10**28; #number of atoms per unit volume(atoms/m^3)\n",
"ro=8.85*10**-12; #permittivity of free space\n",
"E=10**4; #E(Vm^-1)\n",
"e=1.6*10**-19; #charge of electron(c)\n",
"Z=14; #atomic number of silicon \n",
"\n",
"#Calculation\n",
"z=(ro*(rp-1))/N #electronic polarisability(Fm^2)\n",
"mew=z*E; #The dipole moment of each atom(Cm^-3)\n",
"x=y/(Z*e); #The effective distance at this field strength between the centre and the nucleus(m)\n",
"\n",
"#Result\n",
"print \"The dipole moment of each atom in a field is\",round(y*10**35,4),\"*10**-35 C m**-3\"\n",
"print \"The effective distance at this field strength between the centre and the nucleus is\",round(x*10**18,2),\"*10**-18 m\""
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"##Example number 13.3, Page number 357"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"The electronic polarisability is 1.39 *10**-41 Fm**2\n",
"The relative permittivity in hydrogen gas is 1.0015\n"
]
}
],
"source": [
"#importing modules\n",
"import math\n",
"from __future__ import division\n",
"\n",
"#Variable declaration\n",
"d=9.8*10**26; #density of hydrogen gas(atoms/m^3)\n",
"r=0.50*10**-10; #radius of the hydrogen atom(m)\n",
"ro=8.85*10**-12; #permittivity of free space\n",
"\n",
"#Calculation\n",
"z=(4*math.pi*ro*r**3)/10**-41; #electronic polarisability(Fm^2)\n",
"rp=(((d*z*10**-41)/ro)+1); #The relative permittivity in hydrogen gas\n",
"\n",
"#Result\n",
"print \"The electronic polarisability is\",round(z,2),\"*10**-41 Fm**2\"\n",
"print \"The relative permittivity in hydrogen gas is\",round(rp,4)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"##Example number 13.4, Page number 357"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"The static dielectric constant of solid argon is 1.53679\n"
]
}
],
"source": [
"#importing modules\n",
"import math\n",
"from __future__ import division\n",
"\n",
"#Variable declaration\n",
"z=1.75*10**-40; #electronic polarisability(Fm^2)\n",
"d=1.8*10**3; #density of argon atom(Kg/m^3)\n",
"Z=39.95; #atomic weight of argon\n",
"NA=6.025*10**26; #Avagadro number(mole^-1)\n",
"ro=8.85*10**-12; #permittivity of free space\n",
"\n",
"#Calculation\n",
"N=((NA*d)/Z); #The number of atoms/unit volume(atoms/m^3) \n",
"rp=(((N*z)/ro)+1); #The static dielectric constant of solid argon\n",
"\n",
"#Result\n",
"print \"The static dielectric constant of solid argon is\",round(rp,5)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"##Example number 13.5, Page number 366"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Ratio between electronic and ionic polarisability of this material is 1.7376\n"
]
}
],
"source": [
"#importing modules\n",
"import math\n",
"from __future__ import division\n",
"\n",
"#Variable declaration\n",
"er=4.94; #static dielecric constant of a material\n",
"n=2.69; #index of friction\n",
"\n",
"#Calculation\n",
"x=((er-1)*(n+2))/((er+2)*(n-1))-1; #Ratio between ionic and electronic polarisability of this material\n",
"y=1/x; #Ratio between electronic and ionic polarisability of this material\n",
"\n",
"#Result\n",
"print \"Ratio between electronic and ionic polarisability of this material is\",round(y,4)"
]
}
],
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