# 21: Dielectric Materials¶

## Example number 21.1, Page number 27¶

In [8]:
#importing modules
import math
from __future__ import division

#Variable declaration
a=0.629*10**-9;   #lattice parameter(m)
alphaeK=1.26*10**-40;   #electronic polarizability for K+(F/m**2)
alphaeCl=3.408*10**-40;   #electronic polarizability for Cl-(F/m**2)
n=4;   #number of atoms
epsilon0=8.854*10**-12;

#Calculation
alphae=alphaeK+alphaeCl;   #electronic polarizability for KCl(F/m**2)
N=n/(a**3);   #number of dipoles(atoms/m**3)
epsilonr=(N*alphae/epsilon0)+1;   #dielectric constant of KCl

#Result
print "dielectric constant of KCl is",round(epsilonr,4)

dielectric constant of KCl is 1.8474


## Example number 21.2, Page number 27¶

In [12]:
#importing modules
import math
from __future__ import division

#Variable declaration
epsilon0=8.854*10**-12;

#Calculation
alphae=4*math.pi*epsilon0*(R**3);   #electronic polarizability of isolated Se(F/m**2)

#Result
print "electronic polarizability of isolated Se is",round(alphae*10**40,4),"*10**-40 F/m**2"

electronic polarizability of isolated Se is 1.9226 *10**-40 F/m**2


## Example number 21.3, Page number 28¶

In [1]:
#importing modules
import math
from __future__ import division

#Variable declaration
alphae=0.35*10**-40;   #electronic polarizability(F/m**2)
N=2.7*10**25;   #number of atoms(atoms/m**3)
epsilon0=8.854*10**-12;

#Calculation
a=N*alphae/(3*epsilon0);
epsilonr=(1+(2*a))/(1-a);   #dielectric constant of Ne

#Result
print "dielectric constant of Ne is",round(epsilonr,9)

dielectric constant of Ne is 1.000106735


## Example number 21.4, Page number 28¶

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

#Variable declaration
N=2.7*10**25;   #number of atoms(atoms/m**3)
epsilon0=8.854*10**-12;

#Calculation
alphae=4*math.pi*epsilon0*(R**3);   #electronic polarizability of Ar(F/m**2)
a=N*alphae/(3*epsilon0);
epsilonr=(1+(2*a))/(1-a);   #dielectric constant of Ar

#Result
print "dielectric constant of Ar is",epsilonr
print "answer given in the book is wrong"

dielectric constant of Ar is 1.01933559019
answer given in the book is wrong


## Example number 21.5, Page number 29¶

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

#Variable declaration
C=2*10**-6;    #capacitance(F)
epsilonr=80;   #permitivity of dielectric
V=1*10**3;    #applied voltage(V)

#Calculation
E1=(1/2)*C*V**2;   #energy stored in capacitor(J)
C0=C/epsilonr;   #capacitance when dielectric is removed(F)
E2=(1/2)*C0*V**2;   #energy stored in capacitor with vacuum as dielectric(J)
E=1-E2;   #energy stored in capacitor in polarizing the dielectric(J)

#Result
print "energy stored in capacitor is",E1,"J"
print "energy stored in capacitor in polarizing the dielectric is",E,"J"

energy stored in capacitor is 1.0 J
energy stored in capacitor in polarizing the dielectric is 0.9875 J


## Example number 21.6, Page number 30¶

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

#Variable declaration
N=5*10**28;    #number of atoms(per m**3)
alpha=2*10**-40;   #polarizability(Fm**2)
epsilon0=8.854*10**-12;

#Calculation
P=N*alpha;
a=1-(P/(3*epsilon0));
EibyE=1/a;     #ratio of internal field to applied field

#Result
print "ratio of internal field to applied field is",round(EibyE,4)

ratio of internal field to applied field is 1.6038