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
R=0.12*10**-9;   #atomic radius of Se(m)
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
R=0.384*10**-9;   #radius of Ar(m)
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