Chapter 9: Dielectrics

Example 9.1, Page 9.11

In [1]:
# Given 
E = 10**6 # electric field inside the plates in V/m
d = 0.02 # distance between the plates in meter
k = 3 # dielectric constant of slab
e_ = 8.85e-12 # electric permittivity of air in C^2/Nm^2

#Calculations
D = e_*k*E
P = D-e_*E

#Result
print "Polarization vector is %.2e C/m^2 \nDisplacement vector is %.3e C/m^2"%(P,D)

Polarization vector is 1.77e-05 C/m^2 
Displacement vector is 2.655e-05 C/m^2

Example 9.2, Page 9.11

In [4]:
 
# Given 
E1 = 3*10**5 # electric intensity when space between plates evacuated in V/m
E2 = 1*10**5 # electric intensity when space between plates is filled with dielectric in V/m
e_ = 8.85e-12 # electric permittivity of air in C^2/Nm^2

#calculation
sigma = e_*(E1 - E2)

#result
print "The included charge density on the surface of the dielectric is %.2e C/m^2"%sigma

The included charge density on the surface of the dielectric is 1.77e-06 C/m^2

Example 9.3, Page 9.11

In [5]:
# Given 
E = 1*10**5 # electric field strength inside the plates in V/m
d = 6. # distance between the plates in mm
k = 2.8 # dielectric constant of slab
e_ = 8.85e-12 # electric permittivity of air in C^2/Nm^2

#Calculations
P = e_*(k-1)*E
D = e_*k*E
energy_density = 1./2 * k*e_*E**2

#Result
print "Polarization vector is %.1e C/m^2 \nDisplacement vector is %.1eC/m^2 \nEnergy density is %.3f J/m^3"%(P,D,energy_density )

Polarization vector is 1.6e-06 C/m^2 
Displacement vector is 2.5e-06C/m^2 
Energy density is 0.124 J/m^3

Example 9.4, Page 9.12

In [6]:
# Given 
D = 5e-4 # electric displacement vector in C/m^2
P = 4e-4 # electric polarization vector in C/m^2
v = 0.5 # volume of the slab in m^3
e_ = 8.85e-12 # electric permittivity of air in C^2/Nm^2

#Calculations
E= (D-P)/ e_
k = D/(e_*E)
p = P*v
energy_density = 1./2 * k*e_*E**2

#Result
print "Value of relative permittivity is %d \nTotal dipole moment of the slab is %.e C-m"%(k,p) 

Value of relative permittivity is 5 
Total dipole moment of the slab is 2e-04 C-m

Example 9.5, Page .12

In [7]:
# Given that
E = 3e4 # external field in V/m
k = 1.00074 # dielectric constant of gas at N.T.P.
e_ = 8.85e-12 # electric permittivity of air in C^2/Nm^2

#Calculations
x = k-1
P = x*e_*E
N = 6.023e23/22.4e-3
p = P/N

#Result
print "Induce dipole moment of each is %.2e C-m"%p

Induce dipole moment of each is 7.31e-36 C-m

Example 9.6, Page .13

In [8]:
# Given 
E = 3e4 # external field in V/m
k = 1.000041 # dielectric constant of gas at 0 degree centigrate

#calculation
x = k-1

#Result
print "Electric susceptibility at 0 degree centigrate is %.1e"%x

Electric susceptibility at 0 degree centigrate is 4.1e-05