3: Dielectrics

Example number 3.1, Page number 68

In [1]:
#importing modules
import math
from __future__ import division

#Variable declaration
k=78;   #dielectric constant of water
epsilon0=8.9*10**-12;   #dielectric permittivity of free space

#Calculation
epsilon=k*epsilon0;    #dielectric permittivity(C**2/Nm2)
chi=epsilon-epsilon0;    #dielectric susceptibility(C**2/Nm2)

#Result
print "dielectric permittivity is",epsilon,"C**2/Nm2"
print "dielectric susceptibility is",chi,"C**2/Nm2"

dielectric permittivity is 6.942e-10 C**2/Nm2
dielectric susceptibility is 6.853e-10 C**2/Nm2

Example number 3.2, Page number 68

In [4]:
#importing modules
import math
from __future__ import division

#Variable declaration
epsilon=15*10**-12;   #dielectric permittivity(C**2/Nm2)
A=1;    #area of plates(m**2)
q=60*10**-6;    #charge(C)
epsilon0=8.9*10**-12;   #dielectric permittivity of free space

#Calculation
sigma=q/A;    #surface charge density(C/m**2)
chi=epsilon-epsilon0;    #dielectric susceptibility(C**2/Nm2)
E=sigma/epsilon;   #electric field intensity(N/C)
P=chi*E;    #polarization(C/m**2)

#Result
print "electric field intensity is",E/10**6,"*10**6 N/C"
print "polarization is",P*10**6,"*10**-6 C/m**2"
print "susceptibility is",chi,"C**2/Nm2"

electric field intensity is 4.0 *10**6 N/C
polarization is 24.4 *10**-6 C/m**2
susceptibility is 6.1e-12 C**2/Nm2

Example number 3.3, Page number 69

In [6]:
#importing modules
import math
from __future__ import division

#Variable declaration
k=5.4;     #dielectric constant
E=10**6;    #electric field intensity(N/C)
epsilon0=8.9*10**-12;   #dielectric permittivity of free space

#Calculation
D=k*epsilon0*E;     #electric displacement(C/m**2)
Ed=(1/2)*k*epsilon0*(E**2);     #energy density in dielectric(J/m**2)

#Result
print "electric displacement is",D,"C/m**2"
print "answer given in the book is wrong"
print "energy density in dielectric is",Ed,"J/m**2"

electric displacement is 4.806e-05 C/m**2
answer given in the book is wrong
energy density in dielectric is 24.03 J/m**2

Example number 3.4, Page number 69

In [8]:
#importing modules
import math
from __future__ import division

#Variable declaration
chi=35.4*10**-12;    #susceptibility(C**2/Nm2)
epsilon0=8.85*10**-12;   #dielectric permittivity of free space

#Calculation
k=1+(chi/epsilon0);       #dielectric constant
epsilon=epsilon0*k;     #permittivity(C/Nm**2)

#Result
print "dielectric constant is",k
print "permittivity is",epsilon,"C/Nm**2"
print "answer given in the book is wrong"

dielectric constant is 5.0
permittivity is 4.425e-11 C/Nm**2
answer given in the book is wrong