Electricity Magnetism Electricchargesandfields Electricforce Chargesattractorrepeleachotherwithanelectricforce IfpointchargesQ1andQ2aredistancerapart andFistheforceoneach thenaccordingtoCoulomb slaw Thisisanexampleofaninversesquarelaw Ifrdoubles thenforceFdropstoonequarter andsoon Withasuitableconstant theaboveproportioncanbeturnedintoanequation TheunitofchargeforQ1andQ2isthecoulomb C Thevalueofkisfoundbyexperiment Itdependsonthemedium material betweenthecharges Foravacuum kis8 99 10 9Nm2C 2 andiseffectivelythesameforair Inpractice itismoreconvenienttouseanotherconstant 0 andrewritetheequationontheleftinthefollowingform Invacuum 0iscalledthepermittivityoffreespace Itsvalueis8 85 10 12C2N 1m 2 Note Although 4 complicatestheaboveequation itsimplifiesothersderivedfromit Intheaboveequation if sayQ1andQ2arelikecharges e g and thenFispositive SoapositiveFisaforceofrepulsion Similarly itfollowsthatanegativeFisaforceofattraction Electricfield Ifachargefeelsanelectricforce thenitisinanelectricfield IfachargeqfeelsaforceF thentheelectricfieldstrengthEisdefinedlikethis Insymbols Forexample ifachargeof2Cfeelsanelectricforceof10N thenEis5NC 1 Note Electricfieldstrengthisavector Itsdirectionisthatoftheforceonapositive charge Theforceactingonachargeinanelectricfieldcanbefoundbyrearrangingtheequationabove ChargeQproducesanelectricfieldwhichactsonasmallchargeq AsF qE So Theelectricfiledroundacharged sphericalconductorisshownontheright Itisaradialfield r Note Thechargeisonthesurfaceoftheconductor Outsidetheconductor theelectricfieldisthesameasifallthechargewereconcentratedatthecentre andtheaboveequationapplies Insidetheconductor thereisnoelectricfield Theequipotentiallinesareshownindashedline Electricpotential ChargeQcausesanelectricfield Asmallchargeqhasbeenmovedthroughthisfield fromaninfinitedistance wheretheelectricforceiszero topointP TheelectricpotentialV atpointP isdefinedasfollows WhereWistheworkdoneinmovingachargeqfrominfinitytopointP TheSIunitforelectricpotentialisthevolt V Note Electricpotentialisascalar Atinfinity theelectricpotentialiszero Elsewhere theelectricpotentialduetopositivechargeispositive Similarly theelectricpotentialduetoanegativechargeisnegative Linkingpotentialandfieldstrength E r qE V Work WisdoneonasmallchargeqinmovingitfromPtoP inauniformelectricfieldE So P P Thisequationgivestheworkdoneonthecharge So theworkdonebycharge q V Butworkdonebycharge force distancemoved qE r Therefore Incalculusnotation thereisamoregeneralversionofthisequationwhichalsoappliestonon uniformfields Note TheminussignindicatesthatEisinthedirectionofdecreasingpotential Electricpotentialinaradialfield Providedrisnotlessthantheradiusofthesphere Also Combiningthese andusingcalculusgives Note Inthediagramonthepreviouspage eachequipotentiallineisalinejoiningpointsofequalpotential Insidethechargedconductor allpointsareatthesamepotential sothepotentialgradientiszero FromthisitfollowsthatEisalsozero sothereisnoelectricfiledinsidetheconductor Comparingelectricandgravitationalfields Forparticlesofsimilarsize electricforcesareverymuchstrongerthangravitationalones Forexample electricforcesholdatomstogethertoformsolids Electricandgravitationalfieldshavesimilarfeatures Thatiswhytheequationinthisunithaveasimilarformtothoseingravitationalforce However comparingequivalentequations aminussignmaybepresentinonebutabsentfromtheother Thisarisesbecauseofthedifferingforcedirections Gravityisalwaysaforceofattraction Massisalwayspositiveanditproducesagravitationalfieldwhichisdirectedtowardsit Electricchargesmayattractorrepel However ifachargeispositive thenitproducesanelectricfieldwhichisdirectedawayfromit Capacitorsandfields Capacitance Capacitorsstoresmallamountsofelectriccharge Acapacitorcanbechargedbyconnectingabatteryacrossit ThehigherthePD potentialdifference V thegreaterthechargeQstored ExperimentsshowthatQinproportiontoV Therefore Q Visaconstant ThecapacitanceCofacapacitorisdefinedasfollows Insymbols Thehigherthecapacitance themorechargeisstoredforanygivenPD CapacitanceismeasuredinCV 1 knownasafarad F However afaradisverylargeunit andthe F 10 6F ismorecommonlyusedforpracticalcapacitors Energystoredbyacapacitor Workmustbedonetochargeupacapacitor Electricalpotentialenergyisstoredasresult Ifachargeof2CismovedthroughasteadyPDof10V then WorkdoneW QV 2 10 20J So thestoredenergyis20J Numerically thisistheareaunderthegraphbelow Whenacapacitorisbeingcharged QandVarerelatedasinthegraphbelow Asbefore theenergystoredisnumericallyequaltotheareaunderthegraph whichis1 2QV AsC Q V thiscanbeexpressedinthreedifferentways Electricfieldnearachargedplate AmetalspherehasachargeQuniformlydistributedoveritssurface TheelectricfieldEnearthesurfacecanbeexpressedlike ButthesurfaceareaofthesphereA 4 R2 So Thisequationalsoappliestoaflat chargedmetalplateofsurface ParallelPlatecapacitor Thesimplestformofcapacitorismadeupoftwoparallelmetalplates separatedbyanairgap ThecapacitorhasbeenconnectedtoabatterysothatthePDacrossitsplatesisV Asaresult itisstoringachargeQ Thismeansthat