電磁場與電磁波第7(2)講電位靜電場中導體介質(zhì)電通密度

作業(yè)情況1班：人2班：人合計：人情況:1第一頁，共44頁。報考學科門類（專業(yè)）A類考生*B類考生*C類考生*備注總分單科（滿分=100分）單科（滿分>100分）總分單科（滿分=100分）單科（滿分>100分）總分單科（滿分=100分）單科（滿分>100分）哲學[01]270↓36↓54↓260↓33↓50↓250↓30↓45↓

*A類考生：報考地處一區(qū)招生單位的考生。

*B類考生：報考地處二區(qū)招生單位的考生。

*C類考生：報考地處三區(qū)招生單位的考生。

一區(qū)系北京、天津、上海、江蘇、浙江、福建、山東、河南、湖北、湖南、廣東等11省(市)；

二區(qū)系河北、山西、遼寧、吉林、黑龍江、安徽、江西、重慶、四川、陜西等10省(市)；

三區(qū)系內(nèi)蒙古、廣西、海南、貴州、云南、西藏、甘肅、青海、寧夏、新疆等10省(區(qū))。

經(jīng)濟學[02]330↑46↓69↓320↑43↓65↓310↑40↓60↓法學[03]310↓43↓65↓300↓40↓60↓290↓37↓56↓教育學[04](不含體育學[0403])310↑41↓123↓300↑38↓114↓290↑35↓105↓文學[05](不含藝術(shù)學[0504])345↑50↓75↓335↑47↓71↓325↑44↓66↓歷史學[06]275↓36↓108↓265↓33↓99↓255↓30↓90↓理學[07]28037↓56↓27034↓51↓26031↓47↓工學[08](不含照顧專業(yè))27536↓54↓26533↓50↓25530↓45↓農(nóng)學[09]2603248250↓3147240↓3045醫(yī)學[10](不含中醫(yī)學[1005])280↓37↓111↓270↓34↓102↓260↓31↓93↓軍事學[11]305↑42↓63↓295↑39↓59↓285↑36↓54↓管理學[12]330↑46↓69↓320↑43↓65↓310↑40↓60↓體育學[0403]270↓36↓108↓260↓33↓99↓250↓30↓90↓藝術(shù)學[0504]305↓32↓48↓295↓31↓47↓285↓30↓45↓中醫(yī)學[1005]260↓36↓108↓250↓33↓99↓240↓30↓90↓工學照顧專業(yè)（一級學科）*26036↓54↓25033↓50↓24030↓45↓享受少數(shù)民族政策的考生*24030↓45↓24030↓45↓24030↓45↓報考少數(shù)民族高層次骨干人才計劃考生進入復試的初試成績基本要求為總分不低于240分。學術(shù)型研究生招生初試成績基本要求2第二頁，共44頁。報考專業(yè)學位類別A類考生*B類考生*C類考生*備注總分單科（滿分=100分）單科（滿分>100分）總分單科（滿分=100分）單科（滿分>100分）總分單科（滿分=100分）單科（滿分>100分）法律碩士(非法學)[4101]315466930543652954060

*工程碩士照顧專業(yè):冶金工程[430106]、動力工程[430107]、水利工程[430115]、地質(zhì)工程[430118]、礦業(yè)工程[430119]、船舶與海洋工程[430124]、安全工程[430125]、兵器工程[430126]、核能與核技術(shù)工程[430127]、農(nóng)業(yè)工程[430128]、林業(yè)工程[430129]、航空工程[430133]、航天工程[430134]。

*享受少數(shù)民族政策的考生：①報考地處二、三區(qū)招生單位，且畢業(yè)后在國務院公布的民族區(qū)域自治地方就業(yè)的少數(shù)民族普通高校應屆本科畢業(yè)生考生；或者②工作單位在國務院公布的民族區(qū)域自治地方，為原單位定向或委托培養(yǎng)的少數(shù)民族在職人員考生。法律碩士(法學)[4102]310436530040602903756教育碩士[4201]310416230038572903553工程碩士[4301](不含照顧專業(yè))275365426533502553045建筑學碩士[4401]275365426533502553045臨床醫(yī)學碩士[4502]28037111270341022603193工商管理碩士[4601]165↑47↓94↑155↑42↓84↑145↑37↓74↑農(nóng)業(yè)推廣碩士[4701]260324825031472403045獸醫(yī)碩士[4801]260324825031472403045公共管理碩士[4901]165479415544881454182口腔醫(yī)學碩士[5002]28037111270341022603193公共衛(wèi)生碩士[5101]28037111270341022603193會計碩士[5301]330469232043863104080體育碩士[5401]2703610826033992503090藝術(shù)碩士[5501]305324829531472853045風景園林碩士[5601]260324825031472403045漢語國際教育碩士[5701]310416230038572903553翻譯碩士[5801]345507533547713254466社會工作碩士[5901]310436530040602903756工程碩士照顧專業(yè)*260365425033502403045享受少數(shù)民族政策的考生*240304524030452403045報考少數(shù)民族高層次骨干人才計劃考生進入復試的初試成績基本要求為總分不低于240分專業(yè)學位研究生招生初試成績基本要求3第三頁，共44頁。清華大學2010年碩士研究生復試分數(shù)線報考學科門類(專業(yè))總分單科(滿分＝100分)單科(滿分＞100分)備注哲學[01]340

↓50

↓90各院系在達到學校復試分數(shù)基本要求的生源充足的情況下，可根據(jù)本學科、專業(yè)特點及生源和計劃數(shù)制定不低于學?；疽蟮谋驹合祵W科(專業(yè))復試基本要求。經(jīng)濟學[02]360

↑5090

↑法學[03]34050

↓90教育學[04](不含體育學[0403])345

↑50180體育學[0403]320

↑50180文學[05](不含藝術(shù)學[0504])350

↑5090藝術(shù)學[0504]320

↑4080歷史學[06]310

↓50

180理學[07](不含科學技術(shù)史[0712])310

↓50

↓80科學技術(shù)史[0712]340

↓50

90工學[08]330

↑50

80醫(yī)學[10]315

↑50

180管理學[12]350

↑50

90

↑法律碩士(非法學)[4101]340

↑50

90工程碩士[43]3154575建筑學碩士[44]3155080會計碩士[53]33550100藝術(shù)碩士[55]3204080風景園林碩士[56]3155080公共管理碩士(MPA)[4901]20060120工商管理碩士(MBA)[4601]A線

228

↑60120

↑未達到A線但達到B線的考生，申請參加復試的必要條件，請參見經(jīng)濟管理學院MBA復試有關(guān)具體要求。B線

180

↑50100

↑4第四頁，共44頁。電子科技大學二零一零年考研復試分數(shù)線學科第一單元(政治理論)第二單元(外國語)第三單元(業(yè)務課一)第四單元(業(yè)務課二)總分02經(jīng)濟學5040↓707033003法學5040↓707032504教育學5040↓150

325↑05文學050250507070320↑050350407070330↑07理學4035↓6060290↓08工學0808、0809、0810、08114035↓606030008124035↓6060280其他4035↓606029011軍事學4035↓606030012管理學1201、12025040707031512045044707031543工程碩士4035606028046工商管理碩士(MBA)

3990↑

160↑49公共管理碩士(MPA)

4090

1605第五頁，共44頁。Review1.FundamentalPostulatesofElectrostaticsinFreeSpaceDifferentialformIntegralformPostulatesofelectrostaticsinfreespace6第六頁，共44頁。2.Coulomb’sLaw7第七頁，共44頁。3.Gauss’sLawandApplicationsGauss’slawisparticularlyusefulindeterminingtheE-fieldofchargedistributionswithsomesymmetryconditions,suchthatthenormalcomponentoftheelectricfieldintensityisconstantoveranenclosedsurface.TheessenceofapplyingGauss’slawliesfirstintherecognitionofsymmetryconditionsandsecondinthesuitablechoiceofasurfaceoverwhichthenormalcomponentofEresultingfromagivenchargedistributionisaconstant.SuchasurfaceisreferredtoasaGaussiansurface.8第八頁，共44頁。Maintopic1.ElectricPotential2.ConductorsinStaticElectricField3.DielectricsinStaticElectricField4.ElectricFluxDensityandDielectricConstant9第九頁，共44頁。h2h1mgV1V210第十頁，共44頁。1.ElectricPotentialWewanttomaketwomorepointsaboutEq.First,theinclusionofthenegativesignisnecessaryinordertoconformwiththeconventionthatingoingagainsttheEfieldtheelectricpotential

Vincreases.Second,whenwedefinedthegradientofascalarfield,thatthedirectionofVisnormaltothesurfacesofconstantV.hencethefieldlinesorstreamlinesareeverywhere

perpendiculartoequipotentiallinesandequipotentialsurfaces.11第十一頁，共44頁。Electricpotentialdoeshavephysicalsignificance,anditisrelatedtotheworkdoneincarryingachargefromonepointtoanother.Aswedefinedtheelectricfieldintensityastheforceactingonaunittestcharge.Therefore,inmovingaunitchargefrompointP1

topointP2

inanelectricfield,workmustbedoneagainstthefield

andisequaltoAnalogoustotheconceptofpotentialenergyinmechanics,AboveequationrepresentsthedifferenceinelectricpotentialenergyofaunitchargebetweenpointP2andpointP1.

DenotingtheelectricpotentialenergyperunitchargebyV.theelectricpotential,wehave12第十二頁，共44頁。Wehavedefinedapotentialdifference(electrostaticvoltage)betweenpointsP2andP1.Itmakesnomoresensetotalkabouttheabsolutepotentialofapointthanabouttheabsolutephaseofphasorortheabsolutealtitudeofageographicallocation;areferencezero-potentialpoint,areferencezero(usuallyatt=0),orareferencezeroaltitude(usuallyatsealevel)mustfirstbespecified.Inmost(butnotall)casesthezero-potentialpointistakenatinfinity.Whenthereferencezero-potentialpointisnotatinfinity,itshouldbespecificallystated.13第十三頁，共44頁。ElectricPotentialduetoaChargeDistributionForasystemofndiscretepointchargesq1,q2,…,qnTheelectricpotentialdueto

onepointcharge14第十四頁，共44頁。ForavolumechargedistributionForasurfacechargedistribution

Foralinechargedistribution

Asanexample,letusagainconsideranelectricdipoleconsistingofcharges+qand–qwithasmallseparationd.Calculatetheelectricfieldintensityproducedbytheelectricdipole.15第十五頁，共44頁。TheelectricpotentialatPproducedbyanelectricdipolecanbewrittendowndirectly:Solution:16第十六頁，共44頁。Makeatwo-dimensionalsketchoftheequipotentiallinesandtheelectricfieldlinesforanelectricdipole.17第十七頁，共44頁。Example3-9P98-9918第十八頁，共44頁。TheprecedingexampleillustratestheprocedurefordeterminingEbyfirstfindingVwhenGauss’slawcannotbeconvenientlyapplied.However,weemphasizethatifsymmetryconditionsexistsuchthataGaussiansurfacecanbeconstructedoverwhichE·dsisconstant,itisalwayseasiertodetermineEdirectly.ThepotentialV,ifdesired,maybeobtainedfromEbyintegration.19第十九頁，共44頁。2.ConductorsinStaticElectricFieldConductors,semiconductors,andinsulators(ordielectrics);conductivityAssumeforthepresentthatsomepositive(ornegative)chargesareintroducedintheinteriorofaconductor.Anelectricfieldwillbesetupintheconductor,thefieldexertingaforceonthechargesandmakingthemmoveawayfromoneanother.Thismovementwillcontinueuntilallthechargesreachtheconductorsurfaceandredistributethemselvesinsuchawaythatboththechargeandthefieldinsidevansih,thenthestatic(equilibrium)isreached.Insideaconductor(understaticconditions)20第二十頁，共44頁。BoundaryConditions(ataConductor/FreeSpaceInterface)UnderstaticconditionstheEfieldonaconductorsurfaceiseverywherenormaltothesurface.Inotherwords,thesurfaceofaconductorisanequipotentialsurfaceunderstaticconditions.ThenormalcomponentoftheEfieldataconductor/freespaceboundaryisequaltothesurfacechargedensityontheconductordividedbythepermittivityoffreespace.21第二十一頁，共44頁。靜電感應現(xiàn)象Nowletusassumethatweplaceanisolatedconductorinanelectricfield.Theexternallyappliedelectricfieldexertsaforceonthefreeelectronsandcausesthemtomoveinadirectionoppositetothefield.Onesideoftheconductorbecomesnegativelycharged,andtheothersidebecomespositivelycharged.Werefertosuchaseparationofchargesasinducedcharges.Theeffectoftheseinducedchargesistoproduceanelectricfieldwithintheconductorwhichisfinallyequalandoppositetotheexternallyappliedelectricfield.Inotherwords,thenetelectricfieldinsidetheconductoriszerothentheequilibriumstateisreached.22第二十二頁，共44頁。Example3-11P103-10423第二十三頁，共44頁。Dielectricmolecules:polarandnonpolarmolecules.Conductor：

freeelectrons，freecharges，Dielectric：

boundcharges，dielectricbreakdown,dielectricstrengthNonpolarMoleculePolarMolecule正負中心重合3.DielectricsinStaticElectricField24第二十四頁，共44頁。PolarMoleculeNonpolarMoleculeNonpolarMoleculePolarMoleculeEaPolarizationofdielectrics

displacementpolarizationorientationpolarization位移極化取向極化25第二十五頁，共44頁。（a）電介質(zhì)正常狀態(tài)下正負電荷中心重合（b）電介質(zhì)極化狀態(tài)下正負電荷對中心分離（a）電介質(zhì)正常狀態(tài)下正負電荷中心重合（b）電介質(zhì)極化狀態(tài)下正負電荷對中心分離無極分子：位移極化有極分子：取向極化（同時有微小的位移極化）(a)有極分子排列混亂，固有電矩矢量和為零(b)外電場中每個有極分子受到力矩作用而轉(zhuǎn)動(c)在垂直于電場方向的表面上出現(xiàn)極化電荷均勻極化，非均勻極化，面極化電荷，體極化電荷26第二十六頁，共44頁。Equivalentchargedistributionsofpolarizeddielectricsaswheren

isthenumberofmoleculesperunitvolumeandthenumeratorrepresentsthevectorsumoftheinduceddipolemomentscontainedinaverysmallvolumev.ThevectorPisthevolumedensityofelectricdipolemoment.Thedipolemomentdpofanelementalvolumedv’isdp=Pdv’,whichproducesanelectrostaticpotential(seeEq.3-53b):27第二十七頁，共44頁。IntegratingoverthevolumeV’ofthedielectric,weobtainthepotentialduetothepolarizeddielectricWhereR

isthedistancefromtheelementalvolumedv’toafixedfieldpoint.InCartesiancoordinates,PV’dv’RAnditisreadilyverifiedthatthegradientof1/Rwithrespecttotheprimedcoordinatesis28第二十八頁，共44頁。HenceRecallingthevectoridentity,Divergencetheorem,wehaveandlettingA=P

andf=1/R,wecanrewriteas29第二十九頁，共44頁。Comprisonofthenexttwointegralsrevealsthattheelectricpotential(andthereforetheelectricfieldintensityalso)duetoapolarizeddielectricmaybecalculatedfromthecontributionsofsurfaceandvolumechargedistributionshaving,respectively,densities30第三十頁，共44頁。Thesearereferredtoaspolarizationchargedensitiesorbound-chargedensities.Inotherwords,apolarizeddielectricmaybereplacedbyanequivalentpolarizationsurfacechargedensity

psandanequivalentpolarizationvolumechargedensity

pforfieldcalculations:

31第三十一頁，共44頁。summary1.ElectricPotential32第三十二頁，共44頁。2.ConductorsinStaticElectricField3.DielectricsinStaticElectricFieldInsideaconductor(understaticconditions)BoundaryConditions(ataConductor/FreeSpaceInterface)33第三十三頁，共44頁。(a)有極分子排列混亂，固有電矩矢量和為零(b)外電場中每個有極分子受到力矩作用而轉(zhuǎn)動(c)在垂直于電場方向的表面上出現(xiàn)極化電荷4.ElectricFluxDensityandDielectricConstantWeexpecttheelectricfieldintensityduetoagivensourcedistributioninadielectrictobedifferentfromthatinfreespace.Inparticular,thedivergencepostulatedmustbemodifiedtoincludetheeffectofp

;thatis,34第三十四頁，共44頁。WehaveWhere

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

35第三十五頁，共44頁。Thesearereferredtoaspolarizationchargedensitiesorbound-chargedensities.Inotherwords,apolarizeddielectricmaybereplacedbyanequivalentpolarizationsurfacechargedensity

psandanequivalentpolarizationvolumechargedensity

pforfieldcalculations:

4.ElectricFluxDensityandDielectricConstantWeexpecttheelectricfieldintensityduetoagivensourcedistributioninadielectrictobedifferentfromthatinfreespace.Inparticular,thedivergencepostulatedmustbemodifiedtoincludetheeffectofp

;thatis,36第三十六頁，共44頁。IntegralformDifferentialformTheaboveEquationsarethetwofundamentalgoverningdifferentialequat