Dielectric Properties

Example number 6.1, Page number 187

In [1]:
# To calculate the energy stored in the condenser and polarizing the dielectric

#import module
import math
from __future__ import division

#Variable decleration
C=2;    #capacitance in micro farad
C=C*10**-6;    #capacitance in farad
V=1000;         #voltage in Volts
epsilon_r=100;    

#Calculation
W=(C*(V**2))/2;
C0=C/epsilon_r;
W0=(C0*(V**2))/2;
W_0=1-W0;

#Result
print("energy stored in the condenser in Joule is",W);
print("energy stored in the dielectric in Joule is",W_0);

('energy stored in the condenser in Joule is', 1.0)
('energy stored in the dielectric in Joule is', 0.99)

Example number 6.2, Page number 188

In [3]:
# To calculate the ratio between electronic and ionic polarizability

#import module
import math
from __future__ import division

#Variable decleration
epsilon_r=4.94;
N=2.69;     #let n**2 be N

#Calculaion
#(epsilon_r-1)/(epsilon_r+2) = (N*alpha)/(3*epsilon_0)
#alpha = alpha_e+alpha_i
#therefore (epsilon_r-1)/(epsilon_r+2) = (N*(alpha_e+alpha_i))/(3*epsilon_0)
#let (N*(alpha_e+alpha_i))/(3*epsilon_0) be X
X=(epsilon_r-1)/(epsilon_r+2);
#Ez=n^2
#therefore (N-1)/(N+2) = (N*alpha_e)/(3*epsilon_0)
#let (N*alpha_e)/(3*epsilon_0) be Y
Y=(N-1)/(N+2);
#dividing X/Y = (N*(alpha_e+alpha_i))/(N*alpha_e)
#therefore X/Y = 1+(alpha_i/alpha_e)
#let alpha_i/alpha_e be A
R=(X/Y)-1;
R=math.ceil(R*10**4)/10**4;   #rounding off to 4 decimals

#Result
print("ratio between electronic and ionic polarizability is",R);

#answer given in the book is wrong in the second part

('ratio between electronic and ionic polarizability is', 0.5756)

Example number 6.3, Page number 188

In [5]:
# To calculate the dielectric constant of the material

#import module
import math
from __future__ import division

#Variable decleration
N=3*10**28;   #atoms per m^3
alpha_e=10**-40;   #farad m^2
epsilon_0=8.854*10**-12;    #f/m

#Calculation
epsilon_r=1+(N*alpha_e/epsilon_0);
epsilon_r=math.ceil(epsilon_r*10**3)/10**3;   #rounding off to 3 decimals

#Result
print("dielectric constant of the material is",epsilon_r);

('dielectric constant of the material is', 1.339)

Example number 6.4, Page number 189

In [6]:
# To calculate the electronic polarizability of He atoms

#import module
import math
from __future__ import division

#Variable decleration
epsilon_0=8.854*10**-12;    #f/m
epsilon_r=1.0000684;

#Calculation
N=2.7*10**25;               #atoms per m^3
alpha_e=(epsilon_0*(epsilon_r-1))/N;

#Result
print("electronic polarizability of He atoms in Fm^2 is",alpha_e);

('electronic polarizability of He atoms in Fm^2 is', 2.2430133333322991e-41)

Example number 6.5, Page number 189

In [7]:
# To calculate the capacitance and charge

#import module
import math
from __future__ import division

#Variable decleration
epsilon_0=8.854*10**-12;    #f/m
A=100;    #area in cm^2
A=A*10**-4;   #area in m^2
V=100;   #potential in V
d=1;   #plate seperation in cm

#Calculation
d=d*10**-2;    #plate seperation in m
C=(epsilon_0*A)/d;
Q=C*V;

#Result
print("charge on the plates in F is",C);
print("charge on the capacitor in coulomb is",Q);

('charge on the plates in F is', 8.854e-12)
('charge on the capacitor in coulomb is', 8.854e-10)

Example number 6.6, Page number 190

In [9]:
# To calculate the resultant voltage across the capacitors

#import module
import math
from __future__ import division


#Variable decleration
Q=2*10**-10;   #charge in coulomb
d=4;   #plate seperation in mm
d=d*10**-3;    #plate seperation in m
epsilon_r=3.5;
epsilon_0=8.85*10**-12;    #f/m
A=650;    #area in mm^2

#Calculation
A=A*10**-6;    #area in m^2
V=(Q*d)/(epsilon_0*epsilon_r*A);
V=math.ceil(V*10**3)/10**3;   #rounding off to 3 decimals

#Result
print("voltage across the capacitor in Volts is",V);

('voltage across the capacitor in Volts is', 39.735)

Example number 6.7, Page number 190

In [10]:
# To calculate the dielectric displacement

#import module
import math
from __future__ import division


#Variable decleration
V=10;   #potential in volts
d=2*10**-3;    #plate seperation in m
epsilon_r=6;    #dielectric constant
epsilon_0=8.85*10**-12;    #f/m

#Calculation
E=V/d;
D=epsilon_0*epsilon_r*E;

#Result
print("dielectric displacement in cm^-2 is",D);

#answer given in the book is wrong in the 7th decimal point

('dielectric displacement in cm^-2 is', 2.6549999999999994e-07)

Example number 6.8, Page number 191

In [12]:
# To calculate the polarizability and relative permittivity of He

#import module
import math
from __future__ import division


#Variable decleration
R=0.55;    #radius of He atom in angstrom
R=R*10**-10;    #radius of He atom in m
epsilon_0=8.84*10**-12;    #f/m
N=2.7*10**25;

#Calculation
alpha_e=4*math.pi*epsilon_0*R**3;
epsilon_r=(N*alpha_e/epsilon_0)+1;
epsilon_r=math.ceil(epsilon_r*10**6)/10**6;   #rounding off to 6 decimals

#Result
print("polarizability in farad m^2 is",alpha_e);
print("relative permitivity is",epsilon_r);

('polarizability in farad m^2 is', 1.848205241292183e-41)
('relative permitivity is', 1.000057)

Example number 6.9, Page number 191

In [13]:
# To calculate the field strength and total dipole moment

#import module
import math
from __future__ import division


#Variable decleration
V=15;    #potential difference in volts
C=6;    #capacity in micro farad
C=C*10**-6;    #capacity in farad
epsilon_0=8.84*10**-12;    #f/m
epsilon_r=8;
A=360;     #surface area in cm^2

#Calculation
A=A*10**-4;    #surface area in m^2
E=(V*C)/(epsilon_0*epsilon_r*A);
d=epsilon_0*(epsilon_r-1)*V*A;

#Result
print("field strength in V/m is",E);
print("total dipole moment in cm is",d);

#answer for field strength E given in the book is wrong 

('field strength in V/m is', 35350678.73303167)
('total dipole moment in cm is', 3.34152e-11)

Example number 6.10, Page number 191

In [11]:
# To calculate the complex polarisability of material

#import module
import math
from __future__ import division

#Variable decleration
epsilonr=4.36;      #dielectric constant
t=2.8*10**-2;       #loss tangent(t)
N=4*10**28;         #number of electrons
epsilon0=8.84*10**-12;      

#Calculation
epsilon_r = epsilonr*t;
epsilonstar = (complex(epsilonr,-epsilon_r));
alphastar = (epsilonstar-1)/(epsilonstar+2);
alpha_star = 3*epsilon0*alphastar/N;             #complex polarizability(Fm**2)

#Result
print("the complex polarizability in F-m^2 is"'alphastar',alpha_star);
#disp('j',I,R);
#by taking 10^-40 common we get alphastar = (3.5-j0.06)*10^-40 F-m^2

('the complex polarizability in F-m^2 isalphastar', (3.5037933503257222e-40-6.000743833211258e-42j))
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