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1、-ElectricPotentialduetoContinuousChargeDistributionsAPPhysicsCMrs.CoyleElectricPotential–Whatweusedsofar!ElectricPotentialPotentialDifferencePotentialforapointchargePotentialformultiplepointchargesRemember:VisascalarquantityKeepthesignsofthechargesintheequations,s

2、oVispositiveforpositivecharges.YouneedareferenceVbecauseitischangesinelectricpotentialthataresignificant.WhendealingwithpointchargesandchargedistributionsthereferenceisV=0whenrElectricPotentialDuetoaContinuousChargeDistributionHowwouldyoucalculatetheVatpointP?Two

3、WaystoCalculateElectricPotentialDuetoaContinuousChargeDistributionItcanbecalculatedintwoways:Method1:DividethesurfaceintoinfinitesimalelementsdqMethod2:IfEisknown(fromGauss’sLaw)Method1ConsideraninfinitesimalchargeelementdqandtreatitasapointchargeThepotentialatpoi

4、ntPduetodqMethod1Cont’dForthetotalpotential,integratetoincludethecontributionsfromallthedqelementsNote:referenceofV=0iswhenPisaninfinitedistancefromthechargedistribution.Ex25.5:a)VatapointontheperpendicularcentralaxisofaUniformlyChargedRingAssumethatthetotalcharge

5、oftheringisQ.Showthat:Ex25.5:b)FindtheexpressionforthemagnitudeoftheelectricfieldatPStartwithandEx25.6:Finda)Vandb)EatapointalongthecentralperpendicularaxisofaUniformlyChargedDiskAssumeradiusaandsurfacechargedensityofσ.Assumethatadiskisaseriesofmanyringswithwidthd

6、r.Ex25.6:Finda)Vandb)EatapointalongthecentralperpendicularaxisofaUniformlyChargedDiskEx25.7:FindVatapointPadistanceafromaFiniteLineofChargeAssumethetotalchargeoftherodisQ,lengthlandalinearchargedensityofλ.Hint:Method2forCalculatingVforaContinuousChargeDistribution

7、:IfEisknown(fromGauss’sLaw)Thenuse:Ex25.8:FindVforaUniformlyChargedSphere(Hint:UseGauss’sLawtofindE)AssumeasolidinsulatingsphereofradiusRandtotalchargeQForr>R,Ex25.8:FindVforaUniformlyChargedSphereAsolidsphereofradiusRandtotalchargeQForr

8、rgedSphere,GraphThecurveforinsidethesphereisparabolicThecurveforoutsidethesphereisahyperbola