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Un
it
Un
it
Un
it
Un
it4444
1
M
ateria
ls
M
ateria
ls
M
ateria
ls
M
ateria
ls
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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.
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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
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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.,
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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.
-
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Thedisplacementofchargedparticlesundertheac
tionof
theelectr
icfieldtowhichtheyaresub
jected.
a.
Electronicpolarization
,
Polarization
anditstypes
6
.
,
c.
Orientationpolarizationand
d.
Spacechargepolarization.
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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
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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)
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(ii)
WithField
Whenthe
dielectricisplacedinanelectricfield(E),tw
o
phenomenonoccur.
(i)Lorentzforcedueto
theelectricfie
ldtendstoseparate
thenucleusandtheelectroncloudfrom
theirequilibrium
position.
9
(ii)Afterseperation,anattractivecoulombforcearises
betweenthenucleusand
electroncloud
whichtriesto
maintaintheoriginalequ
ilibriumposition.
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Letxbethedisplacementmadebythe
electr
oncloudfromthepositivecor
e
SinceLorentzandCoulo
mbforcesareequal
andoppositeinnature,equilibriumisre
ached.
AtEquilibriu
m Lorentzforce
=
Coulombforce
10
Lorentzforc
e Lorentzforce
=
Charg
exField
Lorentzforce
=
ZeE
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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)
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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
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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.
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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.
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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)
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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)
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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
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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
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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.
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20
eecron
can
onc
poarzaon
e
orce
ue
o
e
externalfie
ldisbalance
dbytheres
toringforce
dueto
coulombatt
raction.
Butfororien
tationpol.res
toringforce
doesnotex
ist.
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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
=
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SpacechargePolarization
Duetothe
accumulationofchargesattheelectrodesorat
theinterfa
cediffusiono
fions,along
thefielddirection
andgivin
grisetore
distribution
ofchargesinthe
dielectric.
22
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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
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Frequenc
yDependence
Atopticalfrequencies(~1015H
z)electronicpolarizationaloneispresent.
At~1013Hzrangeionicpoloccursinadditiontoelectronicpolarization.
At106to1010
Hzrangeionic
polduetoorientationpolgetsaddedwith
electronicpolarization.
whileat102H
zrangespacechargepolarizationalsocontributes.
24
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Internalfield(or)
Localfield(D
erivation)
Whenadielectricmaterialisplacedinanexternalelectric
field,itexertsadipolemo
mentinit.
Twofieldsareexperienced
i.
Macroscop
icelectricfield
duetoextern
alfield.
25
.
.
Thelongrangecoulombfieldcreated
duetodipolesis
knownasinternalfieldorlocalfield.
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26
Assumeanimaginarysmallsphericalcavityaroundanatom(O)
forwhichtheinternalfieldm
ustbecalculatedatitscentre.
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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.
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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)
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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
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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.
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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.
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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)
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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
=
+
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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)
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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
=
+
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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.
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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
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