# 13: Dielectric Properties of Materials¶

## Example number 13.1, Page number 287¶

In :
#importing modules
import math

#Variable declaration
epsilon_0 = 8.85*10**-12;    #Absolute electrical permittivity of free space(F/m)
R = 0.52;       #Radius of hydrogen atom(A)
n = 9.7*10**26;      #Number density of hydrogen(per metre cube)

#Calculation
R = R*10**-10;       #Radius of hydrogen atom(m)
alpha_e = 4*math.pi*epsilon_0*R**3;      #Electronic polarizability of hydrogen atom(Fm**2)

#Result
print "The electronic polarizability of hydrogen atom is", alpha_e, "Fm**2"

The electronic polarizability of hydrogen atom is 1.56373503182e-41 Fm**2


## Example number 13.2, Page number 287¶

In :
#importing modules
import math
from __future__ import division

#Variable declaration
epsilon_0 = 8.854*10**-12;    #Absolute electrical permittivity of free space(F/m)
A = 100;      #Area of a plate of parallel plate capacitor(cm**2)
d = 1;     #Distance between the plates of the capacitor(cm)
V = 100;    #Potential applied to the plates of the capacitor(V)

#Calculation
A= A*10**-4;     #Area of a plate of parallel plate capacitor(m**2)
d = d*10**-2;     #Distance between the plates of the capacitor(m)
C = epsilon_0*A/d;     #Capacitance of parallel plate capacitor(F)
Q = C*V;      #Charge on the plates of the capacitor(C)

#Result
print "The capacitance of parallel plate capacitor is",C, "F"
print "The charge on the plates of the capacitor is",Q, "C"

The capacitance of parallel plate capacitor is 8.854e-12 F
The charge on the plates of the capacitor is 8.854e-10 C


## Example number 13.3, Page number 288¶

In :
#importing modules
import math
from __future__ import division

#Variable declaration
epsilon_0 = 8.854*10**-12;     #Absolute electrical permittivity of free space(F/m)
epsilon_r = 5.0;     #Dielectric constant of the material between the plates of capacitor
V = 15;      #Potential difference applied between the plates of the capacitor(V)
d = 1.5;     #Separation between the plates of the capacitor(mm)

#Calculation
d = d*10**-3;      #Separation between the plates of the capacitor(m)
#Electric displacement, D = epsilon_0*epsilon_r*E, as E = V/d, so
D = epsilon_0*epsilon_r*V/d;      #Dielectric displacement(C/m**2)

#Result
print "The dielectric displacement is",D, "C/m**2"

The dielectric displacement is 4.427e-07 C/m**2


## Example number 13.4, Page number 288¶

In :
#importing modules
import math
from __future__ import division

#Variable declaration
epsilon_0 = 8.854*10**-12;      #Absolute electrical permittivity of free space(F/m)
N = 3*10**28;       #Number density of solid elemental dielectric(atoms/metre cube)
alpha_e = 10**-40;      #Electronic polarizability(Fm**2)

#Calculation
epsilon_r = 1 + (N*alpha_e/epsilon_0);      #Relative dielectric constant of the material
epsilon_r = math.ceil(epsilon_r*10**3)/10**3;     #rounding off the value of epsilon_r to 3 decimals

#Result
print "The Relative dielectric constant of the material is",epsilon_r

The Relative dielectric constant of the material is 1.339


## Example number 13.5, Page number 288¶

In :
#importing modules
import math
from __future__ import division

#Variable declaration
N_A = 6.02*10**23;     #Avogadro's number(per mole)
epsilon_0 = 8.854*10**-12;     #Absolute electrical permittivity of free space(F/m)
epsilon_r = 3.75;      #Relative dielectric constant
d = 2050;      #Density of sulphur(kg/metre cube)
y = 1/3;      #Internal field constant
M = 32;      #Atomic weight of sulphur(g/mol)

#Calculation
N = N_A*10**3*d/M;      #Number density of atoms of sulphur(per metre cube)
#Lorentz relation for local fields give E_local = E + P/(3*epsilon_0) which gives
#(epsilon_r - 1)/(epsilon_r + 2) = N*alpha_e/(3*epsilon_0), solving for alpha_e
alpha_e = (epsilon_r - 1)/(epsilon_r + 2)*3*epsilon_0/N;      #Electronic polarizability of sulphur(Fm**2)

#Result
print "The electronic polarizability of sulphur is",alpha_e, "Fm**2"

The electronic polarizability of sulphur is 3.2940125351e-40 Fm**2


## Example number 13.6, Page number 289¶

In :
#importing modules
import math
from __future__ import division

#Variable declaration
N = 3*10**28;      #Number density of atoms of dielectric material(per metre cube)
epsilon_0 = 8.854*10**-12;     #Absolute electrical permittivity of free space(F/m)
n = 1.6;     #Refractive index of dielectric material

#Calculation
#As (n^2 - 1)/(n^2 + 2) = N*alpha_e/(3*epsilon_0), solving for alpha_e
alpha_e = (n**2 - 1)/(n**2 + 2)*3*epsilon_0/N;      #Electronic polarizability of dielectric material(Fm**2)

#Result
print "The electronic polarizability of dielectric material is",alpha_e, "Fm**2"

The electronic polarizability of dielectric material is 3.029e-40 Fm**2


## Example number 13.7, Page number 289¶

In :
#importing modules
import math
from __future__ import division

#Variable declaration
epsilon_r = 4.9;       #Absolute relative dielectric constant of material(F/m)
n = 1.6;       #Refractive index of dielectric material

#Calculation
#As (n^2 - 1)/(n^2 + 2)*(alpha_e + alpha_i)/alpha_e = N*(alpha_e + alpha_i)/(3*epsilon_0) = (epsilon_r - 1)/(epsilon_r + 2)
#let alpha_ratio = alpha_i/alpha_e
alpha_ratio = ((epsilon_r - 1)/(epsilon_r + 2)*(n**2 + 2)/(n**2 - 1) - 1)**(-1);  #Ratio of electronic polarizability to ionic polarizability
alpha_ratio = math.ceil(alpha_ratio*10**3)/10**3;     #rounding off the value of alpha_ratio to 3 decimals

#Result
print "The ratio of electronic polarizability to ionic polarizability is",alpha_ratio

The ratio of electronic polarizability to ionic polarizability is 1.534

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