Dielectrics
Unit – 1
Sub.- Physics
Introduction
Dielectrics are the materials having electric dipole moment permantly.
Dipole: A dipole is an entity in which equal positive and negative
charges are separated by a small distance..
DIPOLE moment (µele ):The product of magnitude of either of the
charges and separation distance b/w them is called Dipole moment.
µe = q . x  coul – m
q
X
-q
All dielectrics are electrical insulators and they are mainly used to store
electrical energy.
Ex: Mica, glass, plastic, water & polar molecules…
POLARISATION OF DIELECRICS




When we are applying external electric field, it causes the
electron cloud to move away. Thus the centroides of the
positive and negative charges now no longer coincides and as a
result of that an electric dipole is induced in the atom. Thus,
atom is said to be polarized.
Polarization : the process of creating or inducing dipoles in a
dielectric medium by an external field.
On the basis on that dielectrics are the material that have
either permanent diploes or induced in the presence of
external electric field .
They are classified into two categories (1) Non polar (2)polar
Dielectrics

Non Polar Dielectrics : There is no permanent

dipole existence in the absence of an electric field .
Centroids of positive and negative charges of molecules
constituting the dielectric material coincide .

Examples :H2, N2, O2, CO 2

Polar Dielectrics : there is permanent dipole exists


even in the absence of an electric field .
Centroids of posistive and negative charges of molecules
constituting the dielectric material do not coinside even in the
absence of electric field
Examples : HCL , CO
dipole
_
+
Electric field
+
+
+
_
_
_
_
+
+
+
_
_
+
_
+
_
Dielectric atom
Dielectric Constant
Dielectric Constant is the ratio between the permittivity of
the medium to the permittivity of free space.

r 
0
its value changes widely from material to material
For vacuum =1
For all other dielectric it is Ɛr >1.
So, we can write Ɛr=1+χe , χe is susceptibility
The characteristics of a dielectric material are determined
by the dielectric constant and it has no units.
Electric field



The region surrounded by charged body is always under
stress because of electrostatic charge . If a small charge q or
a charged body is placed in this region ,then the charge q or
a charged body will experienced a force according Coulomb
s law . This stressed region around charged body is called
electric field .
Electric field at a point define as the force that acts on a unit
positive charge placed at that point thus E.
According to coulomb law when two point charges Q1 and
Q2 are separated by a distance r, the force of attraction or
repulsion between two charges is given by
Electric Polarization
The process of producing electric dipoles by an electric field is
called polarization in dielectrics.
Polarizability:
The induced dipole moment per unit electric field is called
Polarizability.
The induced dipole moment is proportional to the intensity of
the electric field.
E
  E
  polarizability constant
Electric flux ɸ





(1) Number of lines of force that pass through a surface placed
in the vector field .
(2) As the product of surface area and the components of the
electric field normal to the surface
a unit charge is supposed to emanate one flux.
In the case of an isolated charge q coulomb the flux is
q=ɸ
Is independent of of nature of medium.
Polarization vector


Definition: induced dipole moment per unit
volume of dielectric medium.
P is vector quantity and its direction is along
the direction of applied field .If m is the
average induced dipole moment per unit
molecule and N is the number of molecule per
unit volume then polarization is given by
P=Nµ
V=At ,where A is the area of slab
Thus ,the polarization is also defined as induced surface charge
per unit area
But q/A is the induced charge density .so magnitude of
polarization is equal to the induced charge density.
Electric flux Density (D):
Electric flux density is defined as charge per unit area and it has
same units of dielectric polarization.
Electric flux density D at a point in a free space or air in terms of
Electric field strength is
D0   0 E
- -  (1)
At the same point in a medium is given by
D  E
- -  (2)
As the polarization measures the additional flux density arising
from the presence of material as compared to free space
i.e, D   0E  P
- -  (3)
Using equations 2 & 3 we get
E   0 E  P
( -  0 ) E  P
(or) ( r . 0 -  0 ) E  P
( r  1) 0 .E  P
Electric susceptibility
The polarization vector P is proportional to the total electric
flux density and direction of electric field.
Therefore the polarization vector can be written as,
In a large number of dielectrics it is Found that
polarization is directly Proportional to the
external applied Field E.
P   0 e E
P
e 
0E
Def. The ratio of polarization to net electric field as   0 ( r  1) E
0E
Given by the induced charge on the surface of
e   r 1
Dielectric is called susceptibility.
Relation between polarization P, susceptibity
χ and dielectric constant Ɛr
Lets us consider a parallel plate capacitor between which an
electric field Ɛ0.
 If σ is the surface charge density then gauss law.
E=σ/Ɛ0
(1)
if a dielectric slab is placed between the plates of capacitors , then
due to polarization, charges appear on the two faces of the slab
and establish another field E1 within the dielectric . This field
will be in a direction opposite to that of E0
Resultant value E=E0-E1
(2)
If σs is the surface charge density on the slab then from (1)
E1= σs / Ɛ0
(3)
From (1)(2)(3)

Various polarization processes:
When the specimen is placed inside a d.c.
electric field, polarization is due to four
types of processes….
1.Electronic polarization
2.Ionic polarization
3.Orientation polarization
4.Space charge polarization
Electronic Polarization
When an EF is applied to an atom, +vely charged
nucleus displaces in the direction of field and ẽ could in
opposite direction. This kind of displacement will produce an
electric dipole with in the atom.
i.e, dipole moment is proportional to the magnitude of field
strength and is given by
e E
or
e   e E
where ‘αe’ is called electronic Polarizability constant
It increases with increase of volume of the atom.
This kind of polarization is mostly exhibited in Monatomic
gases.
e  ____  10-4 0F  m2
He
Ne
Ar
0.18
0.35 1.46
It occurs only at optical frequencies (1015Hz)
It is independent of temperature.
Kr
Xe
2.18 3.54
Expression for Electronic Polarization
Consider a atom in an EF of intensity ‘E’ since the nucleus
(+Ze) and electron cloud (-ze) of the atom have opposite
charges and acted upon by Lorentz force (FL).
Subsequently nucleus moves in the direction of field and
electron cloud in opposite direction.
When electron cloud and nucleus get shifted from their normal
positions, an attractive force b/w them is created and the
separation continuous until columbic force FC is balanced with
Lorentz force FL, Finally a new equilibriums state is
established.
E
+Ze
No field
fig(1)
x
In the presence of field fig (2)
fig(2) represents displacement of nucleus and electron
cloud and we assume that the –ve charge in the cloud
uniformly distributed over a sphere of radius R and the
spherical shape does not change for convenience.
Let σ be the charge density of the sphere
 Ze
4 3
R
3
- Ze represent st he t ot alchargein t hesphere.

T hus the- ve chargein thesphereof radius ' x' is
4
q e   .  .x 3
3
 ze 4
3
 4
.

.
x
3 3
.

R
3

 ze 3
 3 x
R
Now Fc 
1
4 0
.
qe .q p
x2

- - - - - (1)
  ze.x 3 
 z 2e 2 x

ze  

- - - - - (2)
2 
3
3
4 0 x  R 
4 0 R
1
Force experienced by displaced nucleus of Strength E is
FL = Eq = ZeE -----(3)
FL  Fc
 z 2e 2 x
4 0 R 3
 ZeE
- - - - - (4)
 zex
E
3
4 0 R
 zex  zex

3
4 0 R
e
dipole moment
 E
e
 e  4 0 R
3
Hence electronic Polaris ability is directly proportional to cube of the
radius of the atom.
Ionic polarization

The ionic polarization occurs, when atoms form
molecules and it is mainly due to a relative displacement
of the atomic components of the molecule in the
presence of an electric field.

When a EF is applied to the molecule, the positive ions
displaced by X1 to the negative side electric field and
negative ions displaced by X2 to the positive side of
field.

The resultant dipole moment µ = q ( X1 + X2)..
+
+
+
Electric field
_
anion
cat ion
_
_
+
+
_
x1 x2
+
_
_
+
_
+
_
Restoring force constant depend upon the mass of the ion
and natural frequency and is given by
F  eE  m.w02 x
or
eE
x
m.w02
eE 1 1
 x1  x2  2 m  M 
w0
Where ‘M’ mass of anion and ‘m’ is mass of cat ion
 ionic
e2 E 1 1
 e( x1  x2 )  2 m  M 
w0
or  ionic 
ionic
E
2
e 1 1
 2 m  M 
w0
This polarization occurs at frequency 1013 Hz (IR).
It is a slower process compared to electronic polarization.
It is independent of temperature.
Orientation Polarization
It is also called dipolar or molecular polarization. The
molecules such as H2 , N2,O2,Cl2 ,CH4,CCl4 etc., does not carry
any dipole because centre of positive charge and centre of
negative charge coincides. On the other hand molecules like
CH3Cl, H2O,HCl, ethyl acetate ( polar molecules) carries
dipoles even in the absence of electric field.
How ever the net dipole moment is negligibly small since all
the molecular dipoles are oriented randomly when there is no
EF. In the presence of the electric field these all dipoles orient
them selves in the direction of field as a result the net dipole
moment becomes enormous.



It occurs at a frequency 106 Hz to 1010Hz.
It is slow process compare to ionic
polarization.
It greatly depends on temperature.
Expression for orientation polarization
N . o2 ri e.E
Po  N . o ri e
 N . o .E
3k T

o 
o2 ri e
3k T
   el ec   io n ic  o ri  4 o R 3 
e2
w02

1
M

1
m
 3k T
o2 ri
This is called Langevin – Debye equation for total Polaris ability in
dielectrics.
Internal fields or local fields
Local field or internal field in a dielectric is the
space and time average of the electric field
intensity acting on a particular molecule in the
dielectric material.
It is also known as a Microscopic field which
acts at an Atom.
Evaluation of internal field
The internal field is electric field acting at an atom of
solid or liquid dielectric subjected to an external
electric field.
The internal field at the atom site ‘A’ can be made up
of four components E1 ,E2, E3 & E4
Which is known as internal field or Local field.
i.e Ein = E1+E2+E3+E4
+ + + + + + + + + ++
_ _ _ _ _ _ _
+
+
+
+
+
Spherical
+
_
Cavity
+
A
_
_
Spherical
Cavity
_
+ + + +
+
_
_
_
_
+ + +
_ _ _ _ _ _ _ _ _
_
E
Dielectric
material
Field E1:
E1 is the field intensity at A due to the charge density
on the plates
From Field theory
D
E1 
0
When dielectric medium is polarized due to external
Electric field E, the displacement vector D is given by,
D
 0E  P
0E  P
By equating these two equations… E 
1
0
P
..........(1)
Deviding the above equation by  0 E1  E 
0
Field E2:
E2 is the field intensity at A due to the charge density
induced on the two sides of the dielectric due to the
Polarization.
E2 
P
0
...........(2)
Field E3:
E3 is the field due to the dipoles within the cavity which
depends on the crystal structure. Here we have considered
for the cubic structure so..
E3  0...........(3)
+ +
+
+
+
+
+
+
+
+
A
_
_
 d
_
E
dA
+
+
_
r
_
_
r
R
p
_
_
_
_
_
_
q
Field E4:
1.This is due to polarized charges on the surface of
the spherical cavity.
dA  2 . pq.qR
dA  2 .r sin  .rd
dA  2 .r sin d
2
Where dA is Surface area between θ & θ+dθ…
2.The total charge present on the surface area dA is…
dq = ( normal component of polarization ) X ( surface
area )
dq  p cos  dA
dq  2r p cos . sin  .d
2
3.The field due to this charge at A, denoted by dE4 is given by
1
dq
dE4 
4 0 r 2
The field in θ = 0 direction
dq cos
dE4 
4 0
r2
1
1
2
dE4 
(2r p cos . sin  .d ) cos
2
4 0 r
P
2
dE4 
cos  . sin  .d
2 0

4.Thus the total field E4
due to the charges on the
surface of the entire
cavity is
E4 
 dE
4
0



0
P
cos2  . sin  .d
2 0
P

2 0

2
cos
 . sin  .d

0
let..x  cos  dx   sin d
P

2 0
1
2
x
 .dx
1
 P x 3 1
 P 11

( )1 
(
)
2 0 3
2 0
3
P
E4 
3 0
The internal field or Lorentz field can be written as
Ei  E1  E2  E3  E4
p
p
p
Ei  ( E  )   0 
o o
3 o
p
Ei  E 
3 o
The above equation is also known as lorentz relation. So it
Can be seen that local or microscopic field is larger than the
macroscopic field E by an additional factor p .
3 o
Classius – Mosotti relation:
Consider a dielectric material having cubic structure
, and assume ionic Polarizability & Orientational
polarizability are zero..
i  0  0
polarization..P  N
P  N e Ei ......where.,    e Ei
P
where., Ei  E 
3 0
P  N e Ei
P
P  N e ( E 
)
3 0
P
P  N e E  N e
3 0
P
P  N e
 N e E
3 0
N e
P (1 
)  N e E
3 0
N e E
P
...................(
1)
N e
(1 
)
3 0
W e known t hatt hepolarizaton
i vect or
P   0 E ( r  1)............(2)
from eq n s (1) & ( 2)
N e E
  0 E ( r  1)
N e
(1 
)
3 0
1
N e
N e E

3 0
 0 E ( r  1)
1
N e
N e E

3 0
 0 E ( r  1)
1
N e
N e

3 0
 0 ( r  1)
1
N e
3
(1 
)
3 0
 r 1
N e
1

3
3 0
(1 
)
 r 1
N e
 1
 r
...... Classius Mosot t irelat ion
3 0
r  2
TYPES OF DIELECTRIC MATERIAL





Dielectric material can be solid, liquid or gas.
High vacuum can also be used as a dielectric.
Solid dielectrics are most commonly use like glass,
rubber, mica etc..
As a liquid dielectric material Transformer oil, cable
oil, Capacitor oil, Vegetable oil etc can be used.
Gaseous dielectric materials are used for both as
insulators and
also as a cooling agents.
For example: Air, Hydrogen, nitrogen, Helium,
Sulphur- dioxide, Propen, methane etc..
1) Solid Dielectric Material:
I) Mica: It is inorganic mineral material made up of silicate of
aluminium with silicate of soda, potash and magnesia.
It is rigid, tough and strong. It has high dielectric strength
and is not affected by moisture.
It is widely used in irons, hot plates and toasters.
II) Glass: It is inorganic material made by the fusion of different
oxides like SiO2, ZnO and MgO.
It is Brittle and hard material and has good dielectric strength
It is mostly used in the capacitors. Also used as dielectric tubes
in radios and television.
III) Asbestos: It is naturally occurring material. In general it
consist of magnesium silicate.
It has low dielectric strength. It is used as insulating material
to prevent current flow in the outer body. It is widely used in
the form of the paper, tap, cloth etc.
IV) Rubber: It is organic polymer. It may be natural or synthetic.
It has good electrical and thermal properties and also
it has good tensile strength.
It is used for the insulating materials on electrical wires.
V) Ceramics: They are generally non-matalic inorganic compounds
such as silicates, aluminates, oxides, carbides, borides etc.
Ceramics can be classified as:
clay products, refractories, and glasses.
Ceramics are hard, strong and dense. They have exellent
dielectric and mechanical properties.
They widely used as insulators in switches, plug holders etc.
They are also used as dielectric in capacitors.
2) Liquid Dielectric Material:
I) Mineral Insulating Oil : These oils are obtained from crude
petroleum. These have good thermal stability.
They are used in Transformers as cooling and insulating
material and also in Capacitors.
Transformer oil, cable oil and capacitor oil belong to the
category of mineral insulating oil.
II) Synthetic Insulating Oil : Askarels, aroclors, sovol and
savtol are a few synthetic oils that are widely used.
They are very much resistant to fire hazards.
Due to longer life and safety in operating condition, these
oils are used as coolants and insulators in high voltage
transformers in place of Transformer oil.
II) Miscellaneous Insulating Oil :
Vaseline, vegetable oils and silicon liquid belongs to these
category. Silicon liquids has thermal stability upto 200 C and
are very costly.
The dielectric strength of these oils are same as mineral oils so
they are also used in the H.V transformers.
3) Gaseous Dielectric Material:
I)
Air : It is naturally available dielectric material.
Dielectric loss is practically zero. The dielectric constant of air
linearly increase with increase in pressure.
It is used as dielectrics in air condensers.
It can be used as an insulator only in low voltage
applications.
II) Nitrogen : It is important gaseous dielectric material. It prevent
oxidation.
It is used in cables and capacitors under pressure.
III) Sulphure Hexafluoride:
It is formed by burning of Sulphure in fluorine atmosphere.
It has superior cooling properties than air and nitrogen.
It is used in the transformers, electrical switches, voltage
stabilizer and X-ray apparatus.
IV) Inert Gases: They are used in electronic tubes and discharge
tubes as insulators.
Properties of Good Dielectric Material
 It should have high resistivity to reduce the leakage current.
 It should have high dielectric strength.
 It should have high mechanical strength.
 It should have high fire resistance.
 It should have low thermal expansion.
 It should have high thermal conductivity.
 It should have low dielectric loss.
 It should have low water absorption quality.
Applications of Dielectrics
1. Capacitors
2. Transformers
3. Polymeric film
4. Electrolytic
5. Power and Distribution transformers
6. Other applications