大学物理学专业英语2

Electricity&MagnetismElectricchargesandfieldsElectricforce:r(+)(+)Q1Q2FFChargesattractorrepeleachotherwithanelectricforce.IfpointchargesQ1andQ2aredistancerapart,andFistheforceoneach,thenaccordingtoCoulomb’slaw:221rQQFThisisanexampleofaninversesquarelaw.Ifrdoubles,thenforceFdropstoonequarter,andsoon.Withasuitableconstant,theaboveproportioncanbeturnedintoanequation:221rQkQFTheunitofchargeforQ1andQ2isthecoulomb(C).Thevalueofkisfoundbyexperiment.Itdependsonthemedium(material)betweenthecharges.Foravacuum,kis8.99×10-9Nm2C-2,andiseffectivelythesameforair.Inpractice,itismoreconvenienttouseanotherconstant,ε0,andrewritetheequationontheleftinthefollowingform:20214rQQFInvacuumε0iscalledthepermittivityoffreespace.Itsvalueis8.85×10-12C2N-1m-2.Note:•Although‘4π’complicatestheaboveequation,itsimplifiesothersderivedfromit.•Intheaboveequation,if,sayQ1andQ2arelikecharges(e.g.–and–),thenFispositive.SoapositiveFisaforceofrepulsion.Similarly,itfollowsthatanegativeFisaforceofattraction.ElectricfieldIfachargefeelsanelectricforce,thenitisinanelectricfield.IfachargeqfeelsaforceF,thentheelectricfieldstrengthEisdefinedlikethis:chargeforceelectricEInsymbolsqFEForexample,ifachargeof2Cfeelsanelectricforceof10N,thenEis5NC-1.Note:•Electricfieldstrengthisavector.Itsdirectionisthatoftheforceonapositive(+)charge.Theforceactingonachargeinanelectricfieldcanbefoundbyrearrangingtheequationabove:qEFChargeQproducesanelectricfieldwhichactsonasmallchargeq.AsF=qErEF=qE204rQqFSo:204rQETheelectricfiledroundacharged,sphericalconductorisshownontheright.Itisaradialfield.rEequipotentialNote:•Thechargeisonthesurfaceoftheconductor.•Outsidetheconductor,theelectricfieldisthesameasifallthechargewereconcentratedatthecentre,andtheaboveequationapplies.•Insidetheconductor,thereisnoelectricfield.•Theequipotentiallinesareshownindashedline.ElectricpotentialChargeQcausesanelectricfield.Asmallchargeqhasbeenmovedthroughthisfield,fromaninfinitedistance(wheretheelectricforceiszero),topointP.∞WorkdoneWElectricpotentialVPqQTheelectricpotentialV(atpointP)isdefinedasfollows:qWVWhereWistheworkdoneinmovingachargeqfrominfinitytopointP.TheSIunitforelectricpotentialisthevolt(V).Note:•Electricpotentialisascalar.•Atinfinity,theelectricpotentialiszero.•Elsewhere,theelectricpotentialduetopositivechargeispositive.Similarly,theelectricpotentialduetoanegativechargeisnegative.LinkingpotentialandfieldstrengthEΔrqEΔVWorkΔWisdoneonasmallchargeqinmovingitfromPtoP’inauniformelectricfieldE.So,PP’VqWThisequationgivestheworkdoneonthecharge.So,theworkdonebycharge=-qΔV.Butworkdonebycharge=force×distancemoved=qEΔrTherefore:rVEIncalculusnotation,thereisamoregeneralversionofthisequationwhichalsoappliestonon-uniformfields:drdVENote:TheminussignindicatesthatEisinthedirectionofdecreasingpotential.ElectricpotentialinaradialfieldProvidedrisnotlessthantheradiusofthesphere:204rQEAlso,drdVECombiningthese,andusingcalculusgives:rQV04Note:•Inthediagramonthepreviouspage,eachequipotentiallineisalinejoiningpointsofequalpotential.•Insidethechargedconductor,allpointsareatthesamepotential,sothepotentialgradientiszero.FromthisitfollowsthatEisalsozero,sothereisnoelectricfiledinsidetheconductor.ComparingelectricandgravitationalfieldsForparticlesofsimilarsize,electricforcesareverymuchstrongerthangravitationalones.Forexample,electricforcesholdatomstogethertoformsolids.Electricandgravitationalfieldshavesimilarfeatures.Thatiswhytheequationinthisunithaveasimilarformtothoseingravitationalforce.However,comparingequivalentequations,aminussignmaybepresentinonebutabsentfromtheother.Thisarisesbecauseofthedifferingforcedirections.Gravityisalwaysaforceofattraction.Massisalwayspositiveanditproducesagravitationalfieldwhichisdirectedtowardsit.Electricchargesmayattractorrepel.However,ifachargeispositive,thenitproducesanelectricfieldwhichisdirectedawayfromit.CapacitorsandfieldsCapacitance:Capacitorsstoresmallamountsofelectriccharge.Acapacitorcanbechargedbyconnectingabatteryacrossit.ThehigherthePD(potentialdifference)V,thegreaterthechargeQstored.ExperimentsshowthatQinproportiontoV.Therefore,Q/Visaconstant.ThecapacitanceCofacapacitorisdefinedasfollows:PDchargeecapacitancInsymbols:VQCThehigherthecapacitance,themorechargeisstoredforanygivenPD.CapacitanceismeasuredinCV-1,knownasafarad(F).However,afaradisverylargeunit,andtheμF(10-6F)ismorecommonlyusedforpracticalcapacitors.EnergystoredbyacapacitorWorkmustbedonetochargeupacapacitor.Electricalpotentialenergyisstoredasresult.Ifachargeof2CismovedthroughasteadyPDof10V,then,WorkdoneW=QV=2×10=20JSo,thestoredenergyis20J.Numerically,thisistheareaunderthegraphbelow.Area=energystoredPD/V0102Charge/CPD/V0VQCharge/CArea=energystoredWhenacapacitorisbeingcharged,QandVarerelatedasinthegraphbelow.Asbefore,theenergystoredisnumericallyequaltotheareaunderthegraph,whichis1/2QV.AsC=Q/V,thiscanbeexpressedinthreedifferentways:CQCVQV22212121storedenergyElectricfieldnearachargedplateAmetalspherehasachargeQuniformlydistributedoveritssurface.TheelectricfieldEnearthesurfacecanbeexpressedl