Dielectric materials

Example number 11.1, Page number 335

In [1]:
#importing modules
import math

#Variable declaration
epsilon_0=8.854*10**-12;
A=10*10*10**-6;    #area of capacitor in m^2
d=2*10**-3;     #distance of seperation in m
C=10**-9;      #capacitance in F

#Calculation
epsilon_r=(C*d)/(epsilon_0*A);
epsilon_r=math.ceil(epsilon_r*10**2)/10**2;   #rounding off to 2 decimals

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

('dielectric constant of material is', 2258.87)

Example number 11.2, Page number 335

In [2]:
#Variable declaration
epsilon_0=8.854*10**-12;
epsilon_r=1.0000684;     #dielectric constant of He gas
N=2.7*10**25;    #concentration of dipoles per m^3

#Calculation
#alpha_e=P/(N*E) and P=epsilon_0(epsilon_r-1)*E
#therefore alpha_e=epsilon_0(epsilon_r-1)/N
alpha_e=(epsilon_0*(epsilon_r-1))/N;

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

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

Example number 11.3, Page number 336

In [3]:
#Variable declaration
epsilon_0=8.854*10**-12;
epsilon_r=6;  #dielectric constant
E=100;    #electric field intensity in V/m

#Calculation
P=epsilon_0*(epsilon_r-1)*E;

#Result
print("polarization in C/m^2 is",P);

('polarization in C/m^2 is', 4.426999999999999e-09)

Example number 11.4, Page number 336

In [5]:
#importing modules
import math

#Variable declaration
epsilon_0=8.854*10**-12;
R=0.158;    #radius of Ne in nm

#Calculation
R=R*10**-9;      #converting nm to m
alpha_e=4*math.pi*epsilon_0*R**3;

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

('electronic polarizability in Fm^2 is', 4.3885458748002144e-40)

Example number 11.5, Page number 336

In [9]:
#importing modules
import math

#Variable declaration
epsilon_0=8.854*10**-12;
C=0.02;      #capacitance in micro farad
epsilon_r=6;  #dielectric constant
t=0.002;     #thickness of mica in cm
d=0.002;    #thickness of metal sheet in cm

#Calculation
C=C*10**-6;    #converting micro farad to farad
d=d*10**-2;    #converting cm to m
A=(C*d)/(epsilon_0*epsilon_r);
A=A*10**3;
A=math.ceil(A*10**4)/10**4;   #rounding off to 4 decimals
A1=A*10;    #converting m**2 to cm**2
A1=math.ceil(A1*10**3)/10**3;   #rounding off to 3 decimals

#Result
print("area of metal sheet in m^2 is",A,"*10**-3");
print("area of metal sheet in cm^2 is",A1);

('area of metal sheet in m^2 is', 7.5296, '*10**-3')
('area of metal sheet in cm^2 is', 75.296)

Example number 11.6, Page number 336

In [10]:
#importing modules
import math

#Variable declaration
epsilon_0=8.854*10**-12;
E=1000;     #electric field in V/m
P=4.3*10**-8;     #polarization in C/m^2

#Calculation
epsilon_r=(P/(E*epsilon_0)+1);
epsilon_r=math.ceil(epsilon_r*10**4)/10**4;   #rounding off to 4 decimals

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

('dielectric constant is', 5.8566)

Example number 11.7, Page number 337

In [11]:
#Variable declaration
epsilon_0=8.854*10**-12;
chi=4.94;    #relative susceptibility
N=10**28;     #number of dipoles per m^3

#Calculation
#polarisation P=N*alpha*E and P=epsilon_0*chi*E. equate the two equations
#epsilon_0*chi*E=N*alpha*E
alpha=(epsilon_0*chi)/N;

#Result
print("polarisability of material in F/m^2 is",alpha);

('polarisability of material in F/m^2 is', 4.373876e-39)
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