2. Dielectrics are the materials having electric dipole moment permantly.Dielectrics are the materials having electric dipole moment permantly.
Dipole:Dipole: A dipole is an entity in which equal positive and negativeA dipole is an entity in which equal positive and negative
charges are separated by a small distance..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
All dielectrics are electrical insulators and they are mainly used to storeAll dielectrics are electrical insulators and they are mainly used to store
electrical energy.electrical energy.
Ex: Mica, glass, plastic, water & polar molecules…Ex: Mica, glass, plastic, water & polar molecules…
X
q -q
Introduction
4. Dielectric ConstantDielectric Constant
Dielectric Constant is the ratio between theDielectric Constant is the ratio between the
permittivity of the medium to the permittivity ofpermittivity of the medium to the permittivity of
free space.free space.
The characteristics of a dielectric material areThe characteristics of a dielectric material are
determined by the dielectric constant and it has nodetermined by the dielectric constant and it has no
units.units.
0ε
ε
ε =r
5. Electric PolarizationElectric Polarization
The process of producing electric dipoles by an electric field isThe process of producing electric dipoles by an electric field is
called polarization in dielectrics.called polarization in dielectrics.
Polarizability:Polarizability:
The induced dipole moment per unit electric field is calledThe induced dipole moment per unit electric field is called
Polarizability.Polarizability.
The induced dipole moment is proportional to the intensity of theThe induced dipole moment is proportional to the intensity of the
electric field.electric field.
Is a Polarizability constantIs a Polarizability constant
constantlitypolarizabi→
=
∝
α
αµ
µ
E
E
6. Polarization vector:Polarization vector:
The dipole moment per unit volume of the dielectricThe dipole moment per unit volume of the dielectric
material is called polarization vector.material is called polarization vector.
V
xq
P
n
i
ii∑=
= 1
7. 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
At the same point in a medium is given by
As the polarization measures the additional flux density arising
from the presence of material as compared to free space
(1)--ED 00 >= ε
(3)--PEDi.e, 0 >+= ε
(2)--ED >= ε
9. Electric susceptibility:Electric susceptibility:
The polarization vector P is proportional to theThe polarization vector P is proportional to the
total electric flux density and direction of electrictotal electric flux density and direction of electric
field.field.
Therefore the polarization vector can be writtenTherefore the polarization vector can be written
1
)1(
0
0
0
0
−=
−
=
=
=
re
r
e
e
E
E
E
P
EP
εχ
ε
εε
ε
χ
χε
10. Various polarization processes:Various polarization processes:
When the specimen is placed inside a d.c.When the specimen is placed inside a d.c.
electric field, polarization is due to four typeselectric field, polarization is due to four types
of processes….of processes….
1.Electronic polarization1.Electronic polarization
2.Ionic polarization2.Ionic polarization
3.Orientation polarization3.Orientation polarization
4.Space charge polarization4.Space charge polarization
11. 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
e
e
e
or
αµ
µ
=
∞
where ‘αe’ is called electronic Polarizability constant
12. It increases with increase of volume of the atom.
This kind of polarization is mostly exhibited in Monatomic
gases.
10____ 2-40
mFe −×=α
HeHe NeNe ArAr KrKr XeXe
0.180.18 0.350.35 1.461.46 2.182.18 3.543.54
It occurs only at optical frequencies (1015
Hz)
It is independent of temperature.
13. 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
seperation continuous until columbic force FC is balanced with
Lorentz force FL, Finally a new equilibriums state is
established.
14. 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.
+Ze
R
No field fig(1)
x
R
In the presence of field fig (2)
E
15. Let σ be the charge density of the sphere
sphere.in thechargetotaltherepresentsZe-
3
4 3
R
Ze
π
σ
−
=
( )
(1)-----
..
.
.
3
4
.q
isx''radiusofspherein thechargeve-theThus
3
3
3
3
4
3
3
4
3
e
x
R
ze
x
R
ze
x
−
=
−
⇒
⇒
π
π
πσ
( ) (2)-----
4
.
4
1.
.
4
1
FNow 3
0
22
3
3
2
0
2
0
c
R
xez
ze
R
xze
xx
qq pe
πεπεπε
−
=
−
==
16. Force experienced by displaced nucleus in EF of Strength E
is FL = Eq = ZeE -----(3)
ee
cL
zex
R
zex
E
R
zex
R
xez
FF
ααπε
πε
πε
momentdipole
E
4
4
(4)-----ZeE
4
3
0
3
0
3
0
22
=
−
=
−
=
−
=
−
=
3
04 Re πεα =∴
Hence electronic Polaris ability is directly proportional to cube of the
radius of the atom.
17. Ionic polarizationIonic polarization
The dielectric material having ionic bonds such as Nacl, show ionic
polarization. Polarization in such ionic crystals arises on account of the ions
displaced from their equilibrium positions by the force of the applied electric
field.
The induced dipole moment due to ionic polarization is proportional to the
applied electric field, i.e.
For the most of the materials, the ionic polarisability is very less than the
electronic polarisability.
ENp
Ep
ii
i
α=
∝
18. Restoring force constant depend upon the mass of the ion and natural frequency
and is given by,
[ ]Mm
w
eE
xx
wm
eE
x
xwmeEF
11
2
0
21
2
0
2
0
.
or
.
+=+∴
=
==
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 displacement between ions causes an increase or decrease in distance
between the atoms, depending on the location of the ion pairs.
The resultant dipole moment µ = e ( X1 + X2)..
19. Where ‘M’ mass of anion and ‘m’ is mass of cat ion
[ ]
[ ]Mm
ionic
ionic
Mmionic
w
e
E
w
Ee
xx
11
2
0
2
11
2
0
2
21
or
)e(
+⇒=
+=+=∴
µ
α
µ
This polarization occurs at frequency 1013
Hz (IR).
It is a slower process compared to electronic polarization.
It is independent of temperature.
20. Orientation Polarization
Orientation polarization occurs in polar substances. These substances exhibit dipole
moment even in the absence of external electric field. Due to random orientations of
dipoles or molecules, the net dipole moment is zero. The random orientation of
dipoles is shown in Figure (a).
When such materials are subjected to an external electric field, the permanent
molecular dipoles rotate about their axis of symmetry to align with the applied field.
The aligned dipoles along the direction of field are shown in Figure (b).
In electronic and ionic polarization processes, the force due to the externally applied
field is balanced by elastic binding forces, but no such forces exist for orientation
polarization. At thermal equilibrium with no external electric field, the permanent
dipoles contribute no net polarization since they are randomly oriented.
21. kT
orie
o
3
2
µ
α =
Expression for orientation polarization
With the application of external electric field, dipole alignment is
largely offset by thermal agitation. The orientation polarization is
strongly temperature dependent; it decreases with increase in the
temperature.
22. Sometimes due to the application of electric field to the dielectric
material, charges accumulate at the electrodes or at the interface due
to sudden change in conductivity shown in Fig. (a) and (b). Under the
influence of applied electric field, the ions are diffused over
appreciable distance, due to which redistribution of charges in the
dielectric medium takes place. The tendency of redistribution of
charges in the dielectric medium in the presence of an external
electric field is known as space charge polarization.
Space Charge Polarization
23. [ ]
kTw
e
R ori
mMooriionicelec
3
4
2
11
2
0
2
3 µ
πεαααα +++=++=∴
This is called Langevin – Debye equation for Total Polarizability
in dielectrics.
Total Polarization
Although the dielectric materials are classified in different groups
based in the their mode of polarization, if a material can experience
all forms of polarization, then its total polarizability can be given as
the sum of electronic, ionic, and orientation polarizability, i.e.
Here the contribution due to space charge polarization is not considered
because it is almost negligible in most common dielectrics. In the above
equations, first two terms on the right hand side are the functions of
molecular structure of the dielectric material which are usually independent
of temperature. Due to this reason, they are also known as deformation
polarisability.
24. Classius – Mosotti relation:Classius – Mosotti relation:
0
0
3
.,
.,......
..
0
ε
αµα
µ
αα
P
EEwhere
EwhereENP
NPonpolarizati
i
ieie
i
+=
==
=
==
Classius-Mosotti equation gives the relation between macroscopic dielectric
constant and microscopic polarizability of non polar dielectric materials.
Consider a dielectric material having cubic structure , and assume ionic
Polarizability & Orientational polarizability are zero.
