M28_KNIG9404_ISM_C28.pdf

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1、28THEELECTRICPOTENTIALConceptualQuestions28.1.(a)Usetheexpressionforthepotentialenergyofapointcharge.1qQ1U1014(πεrqrqr2)1(2)====6Uq221qQ2()r⎛⎞q1⎜⎟()r42πε0r⎝⎠3(b)Usetheexpressionofthepotentialenergyofapointchargeinaparallelplatecapacitor.Uq11Esq1s3===Uq22Es(2)⎛⎞q12⎜⎟2s⎝⎠328.2.(a)

2、Theelectricforceisconservative.SinceΔ=−ΔKUKKUU,.fiif−=−WehaveKUfi==0and0.ThusK=U.Readingfromthegraph,at10fmU=×210J.−12iff(b)At20fm,K+=Utotalenergy−12−12−12=×210J.Readingfromthegraph,U(20fm)110=×J.ThusK(110J)+×=210×=−−12J,soK110×12J.1qq12128.3.(a)Theelectricpotentialenergyofthech

3、argesisU=.Thepotentialenergyvariesas,but4πε0rrbecausethetwochargeshaveoppositesignsthepotentialenergyactuallyincreasesasrincreases.(b)Lessthan.Twooppositechargesslowdownastheymovefartherapart.28.4.(a)Δ=UUU12→→ΔΔ13.=qEswheresisthedistancemeasuredverticallyfrompoint1topoint2.Onlyt

4、heverticaldisplacementmattersherebecausethereisnohorizontalcomponentofEoroftheforce.(b)vv23=.ThechangeinkineticenergyΔK12→isequaltoΔK13→becauseΔ=UU12→→Δ13andthetotalenergyisconstant.dd28.5.UUUUUUacfebd>>=>>.Calculate:Up=−⋅=−EpEcos.φUpa=−Ecos180°=+pEUpd=−Ecos0°=−pEUpb=−Ecos45°=−0

5、.707pEUpe=−Ecos90°=0Upc=−Ecos135°=+0.707pEUpf=−Ecos(90)−°=0©Copyright2013PearsonEducation,Inc.Allrightsreserved.Thismaterialisprotectedunderallcopyrightlawsastheycurrentlyexist.Noportionofthismaterialmaybereproduced,inanyformorbyanymeans,withoutpermissioninwritingfromthepublishe

6、r.28-128-2Chapter2828.6.(a)NoteUq=V.(b)Atx=1m,thetotalenergyEKU=+=+=111J1J2J.AttheturningpointvK==0so20.SinceE=+KU22,20J=+JUU22⇒=2J.Thisoccursatx=3m.28.7.(a)Thecapacitorchargeremainsconstant.NochargeflowsoffthecapacitorplatessobyconservationofchargeQQ12=.QηA(b)Theelectricfieldst

7、rengthalsoremainsconstant:EQ==.,,andAε0areallconstant.εε0028.8.VVVVVVEabcde=>>=.=swheresismeasuredfromthenegativeplate.TheelectricfieldEisconstantinsideaparallel-platecapacitor.VE222ss3mm28.9.(a)====3VE111ss1mmE2η(b)=1.Thefieldinsideaparallel-platecapacitorisaconstant:E=.E1ε01qV

8、r2041πε2r1mm128.10.(a)====Vr1q3mm3124πε01r1qEr2