(带电子之间)

Ch24ElectricPotential1Onegoalofphysicsistoidentifybasicforcesinour2424--1WhatisPhysics1WhatisPhysicsgpyyworld,suchastheelectricforcewediscussedinCh.21.Arelatedgoalistodeterminewhetheraforceisconservative—thatiswhetherwecanfindaconservative—thatis,whetherwecanfindapotentialenergytobeassociatedwiththeforce.Themotivation(動機)forassociatingapotentialThemotivation(動機)forassociatingapotentialenergywithaforceisthatwecanthenapplytheprincipleoftheconservationofmechanicalenergyldThilltoclosedsystems.Thisextremelypowerfulprincipleallowsustocalculatetheresultsofexperimentsforwhichforcecalculationsalonewouldbeverydifficult.calculationsalonewouldbeverydifficult.Experimentally,physicistsandengineersdiscoveredthattheelectricforceisconservativeandthushasan2associatedelectricpotentialenergy.2424--2ElectricPotentialEnergy2ElectricPotentialEnergyWhenanelectrostaticforceactsbetweentwoormorechargedparticleswithinasystemofparticles,wecanassignanelectricpotentialenergyUtothesystemIftheanelectricpotentialenergyUtothesystem.Ifthesystemchangesitsconfiguration(組態)fromaninitialstateitoafinalstatef,theelectrostaticforce(帶電粒子之間)dkW(∫d)thtilThltihdoesworkW(≡∫F•dS)ontheparticles.TheresultingchangeinthepotentialenergyofthesystemisΔU=Uf-Ui=-W(24-1)[保守力(重力、彈力、電力)作功(等速下)造成系統位能變化(減少):W=-ΔU=-(Uf-Ui)]Aswithotherconservativeforces,theworkdonebythe3electrostaticforceispathindependent.SupposeachargedparticleqwithinthesystemiqSupposeachargedparticleqwithinthesystemmovesfrompointitopointfwhileanelectrostaticforcebetweenitandtherestofthettitPiddthtfthFsystemactsonit.Providedtherestofthesystemdoesnotchange,theworkWdonebytheforceontheparticleisthesameforallFpfpathsbetweenpointsiandf.FilltkthffForconvenience,weusuallytakethereferenceconfigurationofasystemofchargedparticlestobethatinwhichtheparticlesareallinfinitelyseparatedfromonepypanother.Also,weusuallysetthecorrespondingreferencepotentialenergytobezero(因為所有帶電粒子都相距無窮遠當然之間電力為零因此可設此時系統電位能為零)4窮遠，當然之間電力為零，因此可設此時系統電位能為零).ΔU=Uf–Ui=-W(24-1)Supposethatseveralchargedparticlescometogetherfrominitiallyinfiniteseparations(initialstatei)toformasysteminitiallyinfiniteseparations(initialstatei)toformasystemofneighboringparticles(finalstatef).LettheinitialpotentialenergyU=0andletWrepresentLettheinitialpotentialenergyUi=0,andletW∞representtheworkdonebytheelectrostaticforcesbetweentheparticlesduringthemovefrominitialstate(相距∞)tofinal相距有限遠此時之間電力設此時系統電位state(相距有限遠，此時之間電力≠0，設此時系統電位能≠0).ThenfromEq.24-1,thefinalpotentialenergyUf≡UofthesystemisUf-U=U=-W(24-2)UofthesystemisUfUi=U=W∞(242)5SampleProblem24-16Solution:WeneedthreeKeyIdeashere:WeneedthreeKeyIdeashere:(1)ThechangeΔUintheelectricpotentialenergyoftheelectronisrelatedtotheworkWdoneontheelectronbytheelectricfield.Equation24-1(ΔU=-W)givestherelation.(2)TheworkdonebyaconstantforceonaparticleundergoingadisplacementisW=-FdundergoingadisplacementisW=Fd.(3)TheelectrostaticforceandtheelectricfieldarerelatedbyF=qE.Thus,ΔU=-W=-Fd=-qEd=-qEdcosθ=-(1.6×10-19C)(150N/C)(520m)cos180o121014J=-1.2×10-14J.Thisresulttellsusthatduringthe520mascent,theelectricpotentialenergyoftheelectrondecreasesby7electricpotentialenergyoftheelectrondecreasesby1.2×10-14J.TACTIC1:ElectricPotentialEnergy;WorkDonebyaFieldAnelectricpotentialenergyisassociatedwithasystemofparticlesasawhole.However,thestatementsinSamplep,pProblem24-1thatassociateitwithonlyoneparticlewithinasystem.Forexample,youmightread,“Anelectroninanelectricfieldhasapotentialenergyof10-7J”Suchelectricfieldhasapotentialenergyof107J.Suchstatementsareoftenacceptable,butyoushouldalwayskeepinmindthatthepotentialenergyisactuallyassociatedwithasystem—here,theelectronplusthechargedparticlesthatsetuptheelectricfield.AlsokeepinmindthatitmakessensetoassignaAlsokeepinmindthatitmakessensetoassignaparticularpotentialenergyvalue,suchas10-7Jhere,toaparticleorevenasystemonlyifthereferencepotential8energyvalueisknown.InSamplePro24-1thepotentialenergyofacharged2424--3ElectricPotential3ElectricPotentialInSamplePro.24-1,thepotentialenergyofachargedparticleinanelectricfielddependsonthechargemagnitude.However,thepotentialenergyperunitchargehasauniquevalueatanypointinanelectricfield.Example:Supposeweplaceatestparticleofpositivecharge1.60×10-19Catapointinanelectricfieldwherethecharge1.60×10Catapointinanelectricfieldwheretheparticlehasanelectricpotentialenergyof2.40×10-17J.ThenthepotentialenergyperunitchargeisSupposewereplacethattestparticlewithonehaving3.20×10-19C.Wewouldfindthatthe2ndparticlehas4.80×10-17J(twicethatofthefirstparticle)Howeverthepotential917J(twicethatofthefirstparticle).However,thepotentialenergyperunitchargewouldbethesame,still150J/C.Thus,theelectricpotentialenergyperunitchargeatapointinanelectricfieldisdefinedastheelectricpotentialVatthatpoint(independentofthechargeqoftheparticle)F→E=F/q(單位電荷所受的力)V≡U/q(24.5)F→E=F/q(單位電荷所受的力)U→V=U/q[單位電荷所具有的電位能(在某一電場E分佈下)]TheelectricpotentialdifferenceΔVbetweenanytwopointsiandfinanelectricfieldisequaltothedifferenceinpotentialenergyperunitchargebetweenthetwopoints:10ΔU=Uf–Ui=-W(24-1)UsingEq.24-1tosubstitute-WforΔUinEq.2