13: Dielectrics

Example number 13.1, Page number 356

In [2]:
#importing modules
import math
from __future__ import division

#Variable declaration
a=3.61*10**-10;    #lattice constant of copper which is Fcc crystal(m)
x=1*10**-18;     #average displacement of the electrons relative to the nucleus(m)
z=29;     #atomic number of copper
n=4;      #number of atoms per unit cell in FCC crystal
e=1.6*10**-19;    #charge of electron(c)

#Calculation
ne=((n*z)/(a*a*a));     #number of electrons(electrons/m^3) 
P=ne*e*x;    #The electron polarisation(C/m^2)

#Result
print "The electron polarisation is",round(P*10**7,3),"*10**-7 C/m^2"

The electron polarisation is 3.945 *10**-7 C/m^2

Example number 13.2, Page number 356

In [19]:
#importing modules
import math
from __future__ import division

#Variable declaration
rp=11.7;   #relative permittivity of silicon
N=4.82*10**28;   #number of atoms per unit volume(atoms/m^3)
ro=8.85*10**-12;   #permittivity of free space
E=10**4;    #E(Vm^-1)
e=1.6*10**-19;   #charge of electron(c)
Z=14;     #atomic number of silicon 

#Calculation
z=(ro*(rp-1))/N     #electronic polarisability(Fm^2)
mew=z*E;       #The dipole moment of each atom(Cm^-3)
x=y/(Z*e);   #The effective distance at this field strength between the centre and the nucleus(m)

#Result
print "The dipole moment of each atom in a field is",round(y*10**35,4),"*10**-35 C m**-3"
print "The effective distance at this field strength between the centre and the nucleus is",round(x*10**18,2),"*10**-18 m"

The dipole moment of each atom in a field is 1.9646 *10**-35 C m**-3
The effective distance at this field strength between the centre and the nucleus is 8.77 *10**-18 m

Example number 13.3, Page number 357

In [3]:
#importing modules
import math
from __future__ import division

#Variable declaration
d=9.8*10**26;    #density of hydrogen gas(atoms/m^3)
r=0.50*10**-10;   #radius of the hydrogen atom(m)
ro=8.85*10**-12;   #permittivity of free space

#Calculation
z=(4*math.pi*ro*r**3)/10**-41;    #electronic polarisability(Fm^2)
rp=(((d*z*10**-41)/ro)+1);        #The relative permittivity in hydrogen gas

#Result
print "The electronic polarisability is",round(z,2),"*10**-41 Fm**2"
print "The relative permittivity in hydrogen gas is",round(rp,4)

The electronic polarisability is 1.39 *10**-41 Fm**2
The relative permittivity in hydrogen gas is 1.0015

Example number 13.4, Page number 357

In [5]:
#importing modules
import math
from __future__ import division

#Variable declaration
z=1.75*10**-40;    #electronic polarisability(Fm^2)
d=1.8*10**3;   #density of argon atom(Kg/m^3)
Z=39.95;    #atomic weight of argon
NA=6.025*10**26;    #Avagadro number(mole^-1)
ro=8.85*10**-12;    #permittivity of free space

#Calculation
N=((NA*d)/Z);     #The number of atoms/unit volume(atoms/m^3) 
rp=(((N*z)/ro)+1);    #The static dielectric constant of solid argon

#Result
print "The static dielectric constant of solid argon is",round(rp,5)

The static dielectric constant of solid argon is 1.53679

Example number 13.5, Page number 366

In [7]:
#importing modules
import math
from __future__ import division

#Variable declaration
er=4.94;   #static dielecric constant of a material
n=2.69;    #index of friction

#Calculation
x=((er-1)*(n+2))/((er+2)*(n-1))-1;     #Ratio between ionic and electronic polarisability of this material
y=1/x;      #Ratio between electronic and ionic polarisability of this material

#Result
print "Ratio between electronic and ionic polarisability of this material is",round(y,4)

Ratio between electronic and ionic polarisability of this material is 1.7376