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 ionic polarization occurs, when atoms formThe ionic polarization occurs, when atoms form
molecules and it is mainly due to a relative displacementmolecules and it is mainly due to a relative displacement
of the atomic components of the molecule in theof the atomic components of the molecule in the
presence of an electric field.presence of an electric field.
When a EF is applied to the molecule, the positive ionsWhen a EF is applied to the molecule, the positive ions
displaced by Xdisplaced by X11 to the negative side electric field andto the negative side electric field and
negative ions displaced by Xnegative ions displaced by X22 to the positive side of field.to the positive side of field.
The resultant dipole momentThe resultant dipole moment µ = q ( Xµ = q ( X11 + X+ X22)..)..
19. 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
.
+=+∴
=
==
20. 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.
21. Orientational 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.
22. It occurs at a frequency 106
Hz to 1010
Hz.
It is slow process compare to ionic
polarization.
It greatly depends on temperature.
24. Internal fields or local fieldsInternal fields or local fields
Local field or internal field in a dielectric is theLocal field or internal field in a dielectric is the
space and time average of the electric fieldspace and time average of the electric field
intensity acting on a particular molecule in theintensity acting on a particular molecule in the
dielectric material.dielectric material.
25. Evaluation of internal fieldEvaluation of internal field
Consider a dielectric be placed between theConsider a dielectric be placed between the
plates of a parallel plate capacitor and let thereplates of a parallel plate capacitor and let there
be an imaginary spherical cavity around thebe an imaginary spherical cavity around the
atom A inside the dielectric.atom A inside the dielectric.
The internal field at the atom site ‘A’ can beThe internal field at the atom site ‘A’ can be
made up of four components Emade up of four components E11 ,E,E22, E, E33 & E& E44..
27. Field EField E11::
EE11 is the field intensity at A due to the charge densityis the field intensity at A due to the charge density
on the plateson the plates
)1(..........
0
1
0
0
1
0
0
1
ε
ε
ε
ε
ε
P
EE
PE
E
PED
D
E
+=
+
=
+=
=
28. Field EField E22::
EE22 is the field intensity at A due to the chargeis the field intensity at A due to the charge
density induced on the two sides of the dielectric.density induced on the two sides of the dielectric.
)2.(..........
0
2
ε
P
E
−
=
Field EField E33::
EE33 is the field intensity at A due to the atomsis the field intensity at A due to the atoms
contained in the cavity, we are assuming a cubiccontained in the cavity, we are assuming a cubic
structure, so Estructure, so E33 = 0.= 0.
29. + +
E
θ θd r
p q
R
dA
r
A
+
+
+
+ +
+
+
+
++
_
_
_
_
_
_
_
_ _
_
_
_
30. Field EField E44::
1.This is due to polarized charges on the surface of1.This is due to polarized charges on the surface of
the spherical cavity.the spherical cavity.
Where dA is Surface area betweenWhere dA is Surface area between θθ && θθ+d+dθθ……
θθπ
θθπ
π
drdA
rdrdA
qRpqdA
sin.2
.sin.2
..2
2
=
=
=
31. 2.The total charge present on the surface area dA is…2.The total charge present on the surface area dA is…
dq = ( normal component of polarization ) X ( surfacedq = ( normal component of polarization ) X ( surface
area )area )
θθθπ
θ
dprdq
dApdq
.sin.cos2
cos
2
=
×=
32. 3.The field due to this charge at A, denoted by dE3.The field due to this charge at A, denoted by dE44 is given byis given by
2
0
4
4
1
r
dq
dE
πε
=
The field inThe field in θθ = 0= 0 directiondirection 2
0
4
cos
4
1
r
dq
dE
θ
πε
=
θθθ
ε
θθθθπ
πε
d
P
dE
dpr
r
dE
.sin.cos
2
cos).sin.cos2(
4
1
2
0
4
2
2
0
4
=
=
33. 4.Thus the total field E4.Thus the total field E44
due to the charges on thedue to the charges on the
surface of the entiresurface of the entire
cavity iscavity is
0
4
0
1
1
3
0
1
1
2
0
0
2
0
0
2
0
0
44
3
)
3
11
(
2
)
3
(
2
.
2
sincos..
.sin.cos
2
.sin.cos
2
ε
εε
ε
θθθ
θθθ
ε
θθθ
ε
π
π
π
P
E
PxP
dxx
P
ddxxlet
d
P
d
P
dEE
=
−−−
⇒
−
=
=
−=→=
=
=
=
−
−
∫
∫
∫
∫
34. The internal field or Lorentz field can be written asThe internal field or Lorentz field can be written as
o
i
ooo
i
i
p
EE
ppp
EE
EEEEE
ε
εεε
3
3
0)(
4321
+=
++−+=
+++=
35. Classius – Mosotti relation:Classius – Mosotti relation:
Consider a dielectric material having cubicConsider a dielectric material having cubic
structure , and assume ionic Polarizability &structure , and assume ionic Polarizability &
Orientational polarizability are zero..Orientational polarizability are zero..
0
0
3
.,
.,......
..
0
ε
αµα
µ
αα
P
EEwhere
EwhereENP
NPonpolarizati
i
ieie
i
+=
==
=
==
38. Ferro electric materials or Ferro electricityFerro electric materials or Ferro electricity
Ferro electric crystals exhibit spontaneousFerro electric crystals exhibit spontaneous
polarization I.e. electric polarization with outpolarization I.e. electric polarization with out
electric field.electric field.
Ferro electric crystals possess high dielectricFerro electric crystals possess high dielectric
constant.constant.
each unit cell of a Ferro electric crystal carrieseach unit cell of a Ferro electric crystal carries
a reversible electric dipole moment.a reversible electric dipole moment.
Examples: Barium Titanate (BaTiOExamples: Barium Titanate (BaTiO33) , Sodium) , Sodium
nitrate (NaNOnitrate (NaNO33) ,Rochelle salt etc..) ,Rochelle salt etc..
39. Piezo- electricityPiezo- electricity
The process of creating electric polarization by mechanicalThe process of creating electric polarization by mechanical
stress is called as piezo electric effect.stress is called as piezo electric effect.
This process is used in conversion of mechanical energy intoThis process is used in conversion of mechanical energy into
electrical energy and also electrical energy into mechanicalelectrical energy and also electrical energy into mechanical
energy.energy.
According to inverse piezo electric effect, when an electricAccording to inverse piezo electric effect, when an electric
stress is applied, the material becomes strained. This strain isstress is applied, the material becomes strained. This strain is
directly proportional to the applied field.directly proportional to the applied field.
Examples: quartz crystal , Rochelle salt etc.,Examples: quartz crystal , Rochelle salt etc.,
Piezo electric materials or peizo electric semiconductors suchPiezo electric materials or peizo electric semiconductors such
as Gas, Zno and CdS are finding applications in ultrasonicas Gas, Zno and CdS are finding applications in ultrasonic
amplifiers.amplifiers.
