Course: B.Tech

Subject: Engineering Physics

Unit: I

Chapter: 2

1

Dielectrics are the materials having electric dipole moment permanently.

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 coulmb.m

All dielectrics are electrical insulators and they are mainly used to store electrical energy.

Ex: Mica, glass, plastic, water & polar molecules…

Xq -q

Introduction

The relative permittivity(εr) is often known as

dielectric const. of medium it can given by,

εr=ε/ε0

Dielectric constant is ratio of permittivity of medium

to permittivity of free space.

The value of capacitance of capacitor is given by,

C0=εrε0A/d

By this eqn we can say that high εr increases

capacity of capacitor.

Dielectric const. of medium

Polar and Nonpolarized MoleculesNon-polar Molecules : The Dielectric material in which

there is no permanent dipole existence in absence of an external field is …..

O=O N N Cl-Cl F-F Br-Br I-I

2 – Compounds made of molecules which are symmetrically shaped

carbon tetra fluoride CF4

propaneC3H8

methane CH4

carbon tetra fluoride CCl4,

carbon dioxideO=C=O

Polar Molecules The Dielectric material in which there is

permanent dipole existence even in absence of an external field is …..

HClhydrogen chloride

carbon monoxideC O

2 – molecules with O, N, or OH at one end – asymmetrical e.g.; CH2Cl2,CH3Cl

waterH2O

unbounded electron pairs bend the molecule

ammonianitrogen trihydrideNH3

alcoholsmethanolCH3OH

Learning Check

Identify each of the following molecules as

1) polar or 2) nonpolarized. Explain.

A. PBr3

B. HBr

C. Br2

D. SiBr4

7

Solution

Identify each of the following molecules as

1) polar or 2) nonpolarized. Explain.

A. PBr3 1) pyramidal; dipoles don’t cancel; polar

B. HBr 1) linear; one polar bond (dipole); polar

C. Br2 2) linear; nonpolarized bond; nonpolarized

D. SiBr4 2) tetrahedral; dipoles cancel; no polar

8

Polarization of Dielectrics

As shown in fig. when an electric field is

applied to dielectric material their

negative & positive charges tend to align

in equilibrium position.

2

They produce electric dipole inside the material.

This phenomenon is known as Polarization.

It can be represented by,

P=polarization

μ= dipole moment

V=Volume

Unit=Cm-2

Now dipole moment depends upon applied electric field.

α polarizability of material.

PV

E

P E

P E

Gauss’s Law In Dielectrics

++

++

++

++

--

--

--

--

E

--

--

--

--

--

--

--

--

--

--

--

--

++ --

++ --

++ --

++ --

++ --

++ --

++ --

++ --

++ --

+q-

q-

q

+

q

-

q

+

q

++

++

++

++

++

++

++

++

++

++

++

E

In absence of

dielectric In presence of

dielectric

0

0

0

0

0

.E ds q

qE A

qE

A

0

0 0

0 0

. '

'

'

E ds q q

q qEA

q qE

A A

V=Ed

So

Now

0 0

d

E Vk

E V

0

0

0 0

0 0 0

'

',

1, ' (1 )

E qE

k kA

q qE

A A

q q qSo

kA A A

then q qk

0

0

So, . '

1(1 )

q

.

E ds q q

q qk

k

k E ds q

This relation true is for parallel plate capacitor Which is Gauss’s law for dielectrics

Three Electric vectors The resultant dielectric field is given by,

Where,

E=Electric field

D=Flux Density or

Displacement vector

P=Polarization

0 0

0 0

0

0

'

',

,

, D

p

q qE

A A

qnow P

A

q PE

A

qE P

A

qnow D

A

So 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

0

0

0

0

( 1)

1

e

e

r

e r

P E

P

E

E

E

Relation between εr א &

Displacement vector,

0

0

0

r 0 0

0

D E P

Now,P=

( - ) E P

(or) ( . - ) E P

( 1) . P

Where,( 1)

r

r

E

E

Types of

polarization 1. Electron polarization

2. Ionic polarization

3. Orientation polarization

4. Space charge

polarization

Electronic polarization

When no external field is applied nucleus of

atom is like in fig. (a)

When external field is applied, displacement

in opposite direction is observed between

nucleus & electrons due to this dipole

moment is induced.

This type of polarization is called Electronic

polarization.

Ex. Germanium, Silicon, Diamond etc…

19

+

-

+

-

-

Electric Field (b)

Ionic Polarization Some materials like ionic crystal does not

possess permanent dipole moment.

Fig. (a) shows natural arrangement of ionic

crystal. When Ele. Field is applied on this type

of material displacement of ions is observed.

Due to an external electric field a positive &

negative ion displaces in the direction opposite

to each other due to which distance between

them is reduced & ionic polarization is

generated.

Ionic polarization is observed in materials like

NaCl, KBr, KCl etc…

Let us consider simple example of NaCl

crystal.

As shown in fig. when crystal is placed in an

external electric field Na+ ion displaces in

one direction & Cl- ion goes in opposite

direction.

3

Orientation polarization Some molecules like H2O, HCl having permanent dipole

moment p0.

In the absence of a field, individual dipoles are arranged in

random way, so net average dipole moment in a unit volume

is zero as shown in fig. (b).

A dipole such as HCl placed in a field experiences a torque

that tries to rotate it to align p0 with the field E.

4

In the presence of an applied field, the

dipoles try to rotate to align parallel to each

other in direction of electric field fig (d).

This type of polarization is Orientation

polarization.

This type of polarization occurs only in polar

substances like H2O, CH3Cl when they are

placed in external field.

Space charge polarization(Interfacial polarization)

A crystal with equal number of mobile positive ions and fixed negative ions.

In the absence of a field, there is no net separation between all the positive charges and all the negative charges.

5

In the presence of an applied field, the mobile positive ions migrate toward the negative charges and positive charges in the dielectric.

The dielectric therefore exhibits Space charge or interfacial polarization.

Energy stored in dielectric field

.

?

.

.

dW F dr

F

dW qE dr

dW E dp

p pP

lA V

0

0

0

2

0

2

0

( 1) .

. .( 1) .

. .( 1) .

1( 1) E

2

1( 1) E

2

?

r

r

r

r

r

p PV

dW EVdP

P E

dW EV dE

dW EV dE

W V

W

V

U

References:Engineering physics By Dr. M N Avadhnulu, S

Chand publication

Engineering physics by K Rajgopalan

http://web.mit.edu/viz/EM/visualizations/coursenot

es/modules/guide05.pdf

Image references links

1. http://www.physics.sjsu.edu/becker/physics51/capacitors.htm

2. https://encrypted-tbn0.gstatic.com/images?q=tbn:ANd9GcSJZq2cY-80x2c9Jzlqs-ebnfPHmznS_SZXueW9fAQFTf9xUzAg4A

3. http://image.slidesharecdn.com/dielectrics-140801000936-phpapp02/95/dielectrics-24-638.jpg?cb=1406869836

4. http://www.pixentral.com/show.php?picture=1SH99qe2FTmMv6M4lmJrV2iNZ8tR

5. http://www.pixentral.com/pics/1LMvZyZGCYX3JZkgQ2rEQMX876K89v1.png