DielectricsDielectricsUnit – 1Unit – 1

Sub.- PhysicsSub.- Physics

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 negative A 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 store All 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…

Xq -q

Introduction

POLARISATION OF DIELECRICSPOLARISATION OF DIELECRICS

When we are applying external electric field, it causes the When we are applying external electric field, it causes the electron cloud to move away. Thus the centroides of the positive electron cloud to move away. Thus the centroides of the positive and negative charges now no longer coincides and as a result of 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 that an electric dipole is induced in the atom. Thus, atom is said to be polarizeto be polarized.d.

Polarization : the process of creating or inducing dipoles in a Polarization : the process of creating or inducing dipoles in a dielectric medium by an external field.dielectric medium by an external field.

On the basis on that dielectrics are the material that have either On the basis on that dielectrics are the material that have either permanent diploes or induced in the presence of external permanent diploes or induced in the presence of external electric field .electric field .

They are classified into two categories (1) Non polar (2)polarThey are classified into two categories (1) Non polar (2)polar

DielectricsDielectrics Non Polar Dielectrics : Non Polar Dielectrics : There is no permanent There is no permanent

dipole existence in the absence of an electric field .dipole existence in the absence of an electric field . Centroids of positive and negative charges of molecules Centroids of positive and negative charges of molecules

constituting the dielectric material coincide .constituting the dielectric material coincide . Examples :HExamples :H2, 2, NN2, 2, OO2, 2, COCO 2 2

Polar Dielectrics :Polar Dielectrics : there is permanent dipole exists there is permanent dipole exists even in the absence of an electric field .even in the absence of an electric field .

Centroids of posistive and negative charges of molecules Centroids of posistive and negative charges of molecules constituting the dielectric material do not coinside even in the constituting the dielectric material do not coinside even in the absence of electric field absence of electric field

Examples : HCL , CO Examples : HCL , CO

+

Electric field

Dielectric atom

+

+

+

+

+

+

+

+

_

__

_

_

_

_

__

dipole

Dielectric Constant Dielectric Constant Dielectric Constant is the ratio between the Dielectric Constant is the ratio between the permittivity of the medium to the permittivity of permittivity of the medium to the permittivity of free space.free space.

its value changes widely from material to material its value changes widely from material to material For vacuum =1For vacuum =1 For all other dielectric it is Ɛr >1.For all other dielectric it is Ɛr >1. So, we can write Ɛr=1+So, we can write Ɛr=1+χχe , e , χχe is susceptibilitye is susceptibility

The characteristics of a dielectric material are The characteristics of a dielectric material are determined by the dielectric constant and it has determined by the dielectric constant and it has no units.no units.

0 r

Electric field Electric field The region surrounded by charged body is always under The region surrounded by charged body is always under

stress because of electrostatic charge . If a small charge q or 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 is placed in this region ,then the charge q or a charged body will experienced a force according Coulomb a charged body will experienced a force according Coulomb s law . This stressed region around charged body is called s law . This stressed region around charged body is called electric field . electric field .

Electric field at a point define as the force that acts on a unit Electric field at a point define as the force that acts on a unit positive charge placed at that point thus E.positive charge placed at that point thus E.

According to coulomb law when two point charges Q1 and According to coulomb law when two point charges Q1 and Q2 are separated by a distance r, the force of attraction or Q2 are separated by a distance r, the force of attraction or repulsion between two charges is given by repulsion between two charges is given by

Electric PolarizationElectric Polarization

The process of producing electric dipoles by an electric field is The 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 called The induced dipole moment per unit electric field is called Polarizability.Polarizability.The induced dipole moment is proportional to the intensity of The induced dipole moment is proportional to the intensity of the electric field.the electric field.

constant lity polarizabi

E

E

Electric flux ɸElectric flux ɸ

(1) Number of lines of force that pass through a surface placed (1) Number of lines of force that pass through a surface placed in the vector field .in the vector field .

(2) As the product of surface area and the components of the (2) As the product of surface area and the components of the electric field normal to the surface electric field normal to the surface

a unit charge is supposed to emanate one flux.a unit charge is supposed to emanate one flux. In the case of an isolated charge q coulomb the flux is In the case of an isolated charge q coulomb the flux is

q=ɸ q=ɸ Is independent of of nature of medium.Is independent of of nature of medium.

Polarization vectorPolarization vector

Definition: Definition: induced dipole moment per unit induced dipole moment per unit volume of dielectric mediumvolume of dielectric medium..

P is vector quantity and its direction is along P is vector quantity and its direction is along the direction of applied field .If m is the the direction of applied field .If m is the average induced dipole moment per unit average induced dipole moment per unit molecule and N is the number of molecule per molecule and N is the number of molecule per unit volume then polarization is given byunit volume then polarization is given by

P=NµP=Nµ

V=At ,where A is the area of slab

Thus ,the polarization is also defined as induced surface charge per unit areaBut 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

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) -- E D 00

(3) -- P E D i.e, 0

(2) -- E D

P.)1(

P E ) - .( (or)

P E ) - (

P E E

0

00r

0

0

Er

Using equations 2 & 3 we get

Electric susceptibilityElectric susceptibility

The polarization vector P is proportional to the total electric The polarization vector P is proportional to the total electric flux density and direction of electric field.flux density and direction of electric field.

Therefore the polarization vector can be written as, Therefore the polarization vector can be written as,

In a large number of dielectrics it is Found thatIn a large number of dielectrics it is Found that

polarization is directly Proportional to the polarization is directly Proportional to the

external applied Field E.external applied Field E.

Def. The ratio of polarization to net electric field asDef. The ratio of polarization to net electric field as

Given by the induced charge on the surface of Given by the induced charge on the surface of

Dielectric is called susceptibility.Dielectric is called susceptibility. 1

)1(

0

0

0

0

re

r

e

e

E

E

E

P

EP

Relation between polarization P, susceptibity Relation between polarization P, susceptibity χχ and dielectric constant Ɛ and dielectric constant Ɛrr

Lets us consider a parallel plate capacitor between which an Lets us consider a parallel plate capacitor between which an electric field Ɛelectric field Ɛ0.0.

If If σσ is the surface charge density then gauss law. is the surface charge density then gauss law.

E=E=σσ/Ɛ/Ɛ0 0 (1)(1)

if a dielectric slab is placed between the plates of capacitors , then due 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 to polarization, charges appear on the two faces of the slab and establish another field Eestablish another field E1 1 within the dielectric . This field will be in within the dielectric . This field will be in a direction opposite to that of Ea direction opposite to that of E00

Resultant value E=EResultant value E=E00-E-E1 1 (2)(2)

If If σσs s is the surface charge density on the slab then from (1)is the surface charge density on the slab then from (1)

EE11== σ σs /s / Ɛ Ɛ0 0 (3)(3)

From (1)(2)(3)From (1)(2)(3)

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 types electric 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 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

e

e

e

or

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.

10 ____ 2-40 mFe

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 (1015Hz) It is independent of temperature.

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.

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.

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

Let σ be the charge density of the sphere

sphere. in the charge total therepresents Ze-

34 3R

Ze

(1)-----

...

.3

4.q

is x'' radius of sphere in the charge ve- theThus

33

334

334

3e

xR

ze

xR

ze

x

(2)----- 4

.

4

1..

4

1F Now

30

22

3

3

20

20

c R

xezze

R

xze

xx

qq pe

Force experienced by displaced nucleus of Strength E is FL = Eq = ZeE -----(3)

ee

cL

zex

R

zex

ER

zex

R

xez

FF

moment dipole E

4

4

(4)----- ZeE 4

30

30

30

22

304 Re

Hence electronic Polaris ability is directly proportional to cube of the radius of the atom.

Ionic polarizationIonic polarization

The ionic polarization occurs, when atoms form The ionic polarization occurs, when atoms form molecules and it is mainly due to a relative displacement molecules and it is mainly due to a relative displacement of the atomic components of the molecule in the of 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 ions When a EF is applied to the molecule, the positive ions displaced by Xdisplaced by X1 1 to the negative side electric field and to the negative side electric field and

negative ions displaced by Xnegative ions displaced by X2 2 to the positive side of field.to the positive side of field.

The resultant dipole moment The resultant dipole moment µ = q ( Xµ = q ( X11 + X + X22)..)..

Electric field+

+

+

+

+

+

+

+

_

__

_

_

_

_

_

1x 2x

anioncat ion

Restoring force constant depend upon the mass of the ion and natural frequency and is given by

Mmw

eExx

wm

eEx

xwmeEF

1120

21

20

20

.

or

.

Where ‘M’ mass of anion and ‘m’ is mass of cat ion

Mmionic

ionic

Mmionic

w

e

E

w

Eexx

1120

2

1120

2

21

or

)e(

This polarization occurs at frequency 1013 Hz (IR).

It is a slower process compared to electronic polarization.

It is independent of temperature.

Orientation PolarizationIt 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.

kTw

eR

kT

ENkT

ENNP

orimMooriionicelec

orieo

oorie

orieo

34

3

..3

...

211

20

23

2

2

Expression for orientation polarization

This is called Langevin – Debye equation for total Polaris ability in dielectrics.

Internal fields or local fieldsInternal fields or local fields

Local field or internal field in a dielectric is the space and Local field or internal field in a dielectric is the space and time average of the electric field intensity acting on a time average of the electric field intensity acting on a particular molecule in the dielectric material. particular molecule in the dielectric material.

It is also known as a Microscopic field which acts at an Atom.It is also known as a Microscopic field which acts at an Atom.

Evaluation of internal fieldEvaluation of internal field

The internal field is electric field acting at an atom of The internal field is electric field acting at an atom of solid or liquid dielectric subjected to an external solid or liquid dielectric subjected to an external electric field.electric field.The internal field at the atom site ‘A’ can be made up The internal field at the atom site ‘A’ can be made up of four components Eof four components E1 1 ,E,E22, E, E3 3 & E& E44

Which is known as internal field or Local field.Which is known as internal field or Local field.

i.e Ei.e Ein in = E1+E2+E3+E4= E1+E2+E3+E4

Spherical Cavity

+ ++ ++ + + + + ++

_ _ _ _ _ _ _ __

E

Dielectricmaterial

Spherical Cavity

A

__

_

__ ___

+ + + + + ++

+

+ ++

+ ++

+

_

_

___

___

Field EField E11::

EE1 1 is the field intensity at A due to the charge density is the field intensity at A due to the charge density

on the plateson the plates

)1(..........0

1

0

01

0

01

PEE

PEE

PED

DE

When dielectric medium is polarized due to external Electric field E, the displacement vector D is given by,

From Field theory

By equating these two equations…

Deviding the above equation by 0

Field EField E22::

EE22 is the field intensity at A due to the charge density induced is the field intensity at A due to the charge density induced

on the two sides of the dielectric due to the Polarization. on the two sides of the dielectric due to the Polarization.

)2.(..........0

2 P

E

Field EField E33::

EE33 is the field due to the dipoles within the cavity which is the field due to the dipoles within the cavity which

depends on the crystal structure. Here we have considered depends on the crystal structure. Here we have considered for the cubic structure so..for the cubic structure so..

)3.(..........03 E

+ +

E

d r

p q

R

dA

r

A

+

+

+

+ ++

+

+++

_

__

___

__ _

__

_

Field EField E44::

1.This is due to polarized charges on the surface of 1.This is due to polarized charges on the surface of the spherical cavity.the spherical cavity.

Where dA is Surface area between Where dA is Surface area between θθ & & θθ+d+dθθ……

drdA

rdrdA

qRpqdA

sin.2

.sin.2

..2

2

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 ( surface dq = ( normal component of polarization ) X ( surface area )area )

dprdq

dApdq

.sin.cos2

cos2

3.The field due to this charge at A, denoted by dE3.The field due to this charge at A, denoted by dE4 4 is given by is given by

20

4 4

1

r

dqdE

The field in The field in θθ = 0 = 0 directiondirection 20

4

cos

4

1

r

dqdE

dP

dE

dprr

dE

.sin.cos2

cos).sin.cos2(4

1

2

04

22

04

4.Thus the total field E4.Thus the total field E44 due to the charges on the due to the charges on the surface of the entire surface of the entire cavity is cavity is

04

0

11

3

0

1

1

2

0

0

2

0

0

2

0

0

44

3

)3

11(

2)

3(

2

.2

sincos..

.sin.cos2

.sin.cos2

PE

PxP

dxxP

ddxxlet

dP

dP

dEE

The internal field or Lorentz field can be written asThe internal field or Lorentz field can be written as

oi

oooi

i

pEE

pppEE

EEEEE

3

30)(

4321

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 .

o

p

3

Classius – Mosotti relation:Classius – Mosotti relation:

Consider a dielectric material having cubic Consider 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

PEEwhere

EwhereENP

NPonpolarizati

i

ieie

i

)1.........(..........)

31(

)3

1(

3

3

)3

(

0

0

0

0

0

e

e

ee

ee

ee

e

ie

NEN

P

ENN

P

ENP

NP

PNENP

PENP

ENP

relation Mosotti Classius......2

1

3

)1

31(

1

3

)1

31(

31

)1(31

)1(31

)1(31

)1()

31(

)2(&)1(eq from

)2...().........1(

on vector polarizati theknown that We

0

0

0

00

00

00

0

0

n

0

r

re

r

e

r

e

r

ee

r

ee

r

ee

re

e

r

N

N

N

NN

E

ENN

E

ENN

EN

EN

s

EP

TYPES OF DIELECTRIC MATERIALTYPES OF DIELECTRIC MATERIAL Dielectric material can be solid, liquid or gas. Dielectric material can be solid, liquid or gas. High vacuum can also be used as a dielectric. High vacuum can also be used as a dielectric. Solid dielectrics are most commonly use like glass, Solid dielectrics are most commonly use like glass,

rubber, mica etc.. rubber, mica etc.. As a liquid dielectric material Transformer oil, cableAs a liquid dielectric material Transformer oil, cable

oil, Capacitor oil, Vegetable oil etc can be used.oil, Capacitor oil, Vegetable oil etc can be used. Gaseous dielectric materials are used for both as Gaseous dielectric materials are used for both as

insulators andinsulators and

also as a cooling agents.also as a cooling agents.

For example: Air, Hydrogen, nitrogen, Helium, For example: Air, Hydrogen, nitrogen, Helium, Sulphur- dioxide, Propen, methane etc..Sulphur- dioxide, Propen, methane etc..

1) Solid Dielectric Material:1) Solid Dielectric Material:I) I) MicaMica: It is inorganic mineral material made up of silicate of : It is inorganic mineral material made up of silicate of aluminium with silicate of soda, potash and magnesia.aluminium with silicate of soda, potash and magnesia.

It is rigid, tough and strong. It has high dielectric strength It is rigid, tough and strong. It has high dielectric strength and is not affected by moisture. and is not affected by moisture.

It is widely used in irons, hot plates and toasters. It is widely used in irons, hot plates and toasters.

II) II) GlassGlass: It is inorganic material made by the fusion of different: It is inorganic material made by the fusion of different oxides like SiO2, ZnO and MgO.oxides like SiO2, ZnO and MgO.

It is Brittle and hard material and has good dielectric strengthIt is Brittle and hard material and has good dielectric strength It is mostly used in the capacitors. Also used as dielectric It is mostly used in the capacitors. Also used as dielectric tubestubes

in radios and television.in radios and television.

III) III) AsbestosAsbestos: It is naturally occurring material. In general it : It is naturally occurring material. In general it consist of magnesium silicate.consist of magnesium silicate. It has low dielectric strength. It is used as insulating materialIt has low dielectric strength. It is used as insulating material to prevent current flow in the outer body. It is widely used into prevent current flow in the outer body. It is widely used in the form of the paper, tap, cloth etc.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