6: Dielectric Properties

Example number 1, Page number 6-23

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

#Variable declaration
alpha_e=10**-40;     #polarisability(Fm**2)
N=3*10**28;          #density of atoms
epsilon0=8.85*10**-12;    

#Calculation
epsilonr=(N*alpha_e/epsilon0)+1;     #dielectric constant

#Result
print "dielectric constant is",round(epsilonr,3)

dielectric constant is 1.339

Example number 2, Page number 6-24

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

#Variable declaration
A=100*10**-4;      #area(m**2)
epsilon0=8.85*10**-12;    
d=1*10**-2;     #seperation(m)
V=100;     #potential(V)

#Calculation
C=A*epsilon0/d;     #capacitance(PF)
Q=C*V;         #charge on plates(C)

#Result
print "capacitance is",C,"F"
print "charge on plates is",Q,"C"

capacitance is 8.85e-12 F
charge on plates is 8.85e-10 C

Example number 3, Page number 6-24

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

#Variable declaration
epsilonr=1.0000684;     #dielectric constant
N=2.7*10**25;   #number of atoms
epsilon0=8.85*10**-12;    

#Calculation
alpha_e=epsilon0*(epsilonr-1)/N;    #polarisability(Fm**2)

#Result
print "polarisability is",alpha_e,"Fm**2"

polarisability is 2.242e-41 Fm**2

Example number 4, Page number 6-24

In [10]:
#importing modules
import math
from __future__ import division

#Variable declaration
A=650*10**-6;      #area(m**2)
epsilon0=8.85*10**-12;    
d=4*10**-3;     #seperation(m)
Q=2*10**-10;    #charge(C)
epsilonr=3.5;   #dielectric constant

#Calculation  
V=Q*d/(epsilon0*epsilonr*A);    #voltage(V)

#Result
print "voltage is",round(V,2),"V"

voltage is 39.73 V

Example number 5, Page number 6-25

In [13]:
#importing modules
import math
from __future__ import division

#Variable declaration
epsilonr=5;     #relative permittivity
V=12;           #potential(V)
d=2*10**-3;     #separation(m) 
epsilon0=8.85*10**-12;    

#Calculation
P=epsilon0*(epsilonr-1)*V/d;     #polarisation(C-m)

#Result
print "polarisation is",P*10**9,"*10**-9 C-m"

polarisation is 212.4 *10**-9 C-m

Example number 6, Page number 6-25

In [16]:
#importing modules
import math
from __future__ import division

#Variable declaration
epsilonr=3.75;       #relative dielectric constant
gama=1/3;     #internal field constant
D=2050;       #density(kg/m**3)
M=32;         #atomic weight(amu)
Na=6.02*10**26;     #avagadro number
epsilon0=8.85*10**-12;    

#Calculation
N=Na*D/M;     #number of atoms per m**3
x=(epsilonr-1)/(epsilonr+2);
alpha_e=x*3*epsilon0/N;     #electronic polarisability(F-m**2)

#Result
print "electronic polarisability is",round(alpha_e*10**40,2),"*10**-40 Fm**2"
print "answer in the book varies due to rounding off errors"

electronic polarisability is 3.29 *10**-40 Fm**2
answer in the book varies due to rounding off errors

Example number 7, Page number 6-26

In [18]:
#importing modules
import math
from __future__ import division

#Variable declaration
e=1.6*10**-19;    #charge(coulomb)
x=0.25*10**-9;    #separation(m)
E=5*10**5;        #intensity of electric field(V/m)
T=300;            #temperature(K) 
KB=1.381*10**-23; #boltzmann constant(J/K)
N=1.6*10**20;     #avagadro number

#Calculation
Pd=N*(e*x)**2*E/(3*KB*T);    #orientational polarisation(C-m)

#Result
print "orientational polarisation is",round(Pd*10**11,4),"*10**-11 C-m"

orientational polarisation is 1.0298 *10**-11 C-m

Example number 8, Page number 6-26

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

#Variable declaration
epsilonr=1.0000684;     #dielectric constant
N=2.7*10**25;   #number of atoms
epsilon0=8.85*10**-12;    
E=10**6;        #electric field(V/m)
Z=2;
e=1.6*10**-19;    #charge(coulomb)

#Calculation
alphae=epsilon0*(epsilonr-1)/N;    #polarisability(Fm**2)
r=(alphae/(4*math.pi*epsilon0))**(1/3);    #radius of electron cloud(m)
d=alphae*E/(Z*e);                   #displacement(m) 

#Result
print "polarisability is",alphae,"Fm**2"
print "radius of electron cloud is",round(r*10**11,3),"*10**-11 m"
print "answer for radius given in the book varies due to rounding off errors"
print "displacement is",round(d*10**16,1),"*10**-16 m"

 polarisability is 2.242e-41 Fm**2
radius of electron cloud is 5.864 *10**-11 m
answer for radius given in the book varies due to rounding off errors
displacement is 0.7 *10**-16 m

Example number 9, Page number 6-27

In [25]:
#importing modules
import math
from __future__ import division

#Variable declaration
A=750*10**-6;      #area(m**2)
epsilon0=8.85*10**-12;    
epsilonr=3.5;      #dielectric constant
d=5*10**-3;        #seperation(m)
Q=2.5*10**-10;     #charge on plates(C)

#Calculation
V=Q*d/(epsilon0*epsilonr*A);     #voltage across plates(V)

#Result
print "voltage across plates is",round(V,1),"V"

voltage across plates is 53.8 V

Example number 10, Page number 6-27

In [33]:
#importing modules
import math
from __future__ import division

#Variable declaration
N=3*10**25;   #number of atoms
epsilon0=8.85*10**-12;    
r=0.2*10**-9; #radius(m)   
E=1;          #field

#Calculation
p=4*math.pi*epsilon0*r**3;        #dipole moment per unit electric field(F-m**2)
P=N*p;                            #polarisation(C-m)
epsilonr=1+(4*math.pi*r**3*N/E);  #dielectric constant
alphae=epsilon0*(epsilonr-1)/N;   #polarisability(Fm**2)

#Result
print "dipole moment per unit electric field is",round(p*10**40,1),"*10**-40 F-m**2"
print "polarisation is",round(P*10**15,1),"*10**-15 C-m"
print "dielectric constant is",round(epsilonr,5)
print "polarisability is",round(alphae*10**40,1),"*10**-40 Fm**2"

dipole moment per unit electric field is 8.9 *10**-40 F-m**2
polarisation is 26.7 *10**-15 C-m
dielectric constant is 1.00302
polarisability is 8.9 *10**-40 Fm**2

Example number 11, Page number 6-28

In [35]:
#importing modules
import math
from __future__ import division

#Variable declaration
N=2.7*10**25;   #number of atoms
epsilon0=8.85*10**-12;    
epsilonr=1.000435;  #dielectric constant

#Calculation
alphae=epsilon0*(epsilonr-1)/N;   #polarisability(Fm**2)

#Result
print "polarisability is",round(alphae*10**40,3),"*10**-40 F-m**2"

polarisability is 1.426 *10**-40 F-m**2

Example number 12, Page number 6-28

In [36]:
#importing modules
import math
from __future__ import division

#Variable declaration
epsilon0=8.85*10**-12;    
epsilonr=4;        #dielectric constant
NA=6.02*10**26;    #avagadro number
D=2.08*10**3;      #density(kg/m**3)
M=32;              #atomic weight(kg)

#Calculation
N=NA*D/M;          #number of atoms
alphae=epsilon0*(epsilonr-1)/N;   #polarisability(Fm**2)

#Result
print "polarisability is",round(alphae*10**40,3),"*10**-40 F-m**2"

polarisability is 6.785 *10**-40 F-m**2