Potential4）潜在的

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1、PotentialAlanMurrayPotential…StartSimply…VE=-V/dE=-(rateofchangeofVwithdistance)0V0

2、E

3、RememberthecapacitorAlanMurray–UniversityofEdinburghE=-V/dShouldreallybeE=-dV/dxAndifV=Mx+c,dV/dx=M=constantThenE=-MasshownIn3D,dV/dxbecomes(dV/dx,dV/dy,dV/dz)=ÑV,soE=-ÑV=-(dV/dx,dV/dy,dV/dz)E=-ÑVAlanMurray

4、–UniversityofEdinburghPotential:Analogy100M150M200M250M300MThesecontourlinesarelinesofequalgravitationalpotentialenergymghWheretheyareclosetogether,theeffectofthegravitationalfieldisstrongThefieldactsinadirectionperpendiculartothecountoursanditpointsinanegativedirection…(i.e.that’sthewayyouwil

5、lfall!)AlanMurray–UniversityofEdinburghPotential-commentsWalkingaroundacontourexpendsnoenergyInaperfectworldi.e.no-onemovesthehillasyouwalk!WalkingtothetopofthehillandbackagainexpendsnoenergyInaperfectworldi.e.–thehillstaysstillandyourecouptheenergyyouexpendwhileclimbingasyoudescend(usingyouri

6、nternalgenerator!)AlanMurray–UniversityofEdinburghElectricFieldsandPotentialsaretheSameMetalelectrodeMetalelectrode0V5V1V2V3V4V5VE-FieldlinesVoltagecontoursAlanMurray–UniversityofEdinburghPotentialDifference:FormalDefinition(L)MetalelectrodeMetalelectrode0V5V5VE-Fieldlinesaxbx1CThePotentialDif

7、ference(Voltage)betweenaandbisthe–theworkdonetomovea1Cchargefromatob1C1C1CAlanMurray–UniversityofEdinburghPotentialDifference:FormalDefinition(L)ThePotentialDifference(Voltage)betweenaandbisthe–theworkdonetomovea1CchargefromatobIn1D,Work=-FdIn3D,Work=-F.dlForce=F=Q´E=+1´E=EWorkdone=-E.dl

8、TotalWorkdone=-òabE.dlAlanMurray–UniversityofEdinburghLineintegral…revisionEdlEdlEdlEdlEdlEdlEdlEdlEdlEdlEdlEdlEdlEAlanMurray–UniversityofEdinburghPotentialDifference=-òabE.dlòabisalineintegralIngeneralmathematics,thevalueofalineintegraldependsuponthepathdltakesfromatobInthispotentialcalculati

9、on,thepathdoesnotmatterSo:choosea“convenient”pathAlanMurray–UniversityofEdinburghEPotentialDifference:WorkedExample–PointchargeQQ(b)(a)1CPlacea1Cchargeat(a)Moveitto(b)Workdoneinthismovementisthepotentialdifference(voltage)between(a)an