# chapter4 :Dielectrics¶

## example 4.4;page no:189¶

In :
#cal of Dipole moment per atom
#intiation of all variables
#given that
import sys
epsilon_r = 1.000074 # Dielectric constant of He at 0C and 1atm
epsilon_0 = 8.854e-12 # Permittivity of free space
E = 100 # Electric field in V/m
n = 2.68e27 # Electron density in no,/m^
N_a = 6e23 # Avogadro number
V = 22.4 # Volume at STP in litter
print("Example 4.4,page no:189")
P = epsilon_0*(epsilon_r-1)*E # Calculation of polarization
N = N_a/(V*1e-3)# Calculation of total number of atoms
p = P/N # dipole moment per atom
print("Dipole moment per atom in Coulomb-meter:"),round(p,42)
# Answer in book is in different form and as 24.45e-40 coulomb-meter

Example 4.4,page no:189
Dipole moment per atom in Coulomb-meter: 2.446e-39


## example 4.6;page no:191¶

In :
#cal of Electronic polarisability and Relative permeability
#intiation of all variables
#given that
import math
import sys
r = 0.055 # Radius of hydrogen atom in nm
n = 9.8e26 # Number of atoms/cc
epsilon_0 = 8.854e-12 # Permittivity of free space
print("Example 4.6,page no:191")
alpha_e = 4*math.pi*epsilon_0*(r*1e-9)**3 # Calculation of electronic polarisability
epsilon_r = 1+n*alpha_e/epsilon_0 # Calculation of relative permeability
print("Electronic polarisability in Fm^2:"),round(alpha_e,44)
print("Relative permeability is:"),round(epsilon_r,6)

Example 4.6,page no:191
Electronic polarisability in Fm^2: 1.851e-41
Relative permeability is: 1.002049


## example 4.8;page no:192¶

In :
#cal of Relative permittivity
#intiation of all variables
#given that
import sys
epsilon_0 = 8.854e-12 # Permittivity of free space
E = 2000 # Electric field in V/m
P = 6.4e-8 # Polarization in C/m^2
print("Example 4.8,page no:192")
epsilon_r = 1+ P/(epsilon_0*E) # Calculation of relative permittivity
print("Relative permittivity is:"),round(epsilon_r,3)

Example 4.8,page no:192
Relative permittivity is: 4.614


## example 4.9;page no:193¶

In :
#cal of Relative permittivity
#intiation of all variables
#given that
import sys
alpha_e = 2e-40 # Electronic polarisability in Fm^2
N = 4e28 # density in atoms/m^3
epsilon_0 = 8.85e-12 # Permittivity of free space
print("Example 4.9,page no:193")
epsilon_r = 1+ N*alpha_e/(epsilon_0) # Calculation of relative permittivity
print("Relative permittivity is:"),round(epsilon_r,5)

Example 4.9,page no:193
Relative permittivity is: 1.90395


# example 4.10;page no:193¶

In :
#cal of Relative permittivity and Electrical susceptibility
#intiation of all variables
#given that
import sys
epsilon = 2.4e-10 # permitivity of a  dielectric material in C^2/N?m^2
epsilon_0 = 8.854e-12 # Permittivity of free space
print("Example 4.10,page no:193")
K = epsilon/epsilon_0  # Calculation of dielectric constant
zai_e = epsilon_0*(K-1) # Calculation of electrical susceptibility
print("Relative permittivity is:"),round(K,2)
print("Electrical susceptibility in C^2/Nm^2:"),round(zai_e,12)

Example 4.10,page no:193
Relative permittivity is: 27.11
Electrical susceptibility in C^2/Nm^2: 2.31e-10


## example 4.11;page no:194¶

In :
#cal of Magnitude of Electrical vector,Electrical Displacement and Electric polarization vector
#intiation of all variables
#given that
import sys
V = 100 # Applied potential in Volt
d = 1 # Separation between plates in cm
k1 = 8 # Dielectric constant
k2 = 9 #dielectric constant
epsilon_0 = 8.854e-12 # Permittivity of free space
print("Example 4.11,page no:194")
E_0 = V/(d*1e-2) # Calculation of electric field
E = E_0/k1*k2 # Calculation of electric field
D = k1*epsilon_0*E # Calculation of electrical displacement vector
P = (k1-1)*epsilon_0*E  # Calculation of electrical polarization
print("Magnitude of Electrical vector in Volt/meter:"),round(E,3) # Answer in book is 1.125e3 Volt/meter
print("Magnitude of Electrical Displacement vector in C/m^2:"),round(D,10)# Answer in book is 8.85e-8C/m^2
print("Magnitude of Electric polarization vector in C/m^2:"),round(P,11)# Answer in book is 7.774e-8C/m^2

Example 4.11,page no:194
Magnitude of Electrical vector in Volt/meter: 11250.0
Magnitude of Electrical Displacement vector in C/m^2: 7.969e-07
Magnitude of Electric polarization vector in C/m^2: 6.9725e-07


## example 4.12;page no:195¶

In :
#cal of Deformational Polarizability and Orientational Polarizability
#intiation of all variables
#given that
alpha_300 = 2.5e-39 # total polarisability in C^2m/N at 300 K
alpha_600 = 1.75e-39 # total polarisability in C^2m/N at 600 K
T1 = 300 # Initial temperature in Kelvin
T2 = 600 # Final Temperature in Kelvin
print("Example 4.12,page no:195")
b = (alpha_300-alpha_600)*T2
al_def_300 = alpha_300 - b/300
al_oriant_300 = b/300
al_oriant_600 = b/600
print("Deformational Polarizability in C^2mN^-1:"),round(al_def_300,40)
print("Orientational Polarizability at degree Celcius in C^2mN^-1:"),round(al_oriant_300,40)
print("Orientational Polarizability at degree Celcius in C^2mN^-1:"),round(al_oriant_600,41)

Example 4.12,page no:195
Deformational Polarizability in C^2mN^-1: 1e-39
Orientational Polarizability at degree Celcius in C^2mN^-1: 1.5e-39
Orientational Polarizability at degree Celcius in C^2mN^-1: 7.5e-40


## example 4.13;page no:202¶

In :
 #cal of Relative permittivity
#intiation of all variables
#given that
#import sys
alpha_e = 1.5e-40 # Electronic polarizability in Fm^2
N = 4e28 # density in atoms/m^3
epsilon_0 = 8.85e-12 # Permittivity of free space
print("Example 4.13,page no:202")
k = N*alpha_e/(3*epsilon_0)
epsilon_r = (1+ k*2)/(1-k)# Calculation of relative permittivity
print("Relative permittivity is:"),round(epsilon_r,2)

Example 4.13,page no:202
Relative permittivity is: 1.88


# example 4.14;page no:202¶

In :
 #cal of Relative permittivity
#intiation of all variables
#given that
#import sys
m = 32 # Atomic weight of sulphur
d = 2.08 # Density in g/cm^3
alpha_e = 3.5e-40 # Electronic polarizability in Fm^2
N_a = 6.022e23 # Avogadro Number
epsilon_0 = 8.85e-12 # Permittivity of free space
print("Example 4.14,page no:202")
N = N_a*d*1e6/m # Calculation of Atoms per unit
k = N*alpha_e/(3*epsilon_0)
epsilon_r = (1+ k*2)/(1-k)# Calculation of relative permittivity
print("Relative permittivity is:"),round(epsilon_r,2)
# Answer in book is 4.17

Example 4.14,page no:202
Relative permittivity is: 4.2


## example 4.15;page no:203¶

In :
 #cal of Percentage ionic polarizability
#intiation of all variables
#given that
#import sys
n = 1.5 # Refractive index
epsilon = 5.6 # Static dielectric constant
print("Example 4.15,page no:203")
per = (1-((n**2-1)/(n**2+2))*(epsilon+2)/(epsilon-1))*100 # Pecentage ionic polarisability
print("Percentage ionic polarizability in pecent:"),round(per,2)
# Answer in book is 5.14 %

Example 4.15,page no:203
Percentage ionic polarizability in pecent: 51.41


## example 4.16;page no:204¶

In :
 #cal of Electronic polarizability
#intiation of all variables
#given that
#import sys
m = 32 # Atomic weight of sulphur
d = 2050 # Density in Kg/m^3
N_a = 6.022e23 # Avogadro Number
epsilon_0 = 8.85e-12 # Permittivity of free space
epsilon_r = 3.75 # Dielectric constant of sulphur
print("Example 4.16,page no:204")
N = N_a*d*1e3/m # Calculation of Atoms per unit
alpha_e = 3*epsilon_0*((epsilon_r-1)/(epsilon_r+2)) / N
print("Electronic polarizability  in Fm^2:"),round(alpha_e,42)

Example 4.16,page no:204
Electronic polarizability  in Fm^2: 3.29e-40


## example 4.17;page no:204¶

In :
#cal of Ratio of electronic to ionic polarizability
#intiation of all variables
#given that
#import sys
n = 1.5 # Refractive index
epsilon = 4. # Static dielectric constant
epsilon_0 = 8.85e-12 # permittivity of free space
print("Example 4.17,page no:204")
k1 = (epsilon-1)/(epsilon+2)
k2 = (n**2-1.)/(n**2+2.)
ratio = 1./((k1/k2)-1.)
print("Ratio of electronic to ionic polarizability is:"),round(ratio,2)

Example 4.17,page no:204
Ratio of electronic to ionic polarizability is: 1.43


## example 4.18;page no:219¶

In :
#cal of Frequency and Phase difference between current and voltage
#intiation of all variables
#given that
import math
t = 1.8e-5 # Relaxation time in second
epsilon_r = 1 # let
print("Example 4.18,page no:219")
f = 1/(2*math.pi*t) # Calculation of frequency
delta = math.atan(epsilon_r/epsilon_r)
phi = 90 - delta*180/math.pi # Calculation of phase difference
print("Frequency in KHz:"),round(f/1e3,2)
print("Phase difference between current and voltage in degree:"),round(phi,0)

Example 4.18,page no:219
Frequency in KHz: 8.84
Phase difference between current and voltage in degree: 45.0