Engineering Physics 2 Unit-4

7/29/2019 Engineering Physics 2 Unit-4

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2/38

A

dielectricisanelectricalinsu

latorthatm

aybe

polarized

bytheactionofanappliedelectricfield.

Whenad

ielectricispla

cedinanelectricfield,electric

charges

donotflow

throughthe

material,as

ina

Dielectrics

Dielectrics

Dielectrics

Dielectrics

2

,

equilibrium

positions

causing

dielectric

polarization:

positivechargesaredisplacedalongth

efieldand

negativec

hargesshiftin

theopposite

direction.

Thiscrea

tesan

inter

nalelectric

field

which

partly

compensatestheexternalfieldinsid

ethedielectric.


3/38

ElectricDipoleMoment

()

Itisequaltotheprodu

ctofmagnitu

deofoneofth

e

chargesandtheperpendiculardistancebetweenthe

m.

=Magnitude

ofchargexdistance

i.e.,

=q.d

(coulombmetre).

3

Theprocessofprod

ucingdipoles

bytheapplicationof

electricfieldiscalledpolarisation.Itis

equaltotheinduced

dipolemomentsproducedperunitvolume.

P=Nm

where,mis

theaveragedipolemomentp

ermoleculean

dNisthe

numberofmoleculesperun

itvolume.

ecrc

oarsao

noroarsa

on

ensy


4/38

Whendielectricissubjectedtoex

ternalelectric

field,if

thedielectricactivelyacce

pttheelectricity,thentheyaretermed

asactivedielectrics.Thus

activedielectricsarethedielectrics

whichcane

asilyadaptitse

lftostorethee

lectricalenerg

yinit.

Examples:Piezo-e

lectrics,Ferro-electric,etc.,

ActiveDielectrics

4

Thes

edielectricsa

realsocalled

insulatingm

aterials.

Conduction

willnottake

placethrough

thisdielectrics.Thus

passivediele

ctricsarethedielectricswhichrestrictsthe

flowof

electricalenergyinit.

Exam

ple:Glass,Mica,etc.,


5/38

Thesemoleculesw

illnothavece

ntreofsymme

try.

Herethece

ntresofpositiveandnegativ

echargeswill

not

coincideandhenceitpos

sessanetdip

olemomentin

it.

Examples:H2O,N

2O,

HCl,NH3,

CO,

CH3OH

etc.

PolarM

olecules

5

Thesemoleculespossescentreofsymmetryandhence

thecentres

ofpositiveand

negativechargescoincides.

Thereforethenetchargeandnetdipolem

omentofthes

e

moleculeswillbezero.

Exam

ples:N2,

H2,

O2,

CH4,

CO2etc.

-


6/38

Thedisplacementofchargedparticlesundertheac

tionof

theelectr

icfieldtowhichtheyaresub

jected.

a.

Electronicpolarization

,

Polarization

anditstypes

6

.

,

c.

Orientationpolarizationand

d.

Spacechargepolarization.


7/38

Electronic

Polarizatio

n

Polarizatio

nwhichoccur

sduetothe

displacementof+velychargednucleus

and

-velychar

gedelectronsinopposite

directions,

whenanexter

nalelectricfield

isapplied.

7

Induceddipolemomente=eE

Monoatomicgasesexh

ibitthiskindo

fpolarization.

Electron

icpolarizabilit

yisproportio

naltothevolu

me

oftheato

msandisindependentofte

mperature.

e=40R

3E


8/38

R

Nucleus(+Ze)

Electroniccloudofcharge(-Ze)

(i)

With

outField

Letusconsideraclassic

almodelofan

atom.

Assumethechargeofnu

cleusofthat

atomis+

Ze.

Thenucleusissurroundedbyanelectroncloudofcharge

8

,

.

Charged

ensityofthech

argedsphere

3

4 3

Ze

=

3

3 4

Ze R

=

Chargede

nsityofthechargedsphere

(1)


9/38

(ii)

WithField

Whenthe

dielectricisplacedinanelectricfield(E),tw

o

phenomenonoccur.

(i)Lorentzforcedueto

theelectricfie

ldtendstoseparate

thenucleusandtheelectroncloudfrom

theirequilibrium

position.

9

(ii)Afterseperation,anattractivecoulombforcearises

betweenthenucleusand

electroncloud

whichtriesto

maintaintheoriginalequ

ilibriumposition.


10/38

Letxbethedisplacementmadebythe

electr

oncloudfromthepositivecor

e

SinceLorentzandCoulo

mbforcesareequal

andoppositeinnature,equilibriumisre

ached.

AtEquilibriu

m Lorentzforce

=

Coulombforce

10

Lorentzforc

e Lorentzforce

=

Charg

exField

Lorentzforce

=

ZeE


11/38

Coulom

bForce

Coulombf

orce

=

Chargex

Field

=

Chargex

Coulombf

orce

=

(+

Ze)x

Total

neagtivech

es

Q

enclosed

inthesphereofradius

arg

(

)

x

x

4

0

2

Q

4

0

2

x

(2)

11

Here

Totalnumb

erof

negativech

es

Q

enclosedin

thesphereofradius

,

arg

(

) x

U V| W|

=

Ch

edensity

ofelectrons

arg

x

Volumeof

thesphere

Density

ofe-sinabove

eqncanbereplacedbyeqn(1

)

3 4

4 3

3

3

Ze

R

x

x

Q

=

=

Zex

R3

3

(3)


12/38

Substitutingeqn(3)

ineqn(2),we

get

C.Force=(+Ze)x

Q

4

0

2

x

Q

=Zex

R3

3

Ze

R

2

2

0

3

4

x

CoulombFo

rce=

12

AtEquilibrium

Loren

tzforce=

Coulombfo

rce

ZeE=

Z

eR

2

2

0

3

4

x

4

0

3

R

E

Ze

x=

x

E


13/38

Induceddipolemoment(e)=Magnitudeo

fchargexdisplacement

=Zex

Substitutingthe

valueofxfrom

equation,wehave

e=

e=

40R3E

Ze

R

E

Ze

4

0

3

13

e

E

e=

eE

wheree=4

0R3(Farad-m2)iscalledelectronicpolariza

tion

whichisproportionaltovolumeoftheatom.


14/38

IonicPolarization

Duetot

hedisplacem

entsofcationsandan

ionsin

opposite

directions

andoccursin

anionicsolidinthe

presenceo

felectricfield.

Thedispla

cementisindependentof

e=

iE

14

.

Example:NaClcrystal,KBr,KCl,etc., W

ithoutfield

W

ithfield

i=

e

m

M

02

1

1

+

F HG

I KJ

Ionicpolariza

bilityisinversely

proportionaltothesquareo

fnatural

frequencyoftheionicmoleculeand

directlypropo

rtionaltoitsr

educed

mass.


15/38

Induceddipolemoment=

magnitudeofchargexdisp

lacement

i=e(x1

+x2)

(1)

wherex1istheshiftofp

ositiveion.x2istheshiftofn

egativeion

Whenthe

fieldisapplie

dtherestoringforceproduc

edis

roort

ionaltothed

islacements

15

For+veio

ns

RestoringforceFx1

F=1x1

For-veions

RestoringforceFx2

F=2x2

1,2istherestoringforc

econstant.

(2)

(3)


16/38

Ifmis

themassof+iveionandM

isthemassof-veion

and0istheangularfrequencythen

1=m0

2

2=M

0

2

For+veion

s

F=m0

2x1

16

(4)

For-veion

senow

=

Equatin

g

eE=m0

2x1

eE

m02

x1=

Simillarly

x2=

eE

M

02

(5)


17/38

i=e(x1

+x2)

Therefore

eE

m

M

02

1

1

+

F HG

I KJ

(x1

+x2)=

(1)

(6)

Sub.(6)in(1

)

i=

eE

m

M

202

1

1

+

F HG

I KJ

17

i=iE

i=

Ionicpolarizabilityisinv

erselyproportionaltothesquare

ofnaturalfrequencyofth

eionicmoleculeanddirectly

proportionaltoitsreduce

dmass.

e

m

M

02

+

F HG

I KJ


18/38

Orientation

Polarization

Orientatio

nalpolarizationtakesplaceon

lyinpolardielectrics.

Permanen

tmoleculard

ipolesinpolardi-electricm

aterials

canrotateabouttheir

axisofsymm

etrytoalign

withan

appliedfie

ldwhichexert

atorqueinthem-O.

Polarization.

18

,

,

,

.,

Cl-hasmo

reelectronegativitythanhydrogen.

Therefore

theCl-atomsp

ullthebondedelectrons

towardsit

morestronglythanhydrogenatoms.

Therefore

evenintheabsenceoffieldthereexistsane

tdipole

moment.

2

3

O

KT

=

0

=

0


19/38

Cl-hasmo

reelectronegativitythanhydrogen.

Therefore

theCl-atomsp

ullthebondedelectrons

towardsit

morestronglythanhydrogenatoms.

Therefore

evenintheabsenceoffieldthereexistsane

tdipole

moment.

19

Bytheappl

icationofelectricfieldthedip

olescanturnonlya

smallang

le.

Whenthetempishigher,thermalagitationwillbegreater.

ThusOrien

tationpolarizationstronglyd

ependsontem

p.


20/38

20

eecron

can

onc

poarzaon

e

orce

ue

o

e

externalfie

ldisbalance

dbytheres

toringforce

dueto

coulombatt

raction.

Butfororien

tationpol.res

toringforce

doesnotex

ist.


21/38

2

3N

E

K

T

=

FromLangevinstheoryofparamagnetism

Netintensityofmagnetization

Sameprin

ciplecanbeappliedtotheapplicationofelectricfield

indielectric

Orientation

P0

polarizatio

n

2

3N

E

KT

=

21

.

O.Pisinverselyproportionaltothetempe

ratureand

proportionaltothe

squareofperm

anentdipolemoment.

P0

=N0E

wh

erea0isorienta

tionalpolarisability.

2

3

O

KT

=


22/38

SpacechargePolarization

Duetothe

accumulationofchargesattheelectrodesorat

theinterfa

cediffusiono

fions,along

thefielddirection

andgivin

grisetore

distribution

ofchargesinthe

dielectric.

22


23/38

P=

Electronic+Ionic+Orientation+Space

charge.

Total

Polarization

=

e

+

i+

o

2

3

KT

+

40R3

+

=

Polarizability.

e

m

M

202

1

1

+

F HG

I KJ

23

Totalpolariz

ation

P

=NE

2

3KT

+

+

40R3

P=NE

e

m

M

202

1

1

+

F HG

I KJ


24/38

Frequenc

yDependence

Atopticalfrequencies(~1015H

z)electronicpolarizationaloneispresent.

At~1013Hzrangeionicpoloccursinadditiontoelectronicpolarization.

At106to1010

Hzrangeionic

polduetoorientationpolgetsaddedwith

electronicpolarization.

whileat102H

zrangespacechargepolarizationalsocontributes.

24


25/38

Internalfield(or)

Localfield(D

erivation)

Whenadielectricmaterialisplacedinanexternalelectric

field,itexertsadipolemo

mentinit.

Twofieldsareexperienced

i.

Macroscop

icelectricfield

duetoextern

alfield.

25

.

.

Thelongrangecoulombfieldcreated

duetodipolesis

knownasinternalfieldorlocalfield.


26/38

26

Assumeanimaginarysmallsphericalcavityaroundanatom(O)

forwhichtheinternalfieldm

ustbecalculatedatitscentre.


27/38

TheinternalfieldEintattheatomsite(O)c

anbeconsidered

toconsist

ofcomponents

namelyE1,E2,E3andE4.

Eint

=

E1+

E2+E3+E4

...(1)

E1-FieldintensityatOduetothecharge

densityontheplates.

E2-Electricfieldduetothepolarised

27

charges(inducedcharges)onth

eplane

surfaceofthe

dielectric.

E3-Electricfieldduetopolarised

chargesinducedonthesurface

ofthe

imaginarysphericalcavity.

E4-Electricf

ieldduetopermanentdipolesoftheatomsinsidethe

sphericalcavityconsidered.


28/38

Macroscopically,wecantak

e

E=E1+

E2

i.e.,E1-th

efieldexternallya

ppliedand

E2-thefieldinducedontheplanesurfaceofthedielectric.

Forhighlysymmetricdiele

ctric

28

eue

o

e

poespresen

nse

em

agnarycavyw

canceleachother.

Therefore,theelectricfieldduetopermanen

tdipolesE4=0.

Eint

=

E+E3

...(2)


29/38

Determin

ationofE3

Letusconsiderasmallareadsonthesurfaceofthesphericalcavity.

Thissmallareamakesanang

ledatanangle

withthedirectionofthefieldE.

ThepolarizationPwillbeparalleltoE.

PNistheco

mponentofpolarization

perpendic

ulartotheareadsand

29

qisthech

argeontheareads.

Hence

PN

=

PCos=

Chargeon

ds

q

=

PCosds

Polarization

isalsodefined

asthesurface

chargesperun

itarea

q d

s


30/38

ThereforeE

lectricfieldinten

sityatOdueto

chargeq'(

Coulomb'slaw)

E

=

q

r

4

0

2

But,chargeonds

q

=Pcosds

P

ds

r

cos

4

0

2

ThereforeElec

tricfieldintensity

atO

E

=

.(3)

30

Thisfieldintensityisalongtheradiusr'anditcanberesolved

intotwo

components

asshowninFig.


31/38

Componentofintensity

paralleltothe

fielddirection

E

x=Ecos

P

ds

r

cos

4

0

2

ButElectricfield

intensityatOE

=P

ds r

cos

cos

4

0

2

Ex=

31

Ex=

s

r

cos

0

2

4

.(4)

Componentofintensityperpendiculartothefielddirection

Ey=Esin

Sincetheperpendicularcomponentsareinoppositedirection,theycancel

outeachoth

er.


32/38

Ringareads=

Circumference

x

thickness

Considerarin

gareadswhichi

sobtainedby

revolvingds

aboutAB.

=

2y

x

rd

=

2rsin

xrd

ds

=

2r2sind

sin

sin

y r

y

r

=

=

.(5)

32

E3=

P

ds

r

cos

2 0

2

4

.(6)

Subeqn.(5)ineqn.(6),weget

2

2

2

0

cos

2

sin

4P

x

r

d

r

=

Electricfieldintensityduetotheelementalring

2

0

cos

sin

2

P

d

=

.(7)


33/38

Electricfieldintensitydueto

chargepresentinthewholesphereis

obtainedbyintegratingeqn.

(7)withinthelimits0to.

2

3

0

0

cos

sin

2

P

d

E

=

2

0

0

cos

sin

2P

d

=

2

2

0

0 3

2

3

2

0

0

cos

sin

cos

(

cos

)

3c

os

cos

(

cos

)

3

d

d

x

xdx

d

=

=

=

2

P

33

2

0

(

1)

(1)

3

2

cos

sin

3

d

=

=

0

2

3x

=3

0

3P

E

=

.(8)

Substitutingeqn.(8)ineqn.(2),w

eget

Eint

=

E+E3

....(2)

(

)

int

0

In

terna

lfield

or

Loca

lf

ield

3P

E

E

=

+


34/38

Clausius-M

osottiEquat

ion

IfNbethenumb

erofmoleculesperunitvolumeanda

themolecularpolarizability

then

Totalpolarization

P=NEint

weknow

=0r

InAir

=1

D=E

..(2)

D=

E+P

..(3)

in

t

P

E

N

=

..(1)

34

Equating(2)and(3)

E=

0E+P

(-0)E=

P

o

P

E

=

..(4)

(

)

int

0

In

terna

lfield

or

Loca

lf

ield

3P

E

E

=

+

..(5)


35/38

Substitu

tingeqn(4)and(5)

int

0

0

3P

E

=

+

0

0

0

0

3

(

)

3

(

)

P

+

=

0

int

2

P

E

+

=

..(6)

in

t

P

E

N

=

..(1) 3

5

0

0

Equating(1)and(2),weget

0

0

0

2

3

P

P

N

+

=

0

0

0

3

2

N

=

+

0

0

0

1

3

2

N

=

+


36/38

0

0

0

3

2

N

=

+0

0

0

1

3

2

N

=

+

0

r

=

0

1

3

2

r r

N

=

+

36

TheaboveequationisClau

sius-Mosottirelation,which

relatesthedielectricconstantofthemate

rialandpolarizability.

Thus,itrelatesmacroscopicquantitydielectricconstantwith

microscopicquantitypolarizability.


37/38

DefineDielectricLos

s

Whenadielectricissubjectedtoanelectricfield,partofthe

electricalen

ergyisdissipatedandlostintheformof

heat.

DefineDiele

ctricBreakdo

wn

37

Whenadielectricissubjec

tedtoveryhighelectricfield,it

mayloseits

resistivityandallowtheflowofcharge.

BreakdownVo

ltage

Dielectr

icStrength

T

hicknessoftheD

ielectric

=

1.intrinsic,

2.Thermal,

3.Discharge

4.Electrochemical

5

.Defect


38/38

Engineering Physics 2 Unit-4

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Transcript of Engineering Physics 2 Unit-4