电磁场与电磁波第7(2)讲电位静电场中导体介质电通密度

作业情况1班：人2班：人合计：人情况:1第一页，共44页。报考学科门类（专业）A类考生*B类考生*C类考生*备注总分单科（满分=100分）单科（满分>100分）总分单科（满分=100分）单科（满分>100分）总分单科（满分=100分）单科（满分>100分）哲学[01]270↓36↓54↓260↓33↓50↓250↓30↓45↓

*A类考生：报考地处一区招生单位的考生。

*B类考生：报考地处二区招生单位的考生。

*C类考生：报考地处三区招生单位的考生。

一区系北京、天津、上海、江苏、浙江、福建、山东、河南、湖北、湖南、广东等11省(市)；

二区系河北、山西、辽宁、吉林、黑龙江、安徽、江西、重庆、四川、陕西等10省(市)；

三区系内蒙古、广西、海南、贵州、云南、西藏、甘肃、青海、宁夏、新疆等10省(区)。

经济学[02]330↑46↓69↓320↑43↓65↓310↑40↓60↓法学[03]310↓43↓65↓300↓40↓60↓290↓37↓56↓教育学[04](不含体育学[0403])310↑41↓123↓300↑38↓114↓290↑35↓105↓文学[05](不含艺术学[0504])345↑50↓75↓335↑47↓71↓325↑44↓66↓历史学[06]275↓36↓108↓265↓33↓99↓255↓30↓90↓理学[07]28037↓56↓27034↓51↓26031↓47↓工学[08](不含照顾专业)27536↓54↓26533↓50↓25530↓45↓农学[09]2603248250↓3147240↓3045医学[10](不含中医学[1005])280↓37↓111↓270↓34↓102↓260↓31↓93↓军事学[11]305↑42↓63↓295↑39↓59↓285↑36↓54↓管理学[12]330↑46↓69↓320↑43↓65↓310↑40↓60↓体育学[0403]270↓36↓108↓260↓33↓99↓250↓30↓90↓艺术学[0504]305↓32↓48↓295↓31↓47↓285↓30↓45↓中医学[1005]260↓36↓108↓250↓33↓99↓240↓30↓90↓工学照顾专业（一级学科）*26036↓54↓25033↓50↓24030↓45↓享受少数民族政策的考生*24030↓45↓24030↓45↓24030↓45↓报考少数民族高层次骨干人才计划考生进入复试的初试成绩基本要求为总分不低于240分。学术型研究生招生初试成绩基本要求2第二页，共44页。报考专业学位类别A类考生*B类考生*C类考生*备注总分单科（满分=100分）单科（满分>100分）总分单科（满分=100分）单科（满分>100分）总分单科（满分=100分）单科（满分>100分）法律硕士(非法学)[4101]315466930543652954060

*工程硕士照顾专业:冶金工程[430106]、动力工程[430107]、水利工程[430115]、地质工程[430118]、矿业工程[430119]、船舶与海洋工程[430124]、安全工程[430125]、兵器工程[430126]、核能与核技术工程[430127]、农业工程[430128]、林业工程[430129]、航空工程[430133]、航天工程[430134]。

*享受少数民族政策的考生：①报考地处二、三区招生单位，且毕业后在国务院公布的民族区域自治地方就业的少数民族普通高校应届本科毕业生考生；或者②工作单位在国务院公布的民族区域自治地方，为原单位定向或委托培养的少数民族在职人员考生。法律硕士(法学)[4102]310436530040602903756教育硕士[4201]310416230038572903553工程硕士[4301](不含照顾专业)275365426533502553045建筑学硕士[4401]275365426533502553045临床医学硕士[4502]28037111270341022603193工商管理硕士[4601]165↑47↓94↑155↑42↓84↑145↑37↓74↑农业推广硕士[4701]260324825031472403045兽医硕士[4801]260324825031472403045公共管理硕士[4901]165479415544881454182口腔医学硕士[5002]28037111270341022603193公共卫生硕士[5101]28037111270341022603193会计硕士[5301]330469232043863104080体育硕士[5401]2703610826033992503090艺术硕士[5501]305324829531472853045风景园林硕士[5601]260324825031472403045汉语国际教育硕士[5701]310416230038572903553翻译硕士[5801]345507533547713254466社会工作硕士[5901]310436530040602903756工程硕士照顾专业*260365425033502403045享受少数民族政策的考生*240304524030452403045报考少数民族高层次骨干人才计划考生进入复试的初试成绩基本要求为总分不低于240分专业学位研究生招生初试成绩基本要求3第三页，共44页。清华大学2010年硕士研究生复试分数线报考学科门类(专业)总分单科(满分＝100分)单科(满分＞100分)备注哲学[01]340

↓50

↓90各院系在达到学校复试分数基本要求的生源充足的情况下，可根据本学科、专业特点及生源和计划数制定不低于学校基本要求的本院系学科(专业)复试基本要求。经济学[02]360

↑5090

↑法学[03]34050

↓90教育学[04](不含体育学[0403])345

↑50180体育学[0403]320

↑50180文学[05](不含艺术学[0504])350

↑5090艺术学[0504]320

↑4080历史学[06]310

↓50

180理学[07](不含科学技术史[0712])310

↓50

↓80科学技术史[0712]340

↓50

90工学[08]330

↑50

80医学[10]315

↑50

180管理学[12]350

↑50

90

↑法律硕士(非法学)[4101]340

↑50

90工程硕士[43]3154575建筑学硕士[44]3155080会计硕士[53]33550100艺术硕士[55]3204080风景园林硕士[56]3155080公共管理硕士(MPA)[4901]20060120工商管理硕士(MBA)[4601]A线

228

↑60120

↑未达到A线但达到B线的考生，申请参加复试的必要条件，请参见经济管理学院MBA复试有关具体要求。B线

180

↑50100

↑4第四页，共44页。电子科技大学二零一零年考研复试分数线学科第一单元(政治理论)第二单元(外国语)第三单元(业务课一)第四单元(业务课二)总分02经济学5040↓707033003法学5040↓707032504教育学5040↓150

325↑05文学050250507070320↑050350407070330↑07理学4035↓6060290↓08工学0808、0809、0810、08114035↓606030008124035↓6060280其他4035↓606029011军事学4035↓606030012管理学1201、12025040707031512045044707031543工程硕士4035606028046工商管理硕士(MBA)

3990↑

160↑49公共管理硕士(MPA)

4090

1605第五页，共44页。Review1.FundamentalPostulatesofElectrostaticsinFreeSpaceDifferentialformIntegralformPostulatesofelectrostaticsinfreespace6第六页，共44页。2.Coulomb’sLaw7第七页，共44页。3.Gauss’sLawandApplicationsGauss’slawisparticularlyusefulindeterminingtheE-fieldofchargedistributionswithsomesymmetryconditions,suchthatthenormalcomponentoftheelectricfieldintensityisconstantoveranenclosedsurface.TheessenceofapplyingGauss’slawliesfirstintherecognitionofsymmetryconditionsandsecondinthesuitablechoiceofasurfaceoverwhichthenormalcomponentofEresultingfromagivenchargedistributionisaconstant.SuchasurfaceisreferredtoasaGaussiansurface.8第八页，共44页。Maintopic1.ElectricPotential2.ConductorsinStaticElectricField3.DielectricsinStaticElectricField4.ElectricFluxDensityandDielectricConstant9第九页，共44页。h2h1mgV1V210第十页，共44页。1.ElectricPotentialWewanttomaketwomorepointsaboutEq.First,theinclusionofthenegativesignisnecessaryinordertoconformwiththeconventionthatingoingagainsttheEfieldtheelectricpotential

Vincreases.Second,whenwedefinedthegradientofascalarfield,thatthedirectionofVisnormaltothesurfacesofconstantV.hencethefieldlinesorstreamlinesareeverywhere

perpendiculartoequipotentiallinesandequipotentialsurfaces.11第十一页，共44页。Electricpotentialdoeshavephysicalsignificance,anditisrelatedtotheworkdoneincarryingachargefromonepointtoanother.Aswedefinedtheelectricfieldintensityastheforceactingonaunittestcharge.Therefore,inmovingaunitchargefrompointP1

topointP2

inanelectricfield,workmustbedoneagainstthefield

andisequaltoAnalogoustotheconceptofpotentialenergyinmechanics,AboveequationrepresentsthedifferenceinelectricpotentialenergyofaunitchargebetweenpointP2andpointP1.

DenotingtheelectricpotentialenergyperunitchargebyV.theelectricpotential,wehave12第十二页，共44页。Wehavedefinedapotentialdifference(electrostaticvoltage)betweenpointsP2andP1.Itmakesnomoresensetotalkabouttheabsolutepotentialofapointthanabouttheabsolutephaseofphasorortheabsolutealtitudeofageographicallocation;areferencezero-potentialpoint,areferencezero(usuallyatt=0),orareferencezeroaltitude(usuallyatsealevel)mustfirstbespecified.Inmost(butnotall)casesthezero-potentialpointistakenatinfinity.Whenthereferencezero-potentialpointisnotatinfinity,itshouldbespecificallystated.13第十三页，共44页。ElectricPotentialduetoaChargeDistributionForasystemofndiscretepointchargesq1,q2,…,qnTheelectricpotentialdueto

onepointcharge14第十四页，共44页。ForavolumechargedistributionForasurfacechargedistribution

Foralinechargedistribution

Asanexample,letusagainconsideranelectricdipoleconsistingofcharges+qand–qwithasmallseparationd.Calculatetheelectricfieldintensityproducedbytheelectricdipole.15第十五页，共44页。TheelectricpotentialatPproducedbyanelectricdipolecanbewrittendowndirectly:Solution:16第十六页，共44页。Makeatwo-dimensionalsketchoftheequipotentiallinesandtheelectricfieldlinesforanelectricdipole.17第十七页，共44页。Example3-9P98-9918第十八页，共44页。TheprecedingexampleillustratestheprocedurefordeterminingEbyfirstfindingVwhenGauss’slawcannotbeconvenientlyapplied.However,weemphasizethatifsymmetryconditionsexistsuchthataGaussiansurfacecanbeconstructedoverwhichE·dsisconstant,itisalwayseasiertodetermineEdirectly.ThepotentialV,ifdesired,maybeobtainedfromEbyintegration.19第十九页，共44页。2.ConductorsinStaticElectricFieldConductors,semiconductors,andinsulators(ordielectrics);conductivityAssumeforthepresentthatsomepositive(ornegative)chargesareintroducedintheinteriorofaconductor.Anelectricfieldwillbesetupintheconductor,thefieldexertingaforceonthechargesandmakingthemmoveawayfromoneanother.Thismovementwillcontinueuntilallthechargesreachtheconductorsurfaceandredistributethemselvesinsuchawaythatboththechargeandthefieldinsidevansih,thenthestatic(equilibrium)isreached.Insideaconductor(understaticconditions)20第二十页，共44页。BoundaryConditions(ataConductor/FreeSpaceInterface)UnderstaticconditionstheEfieldonaconductorsurfaceiseverywherenormaltothesurface.Inotherwords,thesurfaceofaconductorisanequipotentialsurfaceunderstaticconditions.ThenormalcomponentoftheEfieldataconductor/freespaceboundaryisequaltothesurfacechargedensityontheconductordividedbythepermittivityoffreespace.21第二十一页，共44页。静电感应现象Nowletusassumethatweplaceanisolatedconductorinanelectricfield.Theexternallyappliedelectricfieldexertsaforceonthefreeelectronsandcausesthemtomoveinadirectionoppositetothefield.Onesideoftheconductorbecomesnegativelycharged,andtheothersidebecomespositivelycharged.Werefertosuchaseparationofchargesasinducedcharges.Theeffectoftheseinducedchargesistoproduceanelectricfieldwithintheconductorwhichisfinallyequalandoppositetotheexternallyappliedelectricfield.Inotherwords,thenetelectricfieldinsidetheconductoriszerothentheequilibriumstateisreached.22第二十二页，共44页。Example3-11P103-10423第二十三页，共44页。Dielectricmolecules:polarandnonpolarmolecules.Conductor：

freeelectrons，freecharges，Dielectric：

boundcharges，dielectricbreakdown,dielectricstrengthNonpolarMoleculePolarMolecule正负中心重合3.DielectricsinStaticElectricField24第二十四页，共44页。PolarMoleculeNonpolarMoleculeNonpolarMoleculePolarMoleculeEaPolarizationofdielectrics

displacementpolarizationorientationpolarization位移极化取向极化25第二十五页，共44页。（a）电介质正常状态下正负电荷中心重合（b）电介质极化状态下正负电荷对中心分离（a）电介质正常状态下正负电荷中心重合（b）电介质极化状态下正负电荷对中心分离无极分子：位移极化有极分子：取向极化（同时有微小的位移极化）(a)有极分子排列混乱，固有电矩矢量和为零(b)外电场中每个有极分子受到力矩作用而转动(c)在垂直于电场方向的表面上出现极化电荷均匀极化，非均匀极化，面极化电荷，体极化电荷26第二十六页，共44页。Equivalentchargedistributionsofpolarizeddielectricsaswheren

isthenumberofmoleculesperunitvolumeandthenumeratorrepresentsthevectorsumoftheinduceddipolemomentscontainedinaverysmallvolumev.ThevectorPisthevolumedensityofelectricdipolemoment.Thedipolemomentdpofanelementalvolumedv’isdp=Pdv’,whichproducesanelectrostaticpotential(seeEq.3-53b):27第二十七页，共44页。IntegratingoverthevolumeV’ofthedielectric,weobtainthepotentialduetothepolarizeddielectricWhereR

isthedistancefromtheelementalvolumedv’toafixedfieldpoint.InCartesiancoordinates,PV’dv’RAnditisreadilyverifiedthatthegradientof1/Rwithrespecttotheprimedcoordinatesis28第二十八页，共44页。HenceRecallingthevectoridentity,Divergencetheorem,wehaveandlettingA=P

andf=1/R,wecanrewriteas29第二十九页，共44页。Comprisonofthenexttwointegralsrevealsthattheelectricpotential(andthereforetheelectricfieldintensityalso)duetoapolarizeddielectricmaybecalculatedfromthecontributionsofsurfaceandvolumechargedistributionshaving,respectively,densities30第三十页，共44页。Thesearereferredtoaspolarizationchargedensitiesorbound-chargedensities.Inotherwords,apolarizeddielectricmaybereplacedbyanequivalentpolarizationsurfacechargedensity

psandanequivalentpolarizationvolumechargedensity

pforfieldcalculations:

31第三十一页，共44页。summary1.ElectricPotential32第三十二页，共44页。2.ConductorsinStaticElectricField3.DielectricsinStaticElectricFieldInsideaconductor(understaticconditions)BoundaryConditions(ataConductor/FreeSpaceInterface)33第三十三页，共44页。(a)有极分子排列混乱，固有电矩矢量和为零(b)外电场中每个有极分子受到力矩作用而转动(c)在垂直于电场方向的表面上出现极化电荷4.ElectricFluxDensityandDielectricConstantWeexpecttheelectricfieldintensityduetoagivensourcedistributioninadielectrictobedifferentfromthatinfreespace.Inparticular,thedivergencepostulatedmustbemodifiedtoincludetheeffectofp

;thatis,34第三十四页，共44页。WehaveWhere

isthevolumedendityoffreecharges.Wenowdefineanewfundamentalfieldquantity,theelectricfluxdensity,orelectricdisplacement,D,suchthatTheuseofthevectorDenablesustowriteadivergencerelationbetweentheelectricfieldanddistributionoffreechargesinanymediumwithoutthenecessityofdealingexplicitywiththepolarizationvectorPorthepolarizationchargedensityp.

35第三十五页，共44页。Thesearereferredtoaspolarizationchargedensitiesorbound-chargedensities.Inotherwords,apolarizeddielectricmaybereplacedbyanequivalentpolarizationsurfacechargedensity

psandanequivalentpolarizationvolumechargedensity

pforfieldcalculations:

4.ElectricFluxDensityandDielectricConstantWeexpecttheelectricfieldintensityduetoagivensourcedistributioninadielectrictobedifferentfromthatinfreespace.Inparticular,thedivergencepostulatedmustbemodifiedtoincludetheeffectofp

;thatis,36第三十六页，共44页。IntegralformDifferentialformTheaboveEquationsarethetwofundamentalgoverningdifferentialequat