物理chap靜電平衡狀態(tài)

ChapterConductorandDielectricsinElectrostaticFieldEnergyStoredinanElectricField1.1.ctionbetweenelectrostaticfield22-1.AChargedIsolatedConductorConductor:thereexistalotof Insulator(絕緣體):almostno Semiconductor(半導(dǎo)體):betweenAconductorinuniformelectricfieldE:

靜電感electrostaticequilibrium(-+ -+ -

- - - 2.Conditionofelectrostaticequilibrium(TheTheelectricfieldinsideconductormustbeElectricfieldEatandjustoutsidetheconductor'ssurfacemustbeperpendicular EIfitwerenot,thenitwouldhaveacomponentalongtheconductor'ssurfacethatwouldexertsonsurfacecharges,causingthemto3The3Thepotentialofaconductoratanyisconstant.Thesurfaceofaconductorisanequipotentialsurface.( V=Choosetwoarbitrarypointsa&binaVaVbbVaVbbaVaVbE Anotherexpressionoftheconditionofelectrostaticequilibrium3.Distributionofcharges3.Distributionofchargesonconductorunderelectrostaticequilibrium(P495)ChooseanarbitraryG.S.inside EdSq/ ES E0Ed Sq0——thereisnonetchargeinanysmallvolumewithinaconductor. cedonanisolatedconductorwillmoveentirelytothesurfaceoftheconductor.Noneoftheexcesschargewillbefoundwithintheconductor(導(dǎo)體內(nèi)凈電荷為零).22sur SE sur

0 0EEEThemagnitudeoftheEatalocationjustoutsideaconductor(導(dǎo)體外表面)isproportionaltosurfacechargedensityatthatlocationontheconductor.E 0E:producedbyallchargedbodiesinthe:relatedtoallchargedistributionsinthe Anisolatedconductorwitha (P495) Thereisnonetchargeontheinnersurfaceifnochargesinsidethe (腔內(nèi)無電荷時，空腔內(nèi)表面不會有電荷分布Ifthereischarge+qinthe ,thenitinduces–qatinnersurfaceandallexcesschargeremainsontheoutersurfaceoftheconductor.4Thesurfacechargedensityofanisolatedconductorisrelatedtotheradiusatthatlocationontheconductor(導(dǎo)體外表面的電荷密度與4Farawayfromeach V1V2

4π0 4π0

4πr1

2r2PointDischarge(尖端放電++ -++++++ -Electric0

E00big rsmall，big，E4.4.Electrostaticshielding(靜 Thehollowconductorcanshieldexternalelectricfields.+++

E ++ Question:Willtheelectricfieldofouterchargesenterintoconductoror ----+----+-+--++-----+----+-+--++-+-+ Aconductingsphere,ofradiusRandcharge+q,isconcentricwithasphericalconductings ofinnerradiusR1andouterradiusR2.Thiss hasanetchargeofQ.(a)Whatarethechargesontheinnerandoutersurfacesofthes ?(b)Thepotentialofthesphereandthes Sphericalsymmetry,quniformlydistributedonspheresurface.

A Qin=-q(byusingGauss’s conservationof

Potentialofthe Q A 4π

0R Potentialofthesphere q V 4π R4π 4π VAVABV (

)

Q4π R1 4π0R—similarto3chargedspherical inQuestion: IfAandBareconnectedbyalongmetalwire,whateffectswillitresult?Twoparallel-conducting- teswithsamearea(S>d2).TheyarechargedQAandQBrespectively.Findthesurfacedensityateachface.AssumesurfacedensityisFromlawofconservationof1S2S3S4SConsideringpointPB te

S1 3 1 PlotaaussiansurfaceS',we

EdS 1S2SQA3S4S

E1 3BB 00 00 21

QA2S

2

QA teBisconnectedtotheground,Example:TwoconcentricconductingspheresofradiusR1andR2havetotalchargesQ1andQ2,respectively.Iftheinnersphereisgrounded,whatistheelectricchargeontheinnersphere?Solution:Theinnersphereisgroundedanditspotentialiszero.SupposeitselectricchargeisQ'1 0 '

QRQ1 QR Theinnersphereisgrounded,butitselectricchargeisnotdefiniytobezero.Example:Thedistanceofapointcharge+qandthecenterofaunchargedconductingsphereisr.Find:(1)theelectricfieldatthecenterofthesphereduetotheinducedcharge;(2)thepotentialatthecenterduetothechargeandtheinducedcharge;(3)thenetchargeonthesphereifitisgrounded.+q RrOSolution:(1)Atthe+q RrO

EE14πr2 EE1Theelectricfieldduetotheinducedchargeis

E2

q04πr20

V1

V2

4π0R

dqThepotentialatthecenterV

V2

(3)Supposethenetchargeontheconductingsphereq1whenitisgrounded,sothepotentialatthecenter V

qR Example:Findtheinducedchargedensityasshowninthefigure.Solution:Intheconductor,find

atpointpointO’verynearpoint