Chapt 01 Physics

tnorllfitoflJK-1eVK-1

kg

Fm-l

nb-1

tn

,crJs5 eVs

kg,kg

I

in electrical devices.

;nraterials are alsotermedas dielecdics. The difference inthenamebetween dielectric and

iies in the application to which these materials are put. when these-materials are used to

*the flow ofelecticitythroughthemonthe application ofpotentialdifference, thenthey are

btsulators or passive-dieleciics. Ontheotherhand, ifthey are used forcharge storage then

a'fprn

l.zmc

d

Materials srch as glass, rubber, wood and porcelain provide electrical insulation between two

rtors at certain potential difference; and also serve for storing electrical charge under certain

called dielectrics ot active dielectrics'

circumstances.

h an ideal dielecfic material, all the electons are tightly bound to the nucleus ofthe atom' As

rll there are no free elecfons available for conduction. This is the reason for them to be non-

Cenerally, the dielectics are non-metallic materials ofhigh specific resistance and have negativeient ofresistance.

Engineering Physics

Thebehaviourofadielectricmatedalcanbechangedbytheapplicationofanextemal electicWe know that in an atom there is a positively charged nucleus at the cenffe surrounbed

orbitingelecffons (elecfron cloud) whicharenegatively charged.Anisolatedatom does notany dipole moment; since the cenfioid ofthe negative charge distribution and the positivecoincide.

But when an extemal electic field is applied, it causes the elecfon cloud to move away.thecenffoids ofthepositive andnegative chargesnowno longercoincideandas aresultanedipole is induced in the atom. Thus, the atoms are said to be polarised. The Figrne 1. 1 illustatesabove process.

+e

6,rlr-e'

qr

e

6rJr

e-

Qr+E#O

e'

6'lr-e

Q'e-d"d"d

e'e*qqqe-'e-

+E:O

Bl

No polarisationCentroids of positive and negative

charges coincideFigure

Note:' Dipole : Apair of equal and opposite charges separated by a small distance constitutes

an electric dipole.' The product of the magnitude of one of the two charges q and the distance of their

separation r is called the dipole moment p, i.e., p: q x y.Therefore, polarisation is deJined as the process ofcreating or inducing dipoles tn o

dielectricmaterial by anexternal elecnicfietd. Thepolarisation increases withtle fieldup tothecritical rzalue.

On the basis of the polarisation concept, dielectrics are the materials that have eitherpermanent dipoles or induced dipoles in the presence of an applied electricfield. They areclassified into two categories, namely,p olar and non-polardielectrics.

PolarisationNon-coincidence of centroids ofpositive and negative charges

1.1 : Dielectric polarisation

2{Irdma{

l

Physics

field.mdedbynothave

charge

y.Thu,s,electric

the

tnatothe

either

C[electrics

Non-Polar DielectricsA dielectric material in which there is no permanent dipole existence in the absence of anexternalfield is called non-polar dielectric.

This is because, in this type of dielectric, the centroids of the positive and negative charges ofthe molecules constituting the dielectric material coincide.Examples are H2, N2, Oz,C)2and CHo. These molecules are callednon-polar molecules.

Polar Dielectrics-1 dielectric material in which a perrnanent dipole exists even in the absence of an external.freld is called a polar dielectric.

This is because, in this type of dielectric, the centres ofthe positive charges and negativecinrges ofthe molecules constituting the dielectric material do not coincide even in the absence ofmertemalfield.E-amples are H2o, HCI and co. These molecules are called polar molecules.

1. Relative Permittivity, or Dietectric Constant, e,Dielectric characteristics are determined bythe dielectric constant.The dielectric constant, or relative permittivity, e, is defined as the ratio between the

yrmittiviQ of the medium e and the permittivity offree space eo.

Le., Gr- o^o

mdforallotherdielectricsitisalwaysgreaterthan 1. Sinceer> l,wecanwdtee.: I +1",where4 is called electric susceptibility. Permittivity ofa medium lmaLriag inaicates the polarisabL natureofamaterial.

Note:

' tr is a constant for a given isotropic material when the applied field is static (dc) and isreferred to as static dielectric constant. But when the material is subjected to analternating field, it becomes a frequency-dependent complex quantity.

. Values of e. vary with direction in the case of anisotropic materials.

2. Electric Field EThe region surrounding a charged body is always under stress because ofthe electrostatic charge.If a smalll charge q or a charged body is placed in this region, then the charge q or charged body

are

Engineering PhYsics4

will experience a force according coulomb's law' This stressed region around a charged body

is called electric field. mit positive chargeplacedO"nnitioo - Btecfic field at a point is defined as the force that

acts on a r

atthatPoint. ttrr, E:E'

Electric field is a vector quantity. The direction ofthe vector E is that ofthe vector F ' fn'

unit for the electric field is "t*to'Vto"fomb

(NCr) or volVmetre (Vmr ')AccordingtoCoulomb,slaw,whentwopointchargesQ,andQareseparatedbyadistance

q the force ofatffaction or repulsion between the two charges is given as, F = ffi; , where 6

is the permittivity or dielectric constant of the medium in which the charge is placed' For air or

vaculrm t = to = 8.854 x 10-12 Fm-t '

ffi11tfuH*#:T"r".rfk;:* **#T'ff""mffi. The unit positive charge is

sometimes called test charge. EFlux $

Elecric. flux is defined as the number of lines of force thatpass through a surface

pfr""ai"rfr"vectorfield' -

r--^. ^r+LElectric fluxmay alsobe describedmathematically, as theproductofthe

surface

*.u & andthe components ofthe electric field E normal to the surface'

o: E.ai.

Aunitchargeissupposedtoemanateoneflux.Thus,incaseofanisolatedchargeqcoulornb,the flux is Q = q , and is independent ofthe nature ofthe medium'

In such a case' the unit of flux ls

that of charge, i.e., coulomb'

4. Electric Flux DensitYiDefinition-Electricfluxdensityisdefinedasthefluxpassingperunitareaofasection'held

normal to the direction ofthe flux'

Thus, if S flux passes normally through an area Ar#' the flux density is

flux 0 -2D=Ar*:;t*

Electicfluxdensityis avectorquantityhavingbothmagnitudeanddirection'Thedireitionisthatofthe.elecric lines offorce or flux'

6iH

3. ElectricDefinition 1-

Definition 2 -

1.0.,

flllllttrfits

Therelationbetween D and E is, D : eE or D : ro4E .Here,thefluxdensityatany

# in m electric fi eld is tot. times the electric fi eld at that point.

fKrso called as dielectric displacement vector.or electric inducation.

f Folarisation Vector Pft]aisarion vector measures the extent ofpolarisation in a unit volume of dielecffic matter.Eitfun I - It is defined as the induced dipole moment per unit volume of lhe dielectric.

P is a vector quantity and its direction is along the direction ofthe applied field. Ifmis the average induced dipole mompnt per unit molecule and N is the number ofmolecules per unit volume then, the polarisation is given by

P:NPhition 2 - The polarisation P is also defined as the induced surface qharge per unit area.

Theabove definition is explained below.

Dielectric slab

Figure 1.2: Dielectric slab in a capacitor

Irtthepolarisationofthe dielectic slab as awtrole give fise f6*Qand-qinducedcharges onbrespective faces ofa dielectric slab ofthickness t and volume V kep betweenthe two plates ofecryacitor as shown in Figure 1 .2. Therqfore, the dipole moment ofthe slab is given by qt. Thus,tte dipole moment per unit volume ofthe dielectric or the polarisation is given by

,_ 9t,Vot

P : At ['.'V:At,whereAistheareaoftheslab]'

P:+AThus, the polarisation is alio defined as induced sudac

6Engineering physics

.

But' f is tt'" induced charge density. Therefore, magnitude ofporarisation is equal to theinduced charge densi ty.The unit ofpolarisation is Cm-2.

6. Electric Suscepfib itity 4f#[ffiffiTTfr;:Tf;'-: - round that polarisation is directryproportionar to the extemal

Thus, the relrr,", o"lrlf, and E can be given as,p:eoX.EorP I":TEwhere 4 is a constant, calred the dierectric susceptibility ofthe medium.Definition : The ratio ofpolarisation to t,

c h a rg e s o n i ",

u,,o " "

o7 ii "' ;:

"i ::ff :,! : :i, :;l :;ff#,# by t h e i n d u c e d

7' Reration between porarisation fl susc eptibirity 7" and theDielectric Constant e, t 1 vurrt',|)uptttr)

i::H#.*t*aparallelplate capacitoras shorvn in the Figure r.3 betweenwhich an erectric fierdIf o is the surface charge densiff (i.e., charge per ,n it area),then from Gauss law,

E =g'u.

++++++++++

Dielectric slab

Figure 1.3: Fierds in a pararer prate capacitor with dierectric in betweenIfa dierecrric srab is praced between rn" oluj:: ofthe_capacit"r, ,h"r;'tipoturi.utior,;:ffiii:ff"H::f" races orthe sr,J *l *,,urt,h ;;,#;;rd;, witrrin the dierecric. rhis

rhererore, th. ...,#;#;:: l#ij J,:; ^

If o, is tt'" 'ura"" "nulg;*-, l" .e srab then, bv fo,owing equation (1), * .un **t')

,"1

r&bclrics

o-g,:u.

Therefore, from equations (1), (2) and (3),

E: o -o'to to

oE: G*G,E or:P ('.'Polarisationischarge/unitarea)

...(3)

...(4)

...(5)

...(6)

...(7)

...(8)

...(e)

^[ho, by Gauss' law, the electic flux density or elecfic displacement density D is given byD : o @ischarge/unitarea)

IHone, equation (4) can be written aseoE: D-P

D - eoE*Pfu, from elecfiostatics we know that

D: tE:eoerETterefore, equation (8) becomes

eoerE: eoE*P*earanging the above equation we can write

eoE(e.-1): P ...(10)...(1 t)

toE

Ph4weknow

...(12\

us consider an individual atom in a dielectric material. Let the material be subjected to antsic field E. It is found that the induced dipole moment p acquired by the atom is proportional to

oftheelectric fieldE.p EF: CIE

a is the proportionality con stant called polarisability.Its unit is Fm2.

. Polarisability is not a bulk property of the material, but it is the property ofan individualatom or molecule.

toE

x":

(er- l)

x,e

sr- 1'

Engineering Physics

There are four different types ofmechanisms through which electrical polarisation can occur in adielectric material when it is subjected to an extemal elecfric field.

Theyare:1. Electronicpolarisation.2. Ionicpolarisation.3. Orientationpolarisation.4. Space charge or Interfacial polarisation.

1. Electronic PolarisationThe electronic polarisation occurs due to the displacement ofthe positively charged nucleus and thenegativelychargedelecfon cloudin opposite directions within adietectric materialupon applyingan external electric fi eld E.

Thus, the separation createdbetweenthe charges induces a dipole. This process occursthroughout th e mateial andthe material as a whole will be polarised. Elecfonic polarisation is morein liquid and solid dielectrics than in gaseous.

Therefore, the induced dipole moment, F: o. Ewhere cr. is elecfonic polarisability.

The electronic polarisability for a rare gas atom is given by

o" : "" (t-,

- 1)

where N isthe number ofatomsperunitvolume.

Expression for Electronic Polarisability o"Letus considerone ofthe constituent atoms of

a dielectric material in the absence of an electricfield E. Let the radius ofthe atom be R and its atomicnumber be Z as shown in Figure 1.4. Here, thenucleus ofcharge Ze is surroundedbyan electroniccloud ofcharge

-Zn.Infirc atonr, the negative chargedistribution due to its electrons is sphericallysyrnmefic.

Therefore, the charge density for electron cloudisgivenby

Figure 1.4: Atom of a dielectric materialin the absence of an electric field

-Ze -3( Ze \p:.l'*' 4 \nRr/

...(l )But, when an elechic field is applied, the nucleus and the elecfon cloud experien ce aLorentz

force ofmagnitude ZeE inopposite directions. Hence, thenucleus andthe electroncloudarepulledaway from each other.

Electroncloud

Th

lEleclrics

Since the nucleus is much heavier than the&on cloud it is assumed that only the electron&d is displacedupon applying an elecfic field't-a the electron cloud displacement be x withryectto the cenfe ofthe nucleus.

Hence, the Lorentz force acting over the&ctroncloudis-ZeE ...(2)

But according to Gauss theorern, a coulombfractiveforce is saidto act overthenucleusdueb the electron cloud in a sphere of radius x andfis force tends to oppose the displacement.

Thus,thecoulombforce: Ze xE ...(3)Based on coulomb's theorem

Figure 1.5: Atom of a dielectric materialin the presence of an electric field

...(4)

Electroncloud

Totalcharge enclosed in a sphere of radius x (O)":

...(5)

...(6)

...(7)

/---\,1 ze -.,

It':"*i,?"".'ff[,il:'J#:::',"ffi J[",,ffi 1',:i:"iffi"1i#n'1,J"*n""uffiBut, the total charge enclosed in a sphere of radius r is q: e | : *

sfrere p is negative charge densi ty *d:nf is volume ofthe sphere of radius x./

Substituting for p from equation (1), we get

-3( Ze\ 4q: "["*; )"1""tr ,:#

-Zex3 ISubstituting for q in equation (4), we get E : - R, " 4n,*,Hence, equation (3) can be given as (substituting for E from equation (7))

-Zex3 1 -22e2 xcoulombforce : ze, il "7"; : 4*St ...(8)

These two forces, i.e., the Lorentz force and the coulomb foree are equal in magnitude butopposite in direction. As a resulq an equilibrium is reached Hence,.at equilibrium

LorenEforce : Coulombforce

-22e2 x-ZeE: 4rce,R3 ...(e)

l0

or

Engineering physic. ;hmrmmsZex

4zre "R3

Hence, ,- 4rrtoR'"Le ...( I 11

di.p;:H*;fl:'i,ffiT*';*:;f::* croud is proporrionar to the appried nerd E. Due to thisThereforq the induced dipole moment

...(10

...(12)...(13)

A A-l

v, \-/

6CIt: Zex*

._ (+ne"R,

_ ): (Ze) l-j"- tJ (Substituting forx from equation (9))

cr" : 4zeoR' ._.(t+)

"tr#xi;ff":lectuonic polarisabilitv is proportional to the volume ofthe arom and is independent

The polarisation vectorp: NpP: Ncr"E

p : 4zueoR3 EBut' F : 0.EComparing equations ( I 2) and ( I 3 ), we have

But,weknowthat p : eoE (e._ l).'. Equating equations (l 5) and (16), we get

No"E: soE(er-l)or o" : u"(:, -t)

N

...(15)...(16)

...(17)

dFt-rqlon&er

krtemruoft&shrrngG(p

2. lonic polarisationIonic polarisation occurs only in ionic solids such as Nacr which possess ionic bonds. It does notoccur in covalent crystals su.i, * aa_or*f,.o, *a g"r*i r*when ionic solids are subjectedto an extemal electric fierd, the adjacentions ofopposite srgrundergo dispracement as

*"; ; Fi;; i.in . a,rrh.;;;;;cause either an increase orffiffff*istance orsepa'utio,"CJt r.J, trr. utom, aepeffi'upon the locarion ofthe ion

Dieleclrics

ccooocooooococc

E=OPosition of ions in the absence of field Ion displacement due to the applied field

Figure 1.6: lonic polarisation

Expression for lonic Polarisability q[,etanelectric fieldEbeappliedto anionic solidconsistingofone cation andone anionperunitcell,This applied field causes the positive ions and negative ions to get displaced through a distance x,and x, respectively from their equilibrium positions thereby inducing a dipole moment. Thus, theresultant dipole momentperunit cell is

p: e (xr+x2) ...(1)Dueto theapplication ofelecffic fieldarestoringforce is saidto act overthecation andanion.Thus. restoring force

...Q)

...(3)

where B , andp rare restoring force constants of cation and anion. These restoring force constantsdepend upon the mass of the ion and angular frequency of the molecule in which the ions arepresent.

Thus, and x, ...(4)

where m is the mass of cation and M the mass of anion.Substitutingequation (4) in(1), we get

11

e@e

@@@

------+

E+o

@o@

Hence,

But,

F :0rrr:\zxzFF

'r: F, andxr: n

(eE eE)u: el "+----- ^ |' \.ro' Mrllo" )e2E(1 l\

r.l: ---; l-+- 'P" - tD.2 (m ' rvr/

) v: u,o

eE:M.7eErl -

a^ flOo-

...(5)

...(6)

t2 Engineering Physics

.'. Comparing equations (5) and (6), we gete2E( r r \ciE: r;[;*\,r)e2 (1 r\

"'

: ,,'(.,n * Nl)' ...(7)

Thus, ionicpolarisabilityis inverselypropotional tothe square ofthenatural frequencyoftheionic molecule and directly proportional to its reduced rnass.

The ionic polarisability is also independent oftenperatur.

3. Orientation Polarisation (Dipolar Polarisation)Orientationpolarisationoccursindielecficmarerialswhichpossessmolesuleswithpermanentdipolemoment (i.e., in polar molecules).

In the absence of an extemal electric field, because ofrandom orientation ofthe dipoles due tothermal agitationthematerial has netzerodipole moment. Bul underthe influence ofan externalapplied elecfic field, the dipoles undergo rotation so as to reorient along the direction ofthe field asshown in Figure 1.7. Thus, the material itselfdevelops electrical polarisation.

[&cris{' Spae!hryaechdieftdbrftimEeo

Sincethrm**ivityilr

CrdinbcSeinllumtserialsfuImtmiryalr

Total PolrThtotalpeipdeis*iEh,

Siretuqibneghctd.

Thus,fufi

*".*fI

cfwilt

i

r

Figure 1.7: Orientation polarisationt Thispolarisation occursin fenoelectric materials suchas BaTi O, andPbTiO, andproduces

a very high dielectric constant in these materials.Inthe case ofpolardielectics, theorientationalpolarisability oois givenby

p'so: 3k;r

where k" is the Boltmrann constant, T is the temperature and pr is the permanent dipole moment.Thus, the orientationalpolarisabilityis inverselyproportional to absolutetemperature.

--,

E=0Dipole orientation in

the absence of the field

{-

E+0Dipole alignment due to the

applied field

Hencefu

r3

IEcltics

a. Space Charge (lnterfacial Polarisation)flb space chmge polarisation occurs in multiphase dielectric

matprials ' When such marfials arc

diec.red to an .r*a "[rJ. field, especially * t igtr ""e.**"

the charges get amrmrlaed at

ft irerface or ut tt " "rJila"r

i..u*. "r

rrio"rTn*g.i' lonaut'iuity as shown in Figure 1'8'

*,"1Dielectric

o-loo-

el- -Oo-

o-

lr,""r,oo"I-oCIo

oooo

ooE + o GrainboundarY

Accumulation of or interfacecharge at the interfacedue to the aPPlied field

lE

+++++++++

E=OCharge distribution

within the low resistivitYPhase in the

absence of the field

Figure {.8: Space charge polarisation

Since the accumulation of charges with opposite polarity o99urs"at oPPosite parts in the low

sistivity phas", it t uo"t"trrl O"r.rip-*, offi t. tt o*.,i *itt'io tt'" to* resistivity'

Grainboundaries oftenleadto interfacialpolarisation astheycanfap chargesmigratingunder

& influence or* uppriiin# ", ,t o*" in {eure 1 .8. This type ofpolarisation occurs rn some

derials like litao, irNuo, and in certain g#t"',;;;irl"g Liro iNa,o' This polarisation is

**i,,,po,*,ru.ior#HJ,;;##ili"ffi ;;;;ffi ifo'u"ooiherapprications'Total Polarisability o1

rnic'ionicandorientationalThetotat'polarisability t4 of amaterial is thus

givenbythe sumofelecfrt

@isabilities -

^ )-n -F rv0T:o"+cti+cl,o -

r.-:_^r^:r:r.

since the space charge polarisability is very small as compared to otlrer types ofpolmisabilities'

itisneglected-*j*,,t"to,utpotarisabilityof amaterialisgivenby

. e2 f l-l)*F'

cr, : 4neoR3 +;j [;' M J-1krT[Substituting for o"' cr' and oJ

He,nce, the total polarisation P is grvenbyP: NcrrE

p : NE [+nu"n'

.

*(*. *). *'l

t4

The above equation is lcnown as Langevin_Debye equation.

copper is a Fcc crystal with a lattice constant 3.6 A, and atomic number 2g. If the averagedisplacement ofthe electrons relative to the nucleus is i , t o-dm on applying an elechic fieldcalculate the electronic polarisation.

Solution:Given, x:1x 10-18m; a:3.61x 10-10m. Z:29; p:?

For an Fcc crystal, the number of atoms per unit cell is 4.

Numberofelectronsperm3 : erofelectrons/Atom)at

4x29: . -------- :2.465x ldO electrons/m3.(:.01,.10-'o)

Since the electron density in copper is equal to the number of atoms per unit volumeN:2.465 x 1030 atoms/m3.P: NP

:\[xgxy [...p:ex): 2.465x 1030x 1.6 x l0-1e x 1 x 16-ts: 3.944x l0-7 Clnp

.'. P - 3.944xl0aClm2.

Engineering physics tElectrics

Also,

Siliconhas a relativepermittivityof 11.7 at frequencies high enough to ignore allbut its electrical(optical) polarisabilibz. It contains 4.82 x I 028 atoms/m3. Calculate the aipote moment of eachatom in a field of 104 Vm-l, and also find the effective distance at this field strength between thecentre ofthe electron cloudin eachatomand thenucleus.

Solution:Given, q:11.7; N:4.82 x 1028atoms/m3; p:?; x:?

e"(e. -

l)"N

-

8.85 x I0-r2[l 1.7 -t]

" 4.82 x l02E

tr'ormula

0e

p

: 1.9646x l[-3ep-2.:0"E: 1.9646 x tQ-3e y 19a

E:

Erfrics

Also,

: l.g646x 10-3s CIr3V : l.g646x 10-3s Cm-3.P: Zex

, : ! (Forsiliconz:14)Ze

l.g646x 10-35r: l4;r*lo:Ttx = 8.77 x 10-18 m.

x: 8.77 x 10-84.

ExamPle 1.3

Weknow

Calculate the polarisability and relative permittivity in hydrogen gas with a density of; ; ; i0* ab;/m3. Given ihe radius of the hydrogen atom to be 0'50 A'

Solution:Given, N:9.8 x ly26atoms/m3; R:0.50 x 10-l0m; a'":? and Er:?

i

o" : 4rceoR34 x 3.14x.8.85 x 10-12 x (0.50 x 10-193

Cl": 1.389x10-41Fm2'To find e, we know that,

e" x (e. -1)o":

- N -_

or No": e.x(er-l)No. : u-_ I

a'

No. -,t.: to

9.8 x 1026 x l.389 x lOar ,".:@-'er:1.5381x10-3+1

, tr: 1'0015'

The electronic polarisability ofargon atom is I .75 x lH Fm2. What is the static dielecric cmtof solid urgor, if its densityls 1.8 x 103 kg/m3 (given atomic weight of Ar: 39'95andNo : 6.025 x 1026tkmole).

16 Engineering Physics

Solution:Given, a":1.75 x lQ-a0 p*zt p: 1.8 x 103 kgm-3; At. wt:39'95; Er:?To find the numberof atoms/unitvolume

N: IOPAt.wtN = 2.7146x 1028 atoms/m3.

Nct-Weknowthat, t.:

-+lto2.7 146 x 1028 x 1.7 5 x l}ao

6.025x1026 x1.8x10339.95

+1tr8.85 x l0-r2

tr:0.53679+le, = 1.53679.

The internalfield^or the localfield, is the electricfield acting at an atom of a solid orliquid dielectric subjected to an externalfield. It is the resultant of the appliedfield and the.field due to all the surrounding dipoles.

Calculation of the lnternal Field (Local Field)The following method suggested by Lorentz is used to establish the relation between theappliedfield E and the internalfield E,n

The given dielectric is placed in between a parallel plate capacitor and is turifonnly polarised byapplying an extemal field E.

To evaluate Ei,1, we must calculate the total field acting on an atomA(dipole) within thedielectric. For thiiio calculate, imagine a spherical cavity (Lorentz sphere) around the atom A(dipole) inside the dielecfric as shown in Figure 1. 1 1 . Further, it is assumed that the radius r ofthecavity is large compared to the radius ofthe atom. The medium lying extemal to the cavity is treatedas a continuous medium as far as the atomAis concerned.

The interaction of the atom A (dipole) with other dipoles within the cavity is treatedmicroscopically; since the medium very close to the atomA (dipole) within the cpvity is consideredto be discrete.

The intemal field or local field, acting on the central atom (dipole) is thus given by

Eint: E.+E'+F.+E where Eris the field due to the charges on the plates-

he electric field acting at an atom in a dielectric known as the internal field or local field E*, isdifferent from the applied extemal field-

ti:S }eectrics

Parallel plate Spherical cavity

T

Parallel plate+

+

+

+

+

+

+

+

++

++

+

+++

:aj-:

:?.

,iS

r

Dielectric media

lrlrlrFigure 1.9: Calculation of internal field for a cubic structure

E, isthe fieldduetopolarising charges lyingatthe external surface ofthe dielectric medium'Ihrs zi also htown as depolarisationfield.

Q is the field due to polarisation charges lying on the surface ofthe sphere tnlttchis lmotvm asLarentzfield.

Eo is the fielddue to otherdipoles lyingwithin the sphere.

Io Find Ey E2, E, and Eo Values

tutd E1Slren a dielecfiic mediumis polmiseddue to an elecfic fieldE,the displacementvectorD is given:Y

\...(2)

...(3)

D: eoE+PFrom field theory the field at A due to the charge density on the plates is given by,

D: e,rE,Therefore, equating equations (2) and (3), we get

soEt : eoE*PDividing the above equation by eo, we get

Q: e+l-o

...(4)

18 Engineering PhYsics

Field E,E2 isthefieldduetopolarisationchargesonthe extemal surface ofthe dielectic. This fieldacts ina

dilection opposite to the extemal field' Therefore, it is given by

_PEr:--o

Field E,E, is the fieldduetopolarisationcharges onthe surfaceofthe cavity. This fieldvalue is evaluatedas

follows.Consider an enlarged view ofthe cavity as shown in Figure 1 . 1 2 . ln order to calculate this field

actingonthe atomAinthe direction ofthe fieldconsideranelementalring EFGHperpendicularto*re nen oirection. The area ofthe ring shaped element along the surface ofthe sphere is given by

Figure 1 .10: Lorentz field

dA:2nxEKxEF: 2nx rsinQ x rdQ

[whereEF:rd0isthearclength.Fromthefigure,sme:4.Therefore,EK:rsin0]'Hence, dA: 2nPsin0d0 "'(6)From the definition ofpolarisation (defined as induced surface charge per unit area i'e.,

p : *

), the charge q on dA is equal to the product ofthe normal component ofpolarisation and

surface area.

i.e.,

:..(5) fum

ffit

Ih*otttrflF

Th6elt1ry1

Thrs,fucq

Therefce,fufsurfatrd

q --

PN.il

E>

The polarisation P is parallel to E. Its component normal to dA is P*: Pcoso.

Itelectrics

q: Pcos0dA

t9

...Q)

...(8)u

-

SubstitutingfordAfromequation(6)in(7)q : PcosO. 2rcP sin0 d0

j) -

Thus,theelectricfielddEratAduetothechargeqisgivenby(coulomb?slaw)

dE: #7,'

-

Substit,tingforqfromeq,ation(8)intheabove,P cos0.2nr2 sin0d0

to

v

dE:: ---7;FP cos0sin0d0

...(e)2Eo

The above fieldhas two components---one component(cosO) alongthe applied field andtheder component (sinO) perpendicular to the field E.

ThefieldatAduetottreperpendicularconponentiszero. SincetheconponenbarEqynnneticallydistributed aroundthe axis, theywill cancel each other out.

Thus, the component offield along the direction ofthe applied field is

PcosOsin0d0dE, : j:=:xcosO

Lbn

Pcos2 0sin0d0LLo

(10)

Therefore, the fieldatAdueto the surface charge onthe cavityisobtainedbyintegrating overthewhole surface ofthe sphere

ue.,

p1\: q Jcos'esinodo

P O,

:41: * [...i*uosinodo =%7

PE."3 3e"

ind

...(1 l)

20Engineering physic. lltffims

iffimnrurmurumiro n-*f.*, e ,ireae: JProof:Let x =cos0

d-r :- sinOdOWhen 0:0 x:7

ToproveT

J cos2 e sinodo :on

t^J cos" 0sin0d0 :0

2

,

t

J cos' gd (cos 0)

l+,""" r,-jr-,-,t2

a

merffitffionlffi

-CI

b

|Hlcirrrill

I

I *'*-l

r -l+lx-l 23J_, 3

Field EoThis is the field dueto the dipoles withinthe cavitywhichdepends onthe crystal struct,re.This field Eo is zero for

1 yhgricaily symmetric system, i.e., for a cubic structure. Hence,assuming the dielecfic material to be ofa culic structure, Eo is taken to be zero in this calculation.i.e., for a cubic system Eo:0[Elemarts like carborq silicon and germanium have cubic structures.] "'(12)

0 l, ##li' substituting all the four field values from equations (4), (5), ( 1 1) and ( I 2) in equation

lt

Irh

or

Eir,,:B+l-**l*oto to Jtop

Ei., : E +::-Jn ...(13)

The above equation is Lorentz relation. Thus, it is seen that the local field is larger than themacroscopic field E by an additional 12s1ff J_

ffi'v'r,.. 3eo'

ffi' ;:"J:Tr[ffJ:13:td T$:"J'be taken as the average nerd E macroscopicarr,, ffiffi ..'ffi .. E,nt: E+Es Eq:' ffi

Dielectrics

The polarisation for a single atom is given byP : No, Eir,

where crris the totalpolarisability' andE rtheinternalfield'

We knowthat, 0T : 0"* 0i * 0oForacubicstructureelement,sincetherearenolons

cr,: cro: 0

P : Ncr" E,n, ["'o' = o']SubstitutingforE ,

/ p)P : Ncr" [u. r" ,)

WealsoknowthatP: toE(er-1)

Substituting forP in equation (15)' we get

and permanent dipoles

...(14) lt,\.

n.

,,

rl,[b,|fi,Inirfr

l[;

i$

or

)

1

/ p\Nc,. , [" .;] : so E (e, - r)

**. [u *St", -,)) eo E (e,- r)

(o)

Ncr.E[t*fr("-'),J eoE(e.-l)e"(e,

- 1)Nct":El;""G,:,)

3to

3e"2(e, -l) -

3e"2(e' -l): ;JL-tl - e"(e,+2)^ (".-l)No. = ,r" 1n;4

Nct" _

6.-13eo e, +2'

...(1s)

...(16)

...(17)or

Engineering Physics

The above relalion is htown as C/ausias-Mossotli equarion. ll relates the microscopicquantity a"to the macroscopic quantity e,

Note:. Clausius-Mossotti equation in terms of

(a) SusceptibilitYNcr"3e.

(b) Refractive indexAt higher frequencies, i.e., at optical frequencies, only electronic polarisation

occurs. gence, er:n2 (assuming that the material has no map.etic properties) wheren is the refractive index of the material.

# [';e, =1+r"]

Ncr"3uo

n2 -l

n2 +2

(e.+z)(n'z-t)

...(ii)

LIdttd,IF,a

nhf,r{q*

hE{dd--l

IJJ

Example 1.5

The followingdatarefers to adielectric material: er:4.94andfi--2.69,wherenisthe indexofrefraction. Calculate theratio between electronic and ionic polarisability ofthis material.

Solution:d^

Given, er:4.94; n2=2,69t i=?Ncr E, -l

TheClausius-Mossottiequationis *:#

"'(i)

Atopticalfrequencye.:t?;andxfr.lisfrequencyonlyelectronicpolarisationoccurs.Hence,the Clausius-Mossotti equation can be written as

NG" : n'-l3r o n2 +2

Welaowthat, dT: d"* ai* doNeglecting oo,

crt: cr"* crt

.'. Equation (l) becomes xgr:

#Substituting for ccr,

N(o"+o,) _

6,-13eo Er +2

Dividing equation (il1) by equation (fi), we get

(cr" +cr,) _

c[e

(e. -

l)(n'z +f)

...(iii\

=----

[Iebctrics 23

r -

0i @94-t)(2.69+Z)a" - (4.94+2)(2.69-r)

or:cle

(Iegi

, , 0i Q.94)(4.69)a" - (6.94X1.69)o' : r.575s- lc[,e

0.57ss

: 1.7376.

Dielectric materials can be solid liquid or gaseous. Ahigh vacuum can also be used as a dielecfriceventhough ib relative dielecfic constant is onlyunity.Solid dielectrics are most commonly used in electrical engineering; these are very good inzulators.Examples : Porcelain, glass, plastics, rubber, cotton wood and mica.Liquid dielectric materials arebasically ofthree different types, which include (i) mineral insulatingoils,(ii)syntheticinsulatingoils, and(iii)miscellaneous insulatingoils.The function ofinsulating liquids is toprovide electrical insulation andto dissipate heat (coolingagen|.Examples :Transformeroil, cable oil, capacitoroil, vegetable oil, vaseline, silicon liquids. sovolandsovtol.Gaseous dielectric materialsare used both as insulators and as cooling agents.Emmples : Ai,hydrogur, nifogerl heliurn, sulphurdioxidq propane,rn.,t r., sotpt *hexafltroride,3thane,

etc.

1.7.1 Solid DielectricsI . Mica - Mica is an inorganic mineral material, made ofthe silicate ofaluminium with silicates

of sod4 potash and magnesia. It is crystalline in nature and can be divided into very thin flatsheets.

It is rigid, tough and strong. It has high dielectric strength and low dielectric loss. It is notaffectedbymoisture.Mica is widely used in electric irons, hot plates and toasters for insulation purpose. Micapaper is used as insulation in armature and field coils ofrotating machines. Mica is also usd asa dielecfic material in high frequency applications.

24 Engineering PhYsics

2.Gluss-GlassisaninorganicrnaterialmadebythefusionofdifferentoxideslikeSio.,ZnoandMgO.Glass is brittle and hard. It has good mechanical strength

and has low dielectric loss' It is

insolubleinwaterarrdistrlghtychemicalresistanttomostcorrosiveagents.It is used as a dielectric in capacitors. It is used in radio

and television tubes' electric lamps

andlaminatedboards'3. Asbestos-Asbestosisanaturallyoccurringmineralmaterialoffibrousnature'Itgenerally

consists of magnesium silicate'

Ithashighdielectriclossandlowdielectricstrength.Itcanwithstandveryhightemperature.It is used as dielectric or insulating material to prevent currelt

flow in the outer body of

electrical apptia,"e, tit.. electric i.,t*, oven etc' It is widelyused in the form of paper,

taPe, cloth andboard'

4.Rubber-Rubberisanorganicployler;itmaybenaturalorqmthetic.Syntheticrubbersareproducedby copolymerisation ofisobutylene and isoprene'

Rubber has good electrical and thermal properties' It possesses high tensile strength'

Rubber is used in the consffuction of storage battery housings. It is used as h$lating rnaterials

i"t "f.;oi"

*ites, tapes, transformers' motor winding etc'

5. ceramics- ceramics are generally non-metallic inorganic compounds such as silicates'

aluminates, oxides, carbides,borides,nitriJes rrarrya.o*ia"s. ceramics are also calledpotter',s

earth or clay. c.;;J;; .* be classified as: clay products, refractories and glasses'ceramics are hard, stronganddense. Theyrla"" "'""u*'dielectric

and rnechanicalproperties'

They are not urr".,.ouy *Jirtor" *O uy "hemical

agents except with strong acids and alkalies'

They are completely stable at higlr temperatures' - ^^+r.-ro heqterc etc 'l

Ceramics are widely used as insulators for switches, plug holders, cathode heaters etc' They

are also used io "t."t

i"'rto*s and kettles. They are also used as dielectrics in capacitors'

1.7.2 Liquid Dielectrics1 . Minerul insalating oils- These oils are obtained from crude

peffoleum b1. distillation'

These insulating oils possess high oxidationresistance andhave goodttrerrnal stabiliry These

are used in ffansformers and capacitors'

Transformeroilistheimportantmineralinsulatingoilwithhighlielecticsterrgd-r.viscosityarrdcooling prop.ni"- Thi,oil is useA for inst'tatlo""unA "oom[offfansfornrers'

It also maintains

the insulation of the winding'Transformer oil, cable oil and capacitor oil belong to the

category ofmineral insulating oils'

2. Synthetic insulating oils- Askarels, aroclors, sovol and sovtol are a few synthetic insulating

oils that are widely used' --

a r^ c-^L le andSynthetic oils are very much resistant to oxidation and

to fire hazards' Due to longer li1

safetyllr operating conditiors, synthetic oils meusedas coolants andinsulators inhighvoltage

(H V') t *.fot*"tt in place oftransformer oils'

Dielectrics

3. Misdcategnsrery!Vasehused in

1.7.3 Ga

l. Air-AThedi(increeasmin

2. -\-bqgoxid*ioxidbi

3. .Sr.Aframm6IcLrenftrot4e

1. Incn6nf)ielecrics*sreng$redfie iqrmofsr:lcteriakcr

The&xeratingfia,.rlTffiF ialsg[,ryiicarims;

ThectilTrrb{e I-1.

T#

Dieledrics 2s

3' Migcellaneous tnsulating oils -vaseline, vegetable oils and silicon liquids belongto thiscategory' silicon tiquids have thermal stabili-tyup t oziiii*aare costly. The dielectricstuength ofthese liquids is same as that or-inour ofl.. ,h;.;;;;.d in H.v rransformers.vaseline has high viscosity and a high dielecfic constant It is used for impregnation ofpapersused in capacitors.

1.7.3 Gaseous Dielectrics1 ' Air - Air isa naturally available dielectic material. It is the most important insulating material.Thedielectric loss ispracticallyzrro-Thedielecri..o^*,oiuirlo*es

lineralywiththeincrease ofpressure. It is us"aas a aerec;; t, ;ffi;#; #.Jndensers). tt can be usedas an insulation only in low volage application.2' Nitrogen- Nihogen is.an important gaseous dielectric. It is chemically inert. It preventsoxidation and reduces the rate ofdeterioration. In oil mr"a t*.ro.-er., it is used to replaceoxidising atmosphere. rr is arso used i" .d;;-i,.o^ilj; #;;;"rpressure.

3 ' sulphur huafluoride -sulphur hexafluori{e is-formed by buming of sulphur in fluorineatmosphere. It has superior cooling properries than tho.";i;;;nd nitrogen. It has highchemical stability up to I 00"c. It i. *;; h^ro.rr.r.,

.t..ni. ,*iti"s, van de graffgener:ator,voltage stabiliser and X_ray apparatus.4' rnert gasesare used in erecfonic tubes and discharge tubes as insulafors.

il*ffsnt::*:.T',:pqT*srhedi9recri.."^*ri..1_ffi*.il?*ffi .ff IHI:H::":*i&,"n**iJ,";.,####Hjf,T#:,fi }trHhg":i:i:1,T::*ff :::'9,"v;;ilerorganic*i,*g,,i"lffi :H:ff::?#'Tmaterials can be either natural or synthetic.*:*:;::::l#y:3:fr:llfora:pecincappricariondependsonthetemperatureand

ff:l9":":":i::1ll;y:yfl",11.ap.*..i4;;r#;#;";,ftiliH;#1ffi HH:ffi ;ii"tri:::f:f "**:.:ly-,:,1*gtr,.r'"l,i..st,;';;.t;H-,r.ilffi 'ffi "iffi :ryplications; up to 90"C, the materialsG ;;;;;,f;;,"i#;rT#H#

*or#i."'*sification ofinsulating materials based on their thermal stability in service are listed in

Table 1.1 crassification of insurating materiars based on their thermar stabirityoperating Materiatsor@

Cotton, silk, paper, wood, vulcani="d nrtiltrubber etc,

A!)_9olon, sitk, paper or simitar organic materiats wfienerrner tmpregnated or immersed in a liquiddielectric.

(Contd...)

26Engineering physics

Glass Maximum operatins Materials or combinationof materEGtemperature(ii) Films and sheets of cellulose'a""trt" urO otn",cel I u I o s e d e riv ativ es.

Ttsmrltl:

-E trJ : \L:-

CapacitThennjutoirlpdiehl.cry

fiEqr2. Cryr

raltr,3. Capar

u-fseInelcusd- /

4. C@iass6

TransfonInramfum

Tlteapdfinrctiors int1. Solid L

l. Fibrur2. Coumr3. Highq

betrrw4. hessh

2. Liquid ,l. Transfo

maintai2. Fluorm

wifttigl3. Gaseog

(, rhedffi

(O suEfft}.

E 120',C

130"C

155"C

i80"c

Above 180"C

(iii)Variables (enamets) as applied to conductorsPolyurethane, epoxy resins, varnishes, phenolformaldehyde, cellulose triacetate etc. ln general,materials possesing a degree of thermatstability allowing them to be operated attemperature 15"C higher than classA materials.Mica, glass fiber, asbestos and similar inorganicmaterials in built -up form with organic bindingsubtances.Same as class B but with resins which areapproved for class F operations.Mica, asbestos, fiber glass and similar inorganicmaterials in built-up form with suitable bindingsubtances such as silicone resins.Mica, porcelain, glass, quartz and similarinorganic materials.

H

The above list includes the materials that are commonly used as general insulation material intransformers, motors, switchgear, electric iron, electricibu distribution lines and similar electricalequipments.

To avoid breakdown, the dielectric material shouldpossess the followingproperties.1 . It should have high resistivity to reduce leakage current (like sulphur).2. It should have high dielectric sfrength (like mica).3. It should have high mechanical strength (like steel).4. It should have high fire resistance (like silica).5. Itshouldhavehighchemicalinerhress(likeplatimrm)[i.e.,itshouldberesistanttooils,liquids,

gas, acids and alkaliesl.6. It should have low thermal expansion (like invar).7. It should have high thermal conductivi[, (like silver).8. It should have low dielectric loss (like vacuum).9. It should have low water absorption quality (like paraffin wax).

I 0. It should have high quality surface finish (like ebonite).

The dielectric materials based on their nature of state have avarief.J of applications in electricalengineeringfield

,m(fisIth4flicationsofdifferentdielectricmaterialsincapacitorsandtmsformerswiththeirfunctions

below.

role ofdielectric materials in capacitors is to store elecffical energy' Based on the nature

ic materialused, the capacitors fall into different groups'

l- Capacitors with vacuum, air or other gases as dielectric are used in radio frequency and lowfraruqc>, mastring circuits -

Z Cqtar,itors withrninerul oil as dielectric are used inhigfu woTtage applications' where alargevalue ofcaPacitance is required

3. Capacitors with a combination of solid and liquid dielectrics are used in the applicationswhereprecision is not so importantbut ahighvalue capacitance isrequired'

In elecfiic powerdistribution system forpower factorcorrection, this type ofqapacitors are

w(t'-. Examples: Glass, mica, oil impregnated paper dielectric, mineral oil, castor oil'4. Capacitonwithonlysoliddielecfficslikesodiunqglassandtitaniumoxideareusedinlaboratory

as standard caPacitors.

Transformersh transformers, the dielectrics are used as insulators as well as cooling agents'

The applications of different types of solid liquid and gaseous dielectric materials with their

firnctions in tarsformer are listedbelow.

1. Solid Dielectric MaterialsI . Fibrous (class A) materials are used in air cooled and oil cooled transformers'2. Cotton tape is used for insulating the conductors of oil cooled tansformers'3. High quality synthetic resin bonded paper in the form of cylinders is used as an insulator

between core and coils and also between primary and secondary wipdings'

4. press board or press paper is used as a filling, and as a packing mat\al between coil'

2. Liquid Dielectric Materiats \l. Transformer oil - It is a class of mineral insulating oil and is used )s a coolant' It also

maintains the insulation ofthe winding' '-ffia'fansfer

rates together2. Fluorocarbon liquids are used in large transformers to grve highwittr high dielectic stength.

3. Gaseo us Dielectric Materials(r) The usage of nitrogen in transformers prevents oxidation and reduces the rate of

deterioration.(rD Sulphur hexafloride dielecfric is an elecffonegative gas which is used in Uansformen' It is

non- toxic, non-inflarnmable and chemically inert'


. Insulating materials are also termed as dielechics.' Dielecfics are non-metallic materials ofhigh specific resistance and have negative temperature

coeffi cient of resistance.. The dielectric characteristics are determined by the dielectric constant.. Polarisation is defined as the process of creating or inducing dipoles in a dielectric material by

an external electric field.' The internal field, or the local field, is the electric field acting at an atom of a solid or liquid

dielectric subjected to an extemal field.' Based on the state of material, dielectrics are ofthree types, namely, solid, liquid and gaseous.. Based on thermal stability dielechics are classified into seven types.. Dieleckics have major applications in capacitors and transformers.

AssrcruuENT PRoBLEMS

t. Calculate the electronic polarisability of argon atom. Given er: 1.0024 and N: 2.7 "

l02satoms/m3. ( ns.: 1.gffi x l0ro Fm2)The electronic polarisability ofAr atom is I .75 x l0r0 Fm2. Calculate the dielectric constant ofsolid Ar, using Clausius-Mossotti equation. Its density is 1.8 x tO3 kg m-3. lciven atomic wt.39.9s). ( ns.r r.6536)

3. The dielectric constant ofHe gas at NTP is 1.0000684. Calculate the electronic polarisability ofHe atom, if the gas contains 2.7 x l02s atom per m3 and hence evaluate the radius of the helium( ns.: c," = 2.242 x 10-41 Fm2, R: 0.59 A)

Questions with Answersl What are dielectrics?

Dielectrics are the materials used for charge storage, by polarisation of the molecules. They arealso called as active dielectrics. The dielectric material increases the capacitance or chargestorageability of a capacitor.Mention a fewproperties of dielectric materials.(l) Thev are non-metallic materials.

-

(il) They have high specific resistance.(iii) They have negative temperature co-efficient of resistance.

3. Mention the types@lectric material.There are four different types of polarisation mechanisms in the dielectric material.(l) Electronic polarisation.(li) Ionicpolarisation.(lll) Orientation polarisation.(iv) Space charge polarisation.

Dtieleclrts

4. DefrPohanel

5. DsfrPohie_bcti

6. ErpfrEhcrchrgtffii

7. Exph\YhCtmdqiurfopThisrl

8. Eq*iOridfield.I

9. ExpliWberrterryEdipohchargE

10. DefiqIt isfiexteilrdipolGr

11. WhdiI beq[theCItIts exg

12. Defu,Whmamolilas an it

13. MentiqTransfr

14. WhatbThennjtwd

2.

Drblectrics

4. Define polarisation.polarisation is defined as the process of creating or inducing dipoles in a dielectric material byan external electric field. ' 'Define polarisability.Polarisability is the ability of an atom or a molecule to become polarised in the presence of aneJectric field.Explain electronic polarisation.Electonic polarisation is the displacement of the positively charged nucleus and the negativelycharged elecnon cloud in;gpposite directions within a dielecfric material when an extemal electric

field isappliedtoity'Explain ionic polarisation.When ionic solids are subjected to an external electric field the adjacent ions of opposite signundergo displacement. The relative displacement of charged ions in an extemal field is calledionic polarisation.This type ofpolarisation occurs only in ionic crystals.Explain orientation polarisation.Orientation polarisation is a process ofreorientation ofdiploes along the direction ofthe appliedfield. This type of polarisation occurs in polar molecules, which possess permanent dipole moments.

Explain space charge polarisation.When a multiphase ilielectric material is subjected to an external electric field, especially at hightemperature, ihe charges get accumulated at the interface or at the electrodes, thereby inducingdipoles. This process of inducing dipoles in a multiphase dielectric material is called spacecharge polarisation.Define local field.It is the total electric field acting at an atom ofa solid or liquid dielectric when dubjected to anextemal electric field. It is the resultant of the applied field and the field due to the surroundingdipoles.

11. What is Clausius-Mossotti equation? Give the expression'The equation which relates the microscopic quantity ct" to the macroscopic quantity e. is calledthe Clausius-Mossotti equation.Its expression is:

No" t. -l

3eo a, +2 '12. Define dielectric breakdown.

Whenever the external voltage applied to a dielectric material exceeds a citical value, a largeamount of current flows through it, thereby losing its insulating property. This failure of dielectricas an insulating material is called the dielectric breakdown.

13. Mention a few dielectric materials used in capacitors and transformers.Transformer oil, cable oil, cotton tape, press paper and sulphur hexafloride.

14. what is the role of dielectric material in capacitors and transformers?The major role of dielectric material in capacitors is to store electrical energy and in transformerst\>yact as insulators and also as a cooling agents'

29

5.

Ibv

7.

8.

9.m2)of

lvt.36)'. of:itmAl

lre::ge

10.


Additional Questionsl. How does the function of a dielectric differ from an insulator?2. Define dipole.3. Definedipolemoment.4. Explain the phenomenon ofpolarisation in dielectrics.5. What are polar dielectrics? Give examples.6. What are non-polar dielectrics? Give examples.7. Define dielectric constant or relative permittivity.8. Definepolarisationvector.9. Define electric susceptibility.

10. Give the relation between susceptibility and the dielectric constant'I 1. Give the expression for electronic, ionic and orientation polarisabilities.12. Give examples of dielectric materials which can undergo space charge polarisation.13. Give the expression for the internal freld in a dielectric material.14. Express Clausius-Mossotti equation in terms of susceptibility.15. Give the Clausius-Mossotti equation in terms of refractive index.16. Mention a few important properties to be possessed by a good dielectric material-17. Classitr dielectric materials into different types based on the state of material.18. Name a few dielectric materials used in capacitors.19. Name a few dielectric materials used in transformers.20. Classify the dielectric materials based on their thermal stability.21. Name the clasSes of insulating material based on temperature.22. Whatare the different tlpes of liquid dielectric mateial?23. Give examples of gaseous dielectric materials.

Descripl. (i) Explainpolarisationindielectrics.

(li) Disouss in detail the various polarisation mechanisms in a dielectric material.2. Derive an expression for Lorentz field in a dielectric material and'hence arrive at Clausius-

Mossotti equation.3. What is meant by local field ? How it is calculated for a cubic structure ? Deduce Clausius-

Mossotti equation.4. (l) Classiff the dielectric materials based on the state of material.

(ll) In detail explain the application of dielectrics in capacitors and transformers.5. Obtain expressions for electronic and ionic polarisabilities.6. (i) Derive an expression for the internal field in the case of dielectrics.

(li) Deduce Clausius-Mossotti equation. What is its significance.7. Briefly discuss the different types of dielectric materials with examples.8. Discuss in brief the classification of insulating materials based on their thermal stability.

ffitive Answer Quesfions

u-

Irearn&

fTlemateriokt&nrnfteungm

UagDeticrTlemagreticuumsdrces.duoragederioes,

kr this ch6rytrtantprw

Tobeginu,lnithnagnetisml

T1" filagnedrTlv nto oppasit

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Chapt 01 Physics