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1、Electricity Magnetism Electricchargesandfields Electricforce Chargesattractorrepeleachotherwithanelectricforce IfpointchargesQ1andQ2aredistancerapart andFistheforceoneach thenaccordingtoCoulomb slaw Thisisanexampleofaninversesquarelaw Ifrdoubles thenforceFdropstoonequarter andsoon Withasuitableconst
2、ant theaboveproportioncanbeturnedintoanequation TheunitofchargeforQ1andQ2isthecoulomb C Thevalueofkisfoundbyexperiment Itdependsonthemedium material betweenthecharges Foravacuum kis8 99 10 9Nm2C 2 andiseffectivelythesameforair Inpractice itismoreconvenienttouseanotherconstant 0 andrewritetheequation
3、ontheleftinthefollowingform Invacuum 0iscalledthepermittivityoffreespace Itsvalueis8 85 10 12C2N 1m 2 Note Although 4 complicatestheaboveequation itsimplifiesothersderivedfromit Intheaboveequation if sayQ1andQ2arelikecharges e g and thenFispositive SoapositiveFisaforceofrepulsion Similarly itfollows
4、thatanegativeFisaforceofattraction Electricfield Ifachargefeelsanelectricforce thenitisinanelectricfield IfachargeqfeelsaforceF thentheelectricfieldstrengthEisdefinedlikethis Insymbols Forexample ifachargeof2Cfeelsanelectricforceof10N thenEis5NC 1 Note Electricfieldstrengthisavector Itsdirectionisth
5、atoftheforceonapositive charge Theforceactingonachargeinanelectricfieldcanbefoundbyrearrangingtheequationabove ChargeQproducesanelectricfieldwhichactsonasmallchargeq AsF qE So Theelectricfiledroundacharged sphericalconductorisshownontheright Itisaradialfield r Note Thechargeisonthesurfaceoftheconduc
6、tor Outsidetheconductor theelectricfieldisthesameasifallthechargewereconcentratedatthecentre andtheaboveequationapplies Insidetheconductor thereisnoelectricfield Theequipotentiallinesareshownindashedline Electricpotential ChargeQcausesanelectricfield Asmallchargeqhasbeenmovedthroughthisfield fromani
7、nfinitedistance wheretheelectricforceiszero topointP TheelectricpotentialV atpointP isdefinedasfollows WhereWistheworkdoneinmovingachargeqfrominfinitytopointP TheSIunitforelectricpotentialisthevolt V Note Electricpotentialisascalar Atinfinity theelectricpotentialiszero Elsewhere theelectricpotential
8、duetopositivechargeispositive Similarly theelectricpotentialduetoanegativechargeisnegative Linkingpotentialandfieldstrength E r qE V Work WisdoneonasmallchargeqinmovingitfromPtoP inauniformelectricfieldE So P P Thisequationgivestheworkdoneonthecharge So theworkdonebycharge q V Butworkdonebycharge fo
9、rce distancemoved qE r Therefore Incalculusnotation thereisamoregeneralversionofthisequationwhichalsoappliestonon uniformfields Note TheminussignindicatesthatEisinthedirectionofdecreasingpotential Electricpotentialinaradialfield Providedrisnotlessthantheradiusofthesphere Also Combiningthese andusing
10、calculusgives Note Inthediagramonthepreviouspage eachequipotentiallineisalinejoiningpointsofequalpotential Insidethechargedconductor allpointsareatthesamepotential sothepotentialgradientiszero FromthisitfollowsthatEisalsozero sothereisnoelectricfiledinsidetheconductor Comparingelectricandgravitation
11、alfields Forparticlesofsimilarsize electricforcesareverymuchstrongerthangravitationalones Forexample electricforcesholdatomstogethertoformsolids Electricandgravitationalfieldshavesimilarfeatures Thatiswhytheequationinthisunithaveasimilarformtothoseingravitationalforce However comparingequivalentequa
12、tions aminussignmaybepresentinonebutabsentfromtheother Thisarisesbecauseofthedifferingforcedirections Gravityisalwaysaforceofattraction Massisalwayspositiveanditproducesagravitationalfieldwhichisdirectedtowardsit Electricchargesmayattractorrepel However ifachargeispositive thenitproducesanelectricfi
13、eldwhichisdirectedawayfromit Capacitorsandfields Capacitance Capacitorsstoresmallamountsofelectriccharge Acapacitorcanbechargedbyconnectingabatteryacrossit ThehigherthePD potentialdifference V thegreaterthechargeQstored ExperimentsshowthatQinproportiontoV Therefore Q Visaconstant ThecapacitanceCofac
14、apacitorisdefinedasfollows Insymbols Thehigherthecapacitance themorechargeisstoredforanygivenPD CapacitanceismeasuredinCV 1 knownasafarad F However afaradisverylargeunit andthe F 10 6F ismorecommonlyusedforpracticalcapacitors Energystoredbyacapacitor Workmustbedonetochargeupacapacitor Electricalpote
15、ntialenergyisstoredasresult Ifachargeof2CismovedthroughasteadyPDof10V then WorkdoneW QV 2 10 20J So thestoredenergyis20J Numerically thisistheareaunderthegraphbelow Whenacapacitorisbeingcharged QandVarerelatedasinthegraphbelow Asbefore theenergystoredisnumericallyequaltotheareaunderthegraph whichis1
16、 2QV AsC Q V thiscanbeexpressedinthreedifferentways Electricfieldnearachargedplate AmetalspherehasachargeQuniformlydistributedoveritssurface TheelectricfieldEnearthesurfacecanbeexpressedlike ButthesurfaceareaofthesphereA 4 R2 So Thisequationalsoappliestoaflat chargedmetalplateofsurface ParallelPlatecapacitor Thesimplestformofcapacitorismadeupoftwoparallelmetalplates separatedbyanairgap ThecapacitorhasbeenconnectedtoabatterysothatthePDacrossitsplatesisV Asaresult itisstoringachargeQ Thismeansthat
