Polarization property in dielectric

1. Course: Electromagnetic Theory
paper code: EI 503
Course Coordinator: Arpan Deyasi
Department of Electronics and Communication Engineering
RCC Institute of Information Technology
Kolkata, India
Topic: Electrostatics – Dielectric
17-11-2021 Arpan Deyasi, EM Theory 1
Arpan Deyasi
Electromagnetic
Theory

2. Dielectric
It is a type of material in which electrons are bound to their parent nuclei/molecules and
only motion is possible in presence of external electric field is electric displacement of
positive and negative charges along opposite directions
Once the charge displacement has taken place, the material becomes polarized
Polarized material induces dipole moments
Dipole field and external field are comparable in magnitude
17-11-2021 Arpan Deyasi, EM Theory 2
Arpan Deyasi
Electromagnetic
Theory

3. Classification of Dielectric
[i] Polar dielectric
▪ Asymmetric arrangement of atoms, which means centers of gravity of positive
and negative charges don’t coincide, even in absence of external electric field
▪ Owing to net charge separation, material has permanent dipole moment
▪ Ex: Acetone, Water ammonia
17-11-2021 Arpan Deyasi, EM Theory 3
E=0 E≠0
Arpan Deyasi
Electromagnetic
Theory

4. Classification of Dielectric
[ii] Nonpolar dielectric
▪ Symmetric arrangement of atoms, which means centers of gravity of positive and negative
charges coincide in absence of external electric field
▪ Separation of c.g takes place when external field is present
▪ Owing to net charge separation in absence of field, materials do not have permanent dipole
moment
▪ Ex: Benzene, Methane
17-11-2021 Arpan Deyasi, EM Theory 4
E=0 E≠0
Arpan Deyasi
Electromagnetic
Theory

5. Types of Polarization
[i] Electronic Polarization
Bound, negative cloud subject to external electric field is displaced from
equilibrium position relative to positive nucleus
17-11-2021 Arpan Deyasi, EM Theory 5
E
Arpan Deyasi
Electromagnetic
Theory

6. Types of Polarization
[ii] Orientation Polarization
Electric dipoles are oriented parallel to applied electric field opposing thermal
agitation and mutual interacting forces, from their previous random
distribution
17-11-2021 Arpan Deyasi, EM Theory 6
E=0 E≠0
Arpan Deyasi
Electromagnetic
Theory

7. Types of Polarization
17-11-2021 Arpan Deyasi, EM Theory 7
E=0 E≠0
E
[iii] Ionic Polarization
Positive and negative ions of a molecule are displaced in presence of external
electric field
Arpan Deyasi
Electromagnetic
Theory

8. Polarization Density
Polarization density is the vector field that expresses the density of permanent
or induced electric dipole moments in a dielectric material
2
/
P Nqd C m
=
N: number of molecules per unit volume
q: magnitude of charge
d: separation distance between positive charge and negative charge centers
17-11-2021 Arpan Deyasi, EM Theory 8
Arpan Deyasi
Electromagnetic
Theory

9. Polarization Volume Charge Density
Consider a medium consisting of N such polarized
particles per unit volume, where net charge q
contained within an arbitrary volume V is
enclosed by a surface S
Net charge
.
S
Q P ds
= − 
.
V
Q Pdv
= − 

17-11-2021 Arpan Deyasi, EM Theory 9
dS
E
n̂
S
Arpan Deyasi
Electromagnetic
Theory

10. Polarization Volume Charge Density
Net charge in V can be determined by integrating the polarization charge density
over its volume
v
V
Q dv

= 
.
v
V V
dv Pdv
 = − 
 
.
v P
 = −
17-11-2021 Arpan Deyasi, EM Theory 10
Arpan Deyasi
Electromagnetic
Theory

11. Net charge
Polarization Surface Charge Density
.
S
Q P ds
= − 
P
S
Q ds

= 
Again
.
P
S S
ds P ds
 = −
 
ˆ
.
P P n
 = −
17-11-2021 Arpan Deyasi, EM Theory 11
Arpan Deyasi
Electromagnetic
Theory

12. Relation between Polarization Vector and Electric Field
In free space
0E
 
=
Polarization field is directly proportional with electric field
0
P
E


−
 =
When polarization is present, corresponding field works against the external electric field
P E

17-11-2021 Arpan Deyasi, EM Theory 12
Arpan Deyasi
Electromagnetic
Theory

13. Relation between Polarization Vector and Electric Field
0 e
P E
 
=
0
0
eE
E
  

−
 =
0 0 e
E E
   
= −
0 0 e
E E
   
= −
χe is called susceptibility of the material
17-11-2021 Arpan Deyasi, EM Theory 13
Arpan Deyasi
Electromagnetic
Theory

14. Relation between Polarization Vector and Electric Field
0
1
1 e
E

 
 
=  
+
 
The term (1+ χe) is called relative permittivity of the material, defined as εr
17-11-2021 Arpan Deyasi, EM Theory 14
Arpan Deyasi
Electromagnetic
Theory

15. Atomic Polarizability
Polarization density is given by
P pN
=
induced dipole moment
:
p
N: number of atoms per unit volume
Induced dipole moment acquired by the atom 0 e
p E
 
=
αe: number of atoms per unit volume (atomic polarizability)
0 e
P N E
 
 =
17-11-2021 Arpan Deyasi, EM Theory 15
Arpan Deyasi
Electromagnetic
Theory

16. 17-11-2021 Arpan Deyasi, EM Theory 16
Relation between Polarization and Displacement
0 e
P E
 
=
0 e
P
E
 
=
0 r
D E
 
=
0 r
D
E
 
=
0 0
e r
P D
   
 =
Arpan Deyasi
Electromagnetic
Theory

17. 17-11-2021 Arpan Deyasi, EM Theory 17
Relation between Polarization and Displacement
0 0
( 1)
r r
P D
   
=
−
( 1)
r
r
P D


−
=
Arpan Deyasi
Electromagnetic
Theory

18. 17-11-2021 Arpan Deyasi, EM Theory 18
Problem 1
Calculate polarization in a dielectric material with εr = 2.8, if displacement
density is 3⨯10-7 C/m2.
Soln
( 1)
r
r
P D


−
=
7 2
(2.8 1)
3 10 /
2.8
P C m
−
−
=  
2
0.1928 /
P C m

=
Arpan Deyasi
Electromagnetic
Theory