Omar_Elementary Solid State Physics_Lecture10

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1、Chapter8Anelectricdipoleiscomposedoftwooppositechargesofequalmagnitude,qsep-aratedbyadistanced(seeFig.8.1).Themomentofthisdipoleisdefinedby:p=qd←−electricdipolemoment(1)Theelectricfieldassociatedwiththedipoleis(assumingr>>d):13(p·r)−r2pE=(2)4π"0r5whereristhevectorjoiningthedipo

2、letothefieldpoint.Ifadipoleisplacedinanexternalelectric,E,thenthefieldexertsatorqueonthedipole(seeFig.8.2):τ=p×E;τ=pEsinθ←−torqueondipole(3)whereθistheanglebetweenthefieldandthedipole(seeFig.8.2).Thepotentialenergyofthedipoleis:V=−p·E=−pEcosθ←−potentialenergyofdipole(4)=⇒Vsmalle

3、stwhenθ=0◦=⇒dipoletendstoalignitselfwiththefield!Thedipolemomentperunitvolumeis:P=Np←−polarizationofmaterial(5)N=numberofmolecules/unitvolume.Thepolarizationchangestheelectromagneticpropertiesofthemedium:D="0E+P←−displacementvector(6)Note:Ddependsonlyonexternalelectricfield,and

4、iscompletelyindependentofthepolarizationofthemedium!Thus,wemaywrite:D="0E0←−dependsonlyonexternalfieldE0(7)andcomparisonwithEq.(6)yields:1E=E0−Pfieldinsidemedium(8)"0⇓Polarizationmodifiesfieldinsidemedium.Writing:D="E="0"rE=⇒(9)""r=←−relativedielectricconstant(10)"0⇓Electricaland

5、opticalcharacteristicsofthemediumcontainedin"r.Simpleprocedureformeasuringdielectricconstant:Chargeplatesofcapacitor(Fig.8.3)byconnectingthemtobattery.Whenthereisnodielectricinsidecapacitor:•electricfieldproducedbychargesis:E0=V0/LV0=potentialdifference;L=distancebetw.plates(11

6、)Ifadielectricslabisinsertedbetw.theplates,thefieldE0polarizesthemedium:•modifiesthefieldtoE,andthisnewfieldis:E=V/LV0=newpotentialdifference(12)and"r=E0/E←−relativedielectricconstant(13)or"r=V0/V.(14)2Assuming:p=αEα≡polarizabilityofthemolecule(15)⇓P=NαE←−polarization(16)whichupon

7、substitutionintoEq.(6)yields:!"NαD="0E0+NαE="01+E(17)"0!"Nα"r=1+←−goodforgases.(18)"0Defining:P="0χE=⇒χ≡electricsusceptibility,(19)wehave:NαP=NαE=⇒χ=.(20)"0Therefore,Eq.(18)maybewrittenas:""r==1+χ=⇒χgivesdepartureof"fromvacuumvalue.(21)"0SinceN=ρNa/M,whereρ=density,M=molarmass

8、,andNA=Avogadro’snumber,wemayalsowriteEq.(18)as:"r=1+(ρNA/"0M)α←−goo