電磁場與電磁波Electromagnetic

Fieldsand

WavesChapter1Vectoranalysis1.1Vectorfundamentals1-1Scalarsandvectors標(biāo)量和矢量Magnitudeofvectors:Unitvectors（單位矢量）:Scalars（標(biāo)量）:Aquantityhasonlymagnitude.Algebraicdescriptionofvectors:Vectors（矢量）:

Aquantityhasbothmagnitudeanddirection.

Itisusuallyrepresentedbyboldlettersorarrows.Geometricdescriptionofvectors:Avectorisgeometricallydescribedbyasegmentofadirectedstraight-line.GeometricdescriptionofvectorsConstantvectors（常矢量）:Themagnitudeandthedirectionofavectorisconstant.

Vectorsaredescriptedbycoordinatecomponents（坐標(biāo)分量）zxy（1）VectorialadditionandsubtractionTheadditionandsubtractionoftwovectorsfollowtheparallelogramruleingeometrically,asshowninthefigure.Theadditionandsubtractionofoperationobeytheassociativeandcommutativelaws:1-2Vectoralgebraicoperation（矢量的代數(shù)運(yùn)算）矢量的加法矢量的減法TheadditionandsubtractionoftwovectorsinRectangularCoordinateSystem:Associativelaw結(jié)合律Commutativelaw交換律（2）Avectorismultipliedbyascalar（3）Dotproduct（點(diǎn)積）——DotproductofvectorsobeyCommutativelawq矢量與的夾角（4）Crossproduct（叉積）qsinABq矢量與的叉積TheycanbedescribedinRectangularCoordinateSystem：Determinant（行列式）form

:If，thenIf，then(5)Mixedoperationofvectors（混合運(yùn)算）——

Distributivelaw（分配律）——

Distributivelaw（分配律）——

Scalartripleproduct(標(biāo)量三重積）——

Vectortripleproduct(矢量三重積）1.2Scalarfields1.2.1DirectionalderivativeofascalarfieldThedirectionalderivativeofascalarfieldatapointrepresentstherateofchangeofascalarfieldinadirectionfromthepoint1.2ScalarfieldsThedirectionalderivativeofascalarfieldinthedirectionofapointisdefinedasInrectangularcoordinates:Thedirectioncosineofvectoris

，thenVector

Giscomposoedofthreecoordinatecomponents1.2.2Gradientofascalarfieldtheunitvectorofvectorlisthedirectionalderivativeofscalarfunction

alongthedirectionofvectorl

is1.2ScalarfieldsThevectoriscalledthegradientofthescalarfield

,denotedby1.2.2Gradientofascalarfield1.2ScalarfieldsInrectangularcoordinatesystem,theHamiltonianoperatorisdenotedbyThegradientexpressionofthescalarfunction

isWhere1.2ScalarfieldsIncylindricalcoordinatesystemAnimportantpropertyofgradientsisthatthecurlofgradientsisequaltozeroInsphericalcoordinatesystem1.2ScalarfieldsThegradientofascalarfieldisavectorwithafunctionofspacecoordinates.Themagnitudeofthegradientisthemaximumrateofchangeofthescalarfunction,whichisthemaximumdirectionalderivativevalueatthepointThedirectionofthegradientisthedirectionofthemaximumdirectionalderivativeofthepoint,perpendiculartotheisosurface,andpointingtothedirectionoftheincreasingfunctionvalue.thegradientofscalarfieldhasthefollowingthreecharacteristics:1.2Scalarfields

Solution:Accordingtothedefinitionofgradient,thegradientofthescalarfunctioncanbewrittenas

Example1-1givenascalarfunction

,findthegradientatpoint

.

itsmodulusis

Therefore,thegradientatpoint

thatis,themaximumdirectionalderivativeatpointis1.2ScalarfieldsExampleGiveaspatialscalarfield

(x,y,z)=x2＋y2－z：(1)Findthegradientofthescalarfield

atthepointP(1,1,1),andfindtheunitvectorthatcanexpressthedirectionofthegradient；(2)Findthedirectionalderivativeof

alongthedirectionofunitvectorel=

excos60

＋eycos45

＋ezcos60

，andcomparethedirectionalderivativeatpointP(1,1,1)withthegradientofthispoint.Solution:

(1)Usinggradientformula，thegradientatpointPisUnitvectorcanbeexpressedas

(2)Usingtherelationshipbetweenthedirectionalderivativeandgradient，thedirectionalderivativealongthedirectionof

el

canbeobtainedasThevalueofthedirectionalderivativeatpointPcanbeobtainedasThegradientvalueatthepointPcanbeobtainedas

Apparently,

thegradientdescribesthemaximumrateofchangeofatpointP.Thatisthemaximumdirectionalderivative.Sotheformulaisforeveradmitted.1.3VectorFields1.Fluxofavectorfields

Thesurfaceintegralofvector

A

alongadirectedsurface

Siscalledthefluxofthevector

Athroughthedirectedsurface

S,expressedintermsofIfSisaclosedsurface,wegetThedirectedplaneelement——Thedirectedplaneelement——Theunitvectorinthedirectionofthepositivenormalofthedirectedplaneelement1.3.1FluxanddivergenceofvectorfieldThereisapositivesourceintheclosedsurfaceThereisanegativesourceintheclosedsurfaceTheclosedsurfaceisconsideredpassiveThreepossibleoutcomesoffluxofavectorfieldthroughaclosedsurface

Fromamacroscopicperspective,thefluxofaclosedsurfaceestablishestherelationshipbetweenthefluxofavectorfieldthroughtheclosedsurfaceandthesourcewithinthesurfacethatgeneratesthevectorfield.Thephysicalsignificanceofflux:1.3.1Fluxanddivergenceofvectorfield2.Divergenceofvectorfield

Inordertoshowthedistributionoffluxsourcesatanypointinthefield,theconceptoffluxdensity(divergence)isintroduced.

IftheclosedsurfaceS

contractsinfinitelytoapoint,thenthelimitoftheratioofthefluxofvectorA

throughtheclosedsurfaceStothevolumeenclosedbytheclosedsurfaceiscalledthedivergenceofthevectorfieldAatthatpoint,

Inrectangularcoordinatesystem,1.3.1FluxanddivergenceofvectorfieldThedivergenceofvectorfieldAcanbeexpressedasthescalarproductofHamiltonianoperatorandvector

A

Inrectangularcoordinatesystem,thedivergenceofvectorfieldAcanbeexpressedas1.3.1Fluxanddivergenceofvectorfield2.DivergenceofvectorfieldIncylindricalcoordinatesystemInsphericalcoordinatesystemInrectangularcoordinatesystemThedivergenceexpressionofvectorfield

A:1.3.1FluxanddivergenceofvectorfieldThethreecharacteristicsofvectorfielddivergenceareasfollows：Thedivergenceofvectorisascalarandafunctionofspatialcoordinates.Divergencerepresentstheintensityofthefluxsourceofavectorfieldfluxsourceofthevectorfieldwherethedivergenceisnotzero,whichisthebeginningorendofthevectorline.Inapassiveregion,thedivergenceofeachpointiszero.Ifthedivergenceofapointinthefieldisgreaterthanzero,thereisapositivesource.Ifthedivergenceislessthanzero,thereisanegativesourceatthispoint.Ifthedivergenceiszero,thepointispassive.1.3.1Fluxanddivergenceofvectorfield2.Divergenceofvectorfield3.Thedivergence

theorem體積的剖分VS1S2en2en1S

Thedivergencetheoremstatesthatthevolumeintegralofthedivergenceofavectorfieldisequaltothesurfaceintegralofthevectorfieldoveraclosedsurfaceenclosingthevolume.1.3.1Fluxanddivergenceofvectorfield

Thedivergencetheoremhastwoapplications:Intheviewofmathematical,thedivergencetheoremcanrealizetheconversionbetweentheclosedsurfaceintegralofvectorfunctionandthevolumeintegralofscalarfunction.Intheviewoffieldvector,thedivergencetheoremestablishestherelationshipbetweenthefieldinaregionVandthefieldsurroundingtheboundarysurfaceofthatregion.1.3.1Fluxanddivergenceofvectorfield3.Thedivergence

theoremThedivergenceofgradientofthescalarfunction

SecondorderdifferentialoperatorcalledLaplaceoperator

iscalledtheLaplaceoperator,anditsexpressioninrectangularcoordinatesystemis1.3.1FluxanddivergenceofvectorfieldInrectangularcoordinatesystemIncylindricalcoordinatesystemInsphericalcoordinates

system1.3.1FluxanddivergenceofvectorfieldThecirculationcandescribethevortexcharacteristicsofthevectorfieldandthevalueofthecirculationisproportionaltothevalueofthenetvortexsourcesurroundedby

l.1.ThecirculationofvectorfieldsThelineintegralofvectorfield

Aalongthedirectedclosedcurve

liscalledthecirculationofvectorfield

Aalongthecurve,1.3.2ThecirculationandcurlofvectorfieldsThecirculateddensitiesofvector

maybedifferentwithrespecttodirection.Thecirculationcanrepresentthesourceintensitywithvortexcharacteristics.Inordertoreflectthedistributionofvortexsourcesateachpointinthefield,thecirculationdensityisintroduced.2.Thecurlofvectorfield（1）Circulationintensity1.3.2ThecirculationandcurlofvectorfieldsThecurlofavectorfieldrepresentsthemaximumcirculationwithaunitareaofthevector.Characteristic：（2）CurlThecurlofvector

A

hasexpressedasthecrossproductoftheHamiltonoperator▽

andvector

A1.3.2ThecirculationandcurlofvectorfieldsFourcharacteristicsofthecurlofavectorfields:Thecurlofavectorfieldisavectorwithspacecoordinates.Thecurlvalueisthemaximumcirculationdensityatthespecificpoint.Thecurldirectionisthedirectionofthemaximumcirculationdensityatthespecificpoint.Thecirculationdensityofthecurlfieldisnotazeroandnonrotationalfield.Ontheotherhand,thecirculationdensityofthecurlfielddefinedasarotationalfieldanditsdensityiszeroeverywhere.（2）Curl1.3.2Thecirculationandcurlofvectorfields

Rectangularcoordinatesystem

CylindricalcoordinatesystemSphericalcoordinatesystem1.3.2Thecirculationandcurlofvectorfields3.Curltheorem

Thecurltheoremstatesthatthesurfaceintegralofthecurlofavectorfieldisequaltothelineintegralofthevectorfieldoveraclosedpathdefiningthearea.曲面的剖分Oppositedirectionsandequalmagnitudesresultincancellation

Thecurltheoremisanimportanttheoreminvectoranalysisandusedtoelectromagneticfieldtheory.1.3.2ThecirculationandcurlofvectorfieldsThecurltheoremhastwoapplications:

(1)Intheviewofthemathematical,thecurltheoremcanrealizetheconversionbetweenthesurfaceintegralofvectorfunctionandthelooprouteintegralofvectorfunction.

(2)Intheviewofthefield,thecurltheoremestablishestherelationshipbetweenthefieldinthesurfaceandthefieldontheboundarythatdefinestheregion.1.3.2Thecirculationandcurlofvectorfields3.Curltheorem4、散度和旋度的區(qū)別

1.3.2ThecirculationandcurlofvectorfieldsSolution:

GivenExample1-2

Findthedivergenceandcurlofthepositionvector

atanypoint(x,y,z)inspace.ThenSolution:

Example1-3

givenavector,trytosolve1.4Green’sTheorem&Helmholtz’sTheorem1.4.1Green’sTheorem1.LaplaceOperationConcept:——LaplaceoperatorRectangularcoordinatesystemCalculationformula:CylindricalcoordinatesystemSphericalcoordinatesystem

VectorLaplacianoperationConcept:namelyNote:Fornon-perpendicularcomponentsRectangularcoordinatesystem：Suchas：1.4.1Green’sTheorem2.Green’sTheorem

Lettwoscalarfields

and

becontinuousandsecondpartialderivativestotheregionVBasedontherelationshipbetweendirectionalderivativeandgradient,theaboveformulacanalsobewrittenasSV

,

1.4.1Green’sTheoremBasedontheaboveformulas,thefollowingtwoformulascanalsobeobtained:1.4.1Green’sTheoremTheabovetwoequationsarecalledtheGreen'ssecondtheorem.TheabovetwoequationsarecalledtheGreen'sfirsttheorem.SinceGreen'stheoremshowstherelationbetweenthefieldinregionandthefieldontheboundary,wecanuseGreen’stheoremtosolvetheproblemsbetweentheregionalfieldandtheboundaryfield.

Inaddition,Green'stheoremstatestherelationthattwofieldsshouldsatisfy.

Therefore,Green'stheoremiswidelyusedinvectoranalysisandelectromagneticfieldtheory.1.4.1Green’sTheorem

Ifthevectorfieldissingle-valuedeverywhereininfinitespace,anditsderivativeiscontinuousandbounded,andthesourcedistributionisinafiniteregion,thenwhenthedivergenceandcurlofthevectorfieldaregiven,thevectorfieldcanbeexpressedasWhere：

Helmholtz'stheoremstatesthatavectorfieldcanbedeterminedbyitsdivergenceandcurl

inanunboundedspatialregion.1.4.2Helmholtz’sTheoremaboundedregion

Inaboundedregion,thevectorfieldisnotonlyrelatedtothedivergenceandcurlwithintheregion,butalsotothetangentialandnormalcomponentsofthevectorfieldontheregion'sboundary.1.4.2Helmholtz’sTheorem1.Thedivergenceequationandcurlequationconstitutethedifferentialformsofthebasicequationsofavectorfield.Helmholtz'stheoremsummarizesthefundamentalpropertiesofvectorfields,anditssignificanceisextremelyimportant.2.Thefluxalongaclosedsurfaceandthecirculationalongaclosedpathconstitutetheintegralformsofthefundamentalequationsofavectorfield.1.4.2Helmholtz’sTheoremChapterSummaryKeypoints:Threecoordinatesystems,Threedegrees,ThreetheoremsGradient:Itindicatesthedirectionofthemaximumrateofchangeatapointinascalarfield,determinedbythepartialderivativesofthescalarfieldwithrespecttoeachcoordinate.ChapterSummaryDivergence:Itrepresentsthefluxdensityatapointinavectorfield,whichdependsonthepartialderivativesofthefieldcomponentswithrespecttotheirrespectivecoordinates,determinedbytherateofchangeofthefieldcomponentsintheirrespectivedirections.ChapterSummaryCurl:Itrepresentsthemaximumcirculationsurfacedensityatapointinthefield,whichdependsonthedifferentialofeachcoordinatecomponentofthevectorfieldwithrespecttothecoordinateintheperpendiculardirection.Itisdeterminedbytherateofchangeofeachfieldcomponentinthedirectionorthogonaltoit.Divergencetheorem:Itestablishestheconnectionbetweenthesurfaceintegralofaclosedsurfaceandthevolumeintegralofspace.Curltheorem:Itestablishestheconnectionbetweentheclosedcurveintegralandthesurfaceintegralenclosedbyit.Helmholtz’stheorem:Itpointsouttwodirectionsforstudyingspatialvectorfields.ChapterSummary電磁場與電磁波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.等位線的切線等位線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,resultinginpolarizationsurfacecharges2.2.1PolarizationofdielectricsTherelationshipbetweent