電磁場(chǎng)與電磁波Electromagnetic

Fieldsand

WavesChapter2ElectrostaticFields2.1ElectrostaticFieldsinvacuum2.1.1ElectricFieldIntensity（2）Coulomb'slaw（1）Whatiselectrostaticfield?（3）Twotypesof"points"inthefield（4）Theelectricfieldintensitygeneratedbyapointcharge（5）Theelectricfieldintensitywhichisgeneratedbyadistributedcharge2.1.1ElectricFieldIntensity（1）Whatiselectrostaticfield?

Thechargesurroundsaspecialformofmattercalledanelectricfield.

Theelectricfieldactsasamechanicalforceonthechargeinit.①Theelectricfieldcausedbyachargeatrestwithrespecttotheobserverandwhosechargedoesnotchangewithtimeiselectrostaticfield.②Thebasicfieldquantityofelectrostaticfieldiselectricfieldintensity

.electrostaticfield:Theelectricfieldgeneratedbyastationarycharge.Importantcharacteristic:Theelectricfieldexertsaforceonchargeslocatedwithinit.2.1.1ElectricFieldIntensity

Forcebetweentwo-pointchargesq1andq2inaninfinitevacuum:（2）Coulomb’sLawThedielectricconstantofvacuum2.1.1ElectricFieldIntensityElectricfieldforceobeysthesuperpositiontheoremqq1q2q3q4q5q6q72.1.1ElectricFieldIntensity（3）twotypesof"points"：fieldpointandsourcepointThesourcepoint：thelocationofthefieldsource(suchaspointcharge)orThefieldpoint：wherethefieldquantityneedstobedeterminedorThedistancevectorfromthesourcetothefieldpoint:Iftherearemultiplesourcepoints,thedistancevectorfromtheoriginofcoordinatestothesourcepointisTheunitvectorisHasnpointcharges

respectivelylocatedinTheforceactonpointcharge

locatedin(4)ElectricFieldIntensityofapointchargeandasystemofpointchargesWhatifthechargeiscontinuouslydistributed?TheelectricfieldintensityofthepointchargeElectricFieldIntensity——Testcharge

2.1.1ElectricFieldIntensity(5)

ElectricFieldIntensityofdistributedchargeThevolumechargedensity：Thesurfacechargedensity：Thelinechargedensity：Theelementcharge

：2.1.1ElectricFieldIntensityWecandivideanydistributedchargeintomanyelementcharges,andtreateachelementchargeasapointcharge.Inaninfinitevacuum,accordingtothecalculationformulaoffieldintensitygeneratedbypointcharge,theelementfieldintensityatthefieldpoint(r)generatedbytheelementcharge

dq

at(r’)isByapplyingthesuperpositionprinciple,thefieldintensityatthefieldpoint(r)canbeobtainedbyintegratingallthefieldsourcecharges(5)

ElectricFieldIntensityofdistributedchargeElectricfieldgeneratedbychargesinasmallvolumeelementSurfacedistributedchargeLine-distributedchargeElectricfieldintensitygeneratedbyuniformlyvolume-distributedcharge(5)

ElectricFieldIntensityofdistributedchargeElectricfieldintensityofseveraltypicalchargedistributions（infinitelength）（finitelength）均勻帶電直線(xiàn)段均勻帶電圓環(huán)auniformlychargedstraightlinesegment:theaxisofauniformlychargedcircularring:Example:Findtheelectricfieldcausedbyaninfinitelylonglinechargeuniformlydistributedwithlinedensity

invacuum,asshowninthefigure.Whenthedisplacementofq0isdl,theworkdonebytheelectricfieldforceis

ThevoltagefromPtoQis1.Definitionofvoltage2.1.2ElectricPotentialIfq0ismovedfrompointPtopointQ,thetotalworkdonebytheelectricfieldforceisThevoltagebetweentwopointsisequaltotheworkdonebytheelectricfieldforcewhenaunitpositivechargeismovedbetweentwopoints.Thevoltagebetweenanytwopointsinanelectrostaticfieldisequaltothelineintegraloftheelectricfieldintensity.Ifthechargemoves

alonganyclosedpath

intheelectrostaticfield,theworkdonebytheelectricfieldforceisequaltozero.2.Theelectrostaticfieldisaconservationfield2.1.2ElectricPotentialThelooprouteintegraloftheelectricfieldintensityvector

ETheelectrostaticfieldisaconservativefield.3.Definitionandcalculationofpotential2.1.2ElectricPotentialThepotentialofapointinanelectricfieldisdefinedastheworkdonebytheforceoftheelectricfieldtomoveaunitpositivechargefromthatpointtoapointofzeropotential(thereferencepoint).IfpointQistakenasthepotentialreferencepointThepotentialatthereferencepointisobviouslyzero.Thepotentialofapointatinfinityisusuallychosentobezero2.1.2ElectricPotential

ThepotentialofapointchargeqattheoriginofthecoordinatesinavacuumatadistancerIfthefieldsourcehasnpointcharges,thepotentialatthefieldpoint(r)canbeobtainedbyapplyingthesuperpositionprincipleWherethefieldsourcecontainsvariousdistributedcharges3.Definitionandcalculationofpotential2.1.3TherelationshipbetweenelectricfieldintensityandpotentialThecurlofthegradientofanyscalarisequaltozero1.FromEto2.FromtoEBecauseof

，applythecurltheoremtheelectrostaticfieldisanon-rotationalfieldTheelectricfieldintensityisequaltothenegativegradientofpotentialSolution：Example2-2Figureshowsthelinechargeofacircularringwithradiusa(linechargedensity

)onthexOyplaneinvacuum.TrytodeterminethepotentialandelectricfieldintensityatpointPontheaxiszawayfromthecenterofthecircle.Accordingtotheanalysis,thefieldintensityhasonlyzcomponentExample2-3Figureshowsauniformlychargeddiskwithradiusaandsurfacechargedensity

.Findtheelectricfieldintensityontheaxisofthedisk.ThepotentialgeneratedbythechargeontheentirediskatpointPisSolution:Takearingwithradiusrandwidthdr

onthedisk,andthepotentialgeneratedbytheelementcharge

ontheringatpointPontheaxisisTheobtainableelectricfieldintensityisApplythegradientexpressionincylindricalcoordinatesystemIftheradiusofthedisctendstoinfinityExample

Findthepotentialofauniformlychargedwirewithalengthof2Landachargedensityof

.xyzL-L

Solution:Usingcylindricalcoordinates,letthelinechargecoincidewiththez-axis,withthemidpointlocatedatthecoordinateorigin.Duetoaxialsymmetry,theelectricpotentialisindependentofz.When

Theaboveexpressionbecomesinfinitebecausethechargeisnotdistributedwithinafinitearea,andthepotentialreferencepointischosenataninfinitelydistantpoint.Anarbitraryconstantcanbeaddedtotheaboveformula,resultinginSelectingthepointwhereρ=aasthepotentialreferencepoint,wehave①

Electricfieldline(Eline)E

lineisacurveonwhichthedirectionofthetangentlineateachpointisthesameasthedirectionofthefieldintensityatthatpoint.IfdlrepresentstheelementsegmentonE

line，theE=kdl，namelyEx=kdx,Ey=kdy,

Ez=kdz,

andthedifferentialequationoflineinrectangularcoordinatesystemis：2.1.4Thedistributionpatternofthefield②EquipotentialsurfaceandequipotentiallineTheequationoftheequipotentialsurfaceisthefollowingTheequipotentialsurfaceandthefieldlineareperpendiculareverywhere.Thedensertheequipotentialdistribution,thegreaterthefieldintensity.等位線(xiàn)的切線(xiàn)等位線(xiàn)PαEP‘dlExample2-4DeterminetheequationofElineinpointchargefield.zxyP（x,y,z)orqSolution:Supposepointchargeislocatedattheoriginofcoordinates,thenFromdifferentialequation

get2.2ElectrostaticFieldsindielectrics2.2.1Polarizationofdielectrics

Theresponseofamediumtoanelectromagneticfieldcanbedividedintothreecases:

polarization,magnetization,andconduction.

Theparametersthatdescribetheelectromagneticpropertiesofamediumare:

dielectricconstant,magneticpermeability,andconductivity.1.Propertiesofconductorsinelectrostaticequilibrium(1)Thefieldintensityintheconductorshouldbezero;(2)Conductorsareequipotential,andthepotentialsateachpointareequal;(3)Thedirectionofthefieldintensityatanypointontheconductorsurfacemustbeperpendiculartotheconductorsurface;(4)Iftheconductorischarged,thechargecanonlybedistributedonthesurface.2.2.1Polarizationofdielectrics2.dielectricsTheparticlesinsideadielectriccanmoveslightlyundertheactionofanexternalelectricfield,butcannotleavetherangeofmolecules.Thechargecarriedbytheparticlesinsidethedielectriciscalledboundcharge.Anidealmedium,alsocalledaninsulator,isamediumwithzeroelectricalconductivity.

2.2.1Polarizationofdielectrics2.dielectricsThedielectriclosesitsdielectricpropertyandbecomesaconductorundertheactionofastrongenoughelectricfield,whichiscalleddielectricbreakdown.Thecorrespondingvoltageiscalledbreakdownvoltage,andthefieldintensityatthetimeofbreakdowniscalledbreakdownfieldintensity.2.2.1Polarizationofdielectrics3.ElectricdipoleElectricdipolereferstotwoelectricchargeswithoppositesignsandequalvaluesthatareveryclosetoeachother.Electricdipolemoment：Thedirectionofpisfromthenegativechargetothepositivecharge.Anelectricdipolecausesanelectricfieldaroundit,anditisalsosubjecttoaforceinanexternalelectricfield.2.2.1Polarizationofdielectrics4.PolarizationofdielectricUndertheactionofanappliedelectricfield,theboundchargeinthemediumshifts.Thephenomenoniscalledpolarization.Insidethepolarizedmediumappearanumberofelectricdipolesarrangedinroughlythesamedirection,theseelectricdipoleswillproduceanelectricfield.2.2.1Polarizationofdielectrics1）Undertheinfluenceofanexternalelectricfield,adielectricmaterialwillundergopolarization.2）Thedegreeofpolarizationisdeterminedbythemagnitudeoftheelectricdipolemomentwithinthemedium.4.PolarizationofdielectricTheelectricfieldinapolarizedmediumisthecompositeoftheexternallyappliedelectricfieldandtheelectricfieldoftheelectricdipole.2.2.1PolarizationofdielectricsUniformmedium:Thecharacteristicsofthemediumdonotchangewiththechangeofspatialcoordinates.Isotropicmedium:Thecharacteristicsofthemediumdonotchangewiththechangeofthedirectionoftheelectricfieldquantity,otherwiseitisanisotropicmedium,suchasdiode.Linearmedium:theparametersofthemediumdonotchangewiththechangeoftheelectricfieldquantity.4.PolarizationofdielectricCommontermsformediaareasfollows.2.2.1Polarizationofdielectrics5.PolarizationintensityDefinition：thevectorsumoftheelectricdipolemomentintheunitvolumeafterpolarization

Theexperimentalresultsshowthatthepolarizationintensityisproportionaltotheappliedfieldintensityinisotropiclinearmedia

istheelectricpolarizationofthedielectric,apositiverealnumber.2.2.1Polarizationofdielectrics

Afterdielectricpolarization,theremaybeanetresidualchargeinside,whichiscalledthepolarizationvolumecharge6.Furtherdiscussiononpolarizationphenomenon

Afterdielectricpolarization,netresidualchargesmayalsoappearonthedielectricinterface,resultinginpolarizationsurfacecharges2.2.1PolarizationofdielectricsTherelationshipbetweenthebodychargedensity,surfacechargedensityofpolarizationchargeandpolarizationintensity：WhereistheunitvectorinthedirectionoftheouternormalofthemediumsurfaceBasedonthedivergencetheorem2.2.1Polarizationofdielectrics6.Furtherdiscussiononpolarizationphenomenon1.Electricdisplacement

Question:Whenthereisamediumpresentinspace,thepossiblepresenceofpolarizedchargeswithinitwillgenerateanadditionalelectricfield,whichwillaffecttheoveralldistributionoftheelectricfield.So:whencalculatingthetotalelectricfield,isitnecessarytofirstcalculatetheelectricfieldgeneratedbythepolarizedcharges?2.2.2ElectrastaticFieldsindielectrics1.Electricdisplacement

2.2.2ElectrastaticFieldsindielectricsinavacuum:inamedium： Electricdisplacement

:Usingthedivergencetheoremandconsideringunit：C/m2thefluxofelectricdisplacementthroughanyclosedsurfaceinthedielectricisequaltothealgebraicsumoffreechargessurroundedbytheclosedsurface.then

2.2.2ElectrastaticFieldsindielectricsInisotropiclinearmedia：2.2.2ElectrastaticFieldsindielectricstheelectricpolarizability,apositiverealnumber1.ConditionsforusingGauss'slawtocalculateelectricfieldintensityinasimpleanddirectmannerWhenEisuniformlydistributedonS,orwhentheintegralresultisknown!Whatproblempossessessuchcharacteristics?

Aproblemwithsymmetry!2.2.3ApplicationsofGauss’sFluxLawConditions：canbemovedoutsidetheintegralsignoftheGauss’slawforsolvingUnderwhatcircumstances

canbemovedoutsidetheintegralsign?

Sphericalsymmetrydistribution:2.2.3ApplicationsofGauss’sFluxLawAxisymmetricdistribution:2.2.3ApplicationsofGauss’sFluxLaw

Infiniteplanecharge:(a)(b)2.2.3ApplicationsofGauss’sFluxLawSolution:(1)Accordingtothepropertiesofconductorsinelectrostaticfields,thedistributionofchargescanbeobtained.(2)Tofindtheelectricfieldintensity,solvefromtheinsideout.q1-q1q1+q2Example2-5Itisknownthattherearetwoconcentricmetalsphericalshellsinvacuum.TheinnersphericalshellhasradiusR1andchargeq1,andtheoutersphericalshellhasradiusR2andthicknessandchargeq2.Findtheelectricfieldintensityandpotentialeverywhereinthefield.q1-q1q1+q2Tofindthefieldintensityatpointr,applyGauss'sfluxtheoremtodifferentregions,andconstructaGaussianclosedsurfaceasaspherewithradiusrandconcentricwiththeconductor.(3)Tocalculatethepotential,solvefromtheoutsideinward.Weshouldfirstcalculatethepotentialoutsidetheoutersphericalshell,withtheinfinitedistanceasthereferencepoint.Sincetheconductorisanequipotentialbody,thepotentialofeverypartoftheconductorwithintheoutersphericalshellisExample2-6ItisknownthatthereisavolumechargeinavacuumuniformlydistributedinasphereofradiusRwithvolumechargedensityρ.Findtheelectricfieldintensityandpotentialinsideandoutsidethesphere.Solution:(1)Findtheelectricfieldintensity.AccordingtoGauss'sfluxtheoremIfallthecharge

inthesphereisexpressed,and

(2)

FindtheelectricfieldpotentialTofindthepotentialofanypointoutsidethesphere,withinfinityasthereferencepointTakethepotentialofthespheresufaceasthereferencepotential,thepotentialofanypointinthesphereis2.3FundamentalequationsandboundaryconditionsofelectrostaticfieldsDifferentialform:Constitutiverelation：1.ThefundamentalequationsIntegralform:2.3.1Thefundamentalequations1.Theboundaryconditionoftheelectricfieldintensity:Conclusion：thetangentialcomponentoftheelectricfieldintensityisequaltobothsidesoftheinterfaceofthetwodielectric,orthetangentialcomponentofthefieldintensityiscontinuous.2.3.3Boundaryconditionsofelectrostaticfields2.Theboundaryconditionoftheelectricdisplacement:Conclusion：thenormalcomponentoftheelectricdisplacement

attheinterfaceofthetwodielectricisequal,orthenormalcomponentoftheelectricdisplacement

iscontinuous.2.3.3Boundaryconditionsofelectrostaticfields3.Therefractionlaw:介質(zhì)2介質(zhì)12.3.3BoundaryconditionsofelectrostaticfieldsLetthefirstmediumbetheconductorandthesecondmediumbethefreespace.Consideringthatthefieldintensityandelectricdisplacementinsidetheconductor

bezero.2.3.4BoundaryconditionsattheinterfacebetweenconductoranddielectricThechargecanonlybedistributedontheconductorsurface(theinterfacebetweenthetwomedia)whentheconductorischarged.Whereisthechargesurfacedensityoftheconductorsurface2.3.4BoundaryconditionsattheinterfacebetweenconductoranddielectricInstructions：Inadielectric,thefieldintensityandelectricdisplacementadjacenttotheconductorsurfaceareperpendiculartotheconductorsurface.

Thevalueoftheelectricdisplacementisequaltothesurfacechargedensityofthepoint.2.4Poisson’s

equation,Laplace’s

equation

anduniqueness

theoremIntheactiveregion:ForuniformmediumthePoissonequationoftheelectrostaticfieldInthepassiveregion:theLaplaceequationoftheelectrostaticfield2.4.1Poisson’s

equationandLaplace’s

equationExample2-8

Foranaircapacitorwithparallelplates,thevoltageU0

betweenthetwoplatesandthechargewithabodydensityof

isevenlydistributedbetweenthetwoplates.Theedgeeffectisignoredandtheelectricfielddistributioniscalculated.Solution:A

coordinatesystemisestablished,potentialφisonlyafunctionofxcoordinate.Poissonequationissimplifiedfromthesecondorderpartialdifferentialequationtothefollowingtotaldifferentialequation:IntegratetheabovetotaldifferentialequationtoobtainthegeneralsolutionoftheequatioApplythegivenboundaryvalue:Wecanfindtheintegralconstant:Wegetthedistributionfunctionofthepotential

φFindthenegativegradientofpotentialtoobtaintheelectricfieldintensity

φGivenavalueof

or

ontheboundarysurfaceSofthedomainV,thePoissonequationorLaplaceequationhasauniquevalueinthedomainV.2.4.2Uniqueness

theoremsignificantimportanceTheconditionsfortheuniquenessofsolutionstotheelectrostaticfieldboundaryvalueproblemItprovidesatheoreticalbasisforvarioussolvingmethodsofstaticfieldboundaryvalueproblemsItprovidesacriterionforthecorrectnessofthesolutionThestatementoftheuniquenesstheoremThethreeinvariantconditionssatisfiedbytheuniquenesstheoremaresummarizedbyPoissonequationasfollows.Thechargeanditsdistributionareinvariantinthesolvingdomain.Thedielectricinthesolvingdomainisinvariant.Theboundaryconditionsattheinterfacedonotchange.IfPoissonequationisdeterministic,thethreeinvariantsaresatisfied.Thesolutionoftheequationisuniquenomatterwhatmethodisusedtosolveit,andtheobtainedsolutionisvalideverywhereinthefieldAccordingtotheuniquenesstheorem,youcansolveaprobleminanyoneofmoreconvenientways,aslongasthegivenconditionsaresatisfied,thesolutioniscorrect.2.4.2Uniqueness

theorem2.5MethodofImages1.TheimageofapointchargeagainstaninfinitegroundedconductorplaneTheresultiscorrectbecauseitsatisfiestheboundaryconditionsoftheoriginalproblem.2.5.1ImageofthegroundingconductorplaneimagechargePotentialfunctionWhen

z=0，有效區(qū)域qqPotentialfunctionintheupperhalfspace(z≥0)qTheinducedchargedensityontheconductorplaneisThetotalinducedchargeontheconductorplaneisExample2-9Findtheinducedchargedistributiononthegroundcausedbyapointchargeqintheairwithdistancedfromtheground.TheinducedsurfacechargedensityisSolution:Thedirectionofthefieldintensityistowardstheground,anditsmagnitudeisthefollowing:Byusingtheareaintegralofthesurfacechargedensity,thetotalinducedchargeonthewholegroundcanbeobtainedfrom2.5.2TheimageofapointchargeattheinterfaceoftwoinfinitedielectricplaneFigure1Characteristics:Undertheinfluenceoftheelectricfieldofapointcharge,thedielectricbecomespolarized,resultingintheformationofapolarizedchargedistributiononthedielectricinterface.Atthispoint,theelectricfieldatanypointinspaceisjointlygeneratedbythepointchargeandthepolarizedcharges.Question:AsshowninFigure1,theinterfacebetweentwodifferentdielectricswithdielectricconstantsε1andε2isaninfinitelylargeplane.Thereisapointchargeqindielectric1,locatedatadistancehfromtheinterfaceplane.2.5.2TheimageofapointchargeattheinterfaceoftwoinfinitedielectricplaneFigure2Analysismethod:Whencalculatingthepotentialindielectric1,theimagechargeslocatedindielectric2areusedtoreplacethepolarizedchargesontheinterface,andtheentirespaceisconsideredtobefilledwithauniformdielectricwithadielectricconstantofε1Thepotentialinmedium1is

Whencalculatingthepotentialindielectric2,theimagechargeslocatedindielectric1areusedtoreplacethepolarizedchargesontheinterface,andtheentirespaceisregardedasfilledwithauniformdielectricwithadielectricconstantofε2.Thepotentialindielectric2isFigure32.5.2TheimageofapointchargeattheinterfaceoftwoinfinitedielectricplanegetDescription:Foraninfinitelylonglinecharge(perunitlength)locatedneartheinterfaceofaninfinitelylargeflatsurfacemediumandparalleltotheinterface,itsimagechargeisUtilizetheboundaryconditionssatisfiedbythepotential2.5.2Theimageofapointchargeattheinterfaceoftwoinfinitedielectricplane2.6CapacitanceandPartialCapacitance2.6CapacitanceandpartialcapacitanceCapacitorsplayanimportantroleintuning,by-pass,couplingandfilteringcircuits.Theycanbeusedintuningcircuitsoftransistorradios,couplingcircuitsandby-passcircuitsofcolorTVsets,etc.isdefinedastheratioofthecharge

qitcarriestoitspotential

,thatis

Capacitanceofanisolatedconductor:

Thecapacitanceofacapacitorcomposedoftwoconductorswithequalbutoppositecharges(±q)is

Thecapacitanceofacapacitorisrelatedtotheshape,size,mutualpositionandmediumbetweenconductors,buthasnothingtodowiththeelectrificationofconductors.2.6.1CapacitanceSolutio：Assumesthattheinnerconductorchargeforq,andevenlydistributedinthesurfaceoftheconductorball,ThevoltagebetweentwoconcentricconductorspheresisThecapacitanceofthesphericalcapacitorisWhen

Example2-10AsshowninFigure,thesphericalradiusoftheinnerconductorisa,andtheinnerradiusoftheoutershellisb.Thecapacitanceofthesphericalcapacitoriscalculated.capacitanceofanisolatedconductorballExample

Considertheparalleldouble-conductortransmissionline,

theradiusoftheconductorisa,andtheaxialdistancebetweenthetwoconductorsisD,whereD>>a.Calculatethecapacitanceperunitlengthofthetransmissionline.Solution:ApplyingGauss'stheoremandthesuperpositionprinciple,wecanobtainPotentialdifferencebetweentwoconductorsThecapacitanceperunitlengthis2.6.1CapacitanceExample:Theradiusoftheinnerconductorofacoaxiallineisa,theradiusoftheouterconductorisb,andtheuniformmediumfilledbetweentheinnerandouterconductorshasadielectricconstantofε.Calculatethecapacitanceperunitlengthofthecoaxialline.PotentialdifferencebetweeninnerandouterconductorsSolution:ApplyingGauss'stheorem,wecanobtaintheelectricfieldintensityatanypointbetweentheinnerandouterconductorsasTherefore,thecapacitanceperunitlengthofthecoaxiallineiscoaxialline2.6.1Capacitance

thevoltagebetweenanytwoconductorsisnotonlyaffectedbyitsowncharge,butalsobythechargeonotherconductors.Theconceptofcapacitanceneedstobeextendedandtheconceptofpartialcapacitanceisintroduced.InasystemcomposedofNconductors,duetothelinearrelationshipbetweenpotentialandthechargecarriedbyeachconductor,thepotentialofeachconductoris式中：——selfpotentialcoefficient——mutualpotentialcoefficient（1）potentialcoefficient2.6.2PartialCapacitanceIfthepotentialofeachconductorisknown,theelectricquantityofeachconductorcanbeexpressedasWhere：——Selfinductioncoefficient——Mutualinductioncoefficient（2）inductioncoefficient2.6.2PartialCapacitanceExpresstheelectricquantityofeachconductorasWhere：（3）partialcapacitance——Partialcapacitancebetweenconductoriandconductorj——Thepartialcapacitancebetweenconductoriandtheground2.6.2PartialCapacitance2.7Electrostaticenergyandelectrostaticforce2.7靜電能量與靜電力

Thefieldenergyisequaltothetotalworkdonebytheexternalpowersourceduringtheestablishmentofthiselectricfield。

Theenergyofanelectrostaticfieldoriginatesfromtheenergyprovidedbyexternalsourcesduringtheprocessofestablishingachargesystem.

Themostfundamentalcharacteristicofanelectrostaticfieldisitsforceoncharges,indicatingthattheelectrostaticfieldpossessesenergy.

Duringthechargingprocess,theexternalpowersourcemustovercometheinteractionforcebetweenchargesandperformwork.

Thesystemischargedfromzero,andthefinalchargeisqandthepotentialis

.Atacertainpointduringthechargingprocess,thechargeisαqandthepotentialisα

.(0≤α≤1)

Whenαincreasesto(α+dα),theworkdonebytheexternalpowersourceis:α

(qdα).Integratingαfrom0to1,weobtainthetotalworkdonebytheexternalpowersource2.7.1Therelationshipbetweenelectrostaticenergyandpotential

Accordingtothelawofconservationofenergy,thisworkisequivalenttotheelectricfieldenergyWepossessedbyachargedbodywithachargeofq,thatisForavolumedistributionofchargewithachargedensityρ,theelectricfieldenergypossessedbythechargeρdVwithinavolumeelementdVis2.7.1TherelationshipbetweenelectrostaticenergyandpotentialTheelectricfieldenergyofavolume-distributedchargesisForsurface-distributedchargesForachargedsystemcomposedofmultipleconductor