E6導(dǎo)體與電介質(zhì)課件

§1ConductorsintheElectrostaticField§2DielectricsandPolarization

intheElectricField§3CapacitanceandCapacitor§4TheEnergyofElectricfield

Chapter6ConductorsandDielectricsintheElectrostaticField§5Application1Electrostaticinduction§1ConductorsintheElectrostaticField+++++++++感應(yīng)電荷+2ElectrostaticEquilibriumInelectrostaticequilibrium,allthefreeelectronareatrest.達(dá)到靜電平衡時(shí)，所有自由電子都處于靜止?fàn)顟B(tài)。++++++++Proving1Notangentialcomponentcanexist。導(dǎo)體表面附近電場(chǎng)強(qiáng)度垂直于等勢(shì)面。Proving2++++++++++++3DistributionofChargea)AllofthechargesisonthesurfaceoftheconductorProve：b)TheelectricfieldonthesurfaceofaconductorsNote:Thefieldatthesurfaceoftheconductor(andjustoutside)c)DistributionofChargeofSphericalConductorRestrictingfactors：theelectricfieldiszeroinsideaconductor.E=0Conductorshell（腔）(1)NochargeinaconductorshellaTheelectricfieldiszeroinsideinsideconductorandshell導(dǎo)體內(nèi)、空腔內(nèi)場(chǎng)強(qiáng)皆為零；bTheconductorandshellareequipotential

導(dǎo)體、空腔為等勢(shì)體；cThechargemustlieonthesurface

內(nèi)表面處處沒(méi)有電荷，電荷只分布在外表面.(2)AchargeqinaconductorshellOntheinnersurfaceoftheshellthechargeis

-q.Ontheoutersurfaceoftheshellthechargeisq.ItisdeterminedbyGauss’slaw.兩球半徑分別為R1、R2，帶電量q1、q2，設(shè)兩球相距很遠(yuǎn)，當(dāng)用導(dǎo)線將彼此連接時(shí)，電荷將如何分布？解用導(dǎo)線連接后，兩球帶電量之和守恒R2R1如果兩球相距較近，結(jié)果怎樣？例2思考已知導(dǎo)體球殼A帶電量為Q，導(dǎo)體球B帶電量為q

(1)將A接地后再斷開，電荷和電勢(shì)的分布；解A與地?cái)嚅_后,ArR1R2B-q電荷守恒(2)再將B接地，電荷的分布。內(nèi)表面電荷為-qA接地時(shí)，外表面電荷設(shè)為Q設(shè)B的電量為根據(jù)孤立導(dǎo)體電荷守恒例3求(1)(2)B球圓心處的電勢(shì)總結(jié)(有導(dǎo)體存在時(shí)靜電場(chǎng)的計(jì)算方法)1.靜電平衡的條件和性質(zhì):

2.電荷守恒定律3.確定電荷分布,然后求解靜電感應(yīng)電暈放電可靠接地帶電云避雷針的工作原理++++－－－－－++－+5ElectrostaticScreening靜電屏蔽ElectrostaticScreening:InsulatingtheinfluenceofelectricfieldusingconductorshellNomatterthechangeofchargeAtheforceonBchargealwaysiszero.A電荷變化,B電荷受力總是為零。Thechargeinsideshellcanbeshielded殼可以屏蔽內(nèi)部IfthechargeBischanged,theforceonthechargeAischangedtoo.B電荷變化，A電荷受力會(huì)變化。ThechargeAoutsideshellcannotbeshielded殼不能屏蔽外邊電荷A。A。BIftheshellistheground,theinfluencebetweenAandBisnotexist.接地導(dǎo)體殼，可以使殼內(nèi)外的電荷彼此不影響。用空腔導(dǎo)體屏蔽外電場(chǎng)++++++++接地空腔導(dǎo)體屏蔽內(nèi)電場(chǎng)腔外電場(chǎng)不影響腔內(nèi)腔內(nèi)電場(chǎng)不影響腔外電介質(zhì)中不存在自由電荷，在電場(chǎng)中會(huì)發(fā)生極化現(xiàn)象。極性介質(zhì)：HCl、SO2、H2O等，非極性介質(zhì)：O2H2CO2§2DielectricsandDielectricPolarization無(wú)極分子：（氫、甲烷、石蠟等）有極分子：（水、有機(jī)玻璃等）電介質(zhì)1Dielectricpolarization無(wú)外電場(chǎng)時(shí)，電偶極矩取向雜亂或?yàn)榱?，整個(gè)介質(zhì)呈電中性。當(dāng)有外電場(chǎng)時(shí)，非極性分子產(chǎn)生極化，極性分子趨向外場(chǎng)排列，介質(zhì)表面產(chǎn)生束縛電荷。E----+-+-+-+-+-+-+-+-+-+-+-+束縛電荷′E0E-+-+-+-+-+-+-+-+-+-+-+-+束縛電荷′E0E位移極化取向極化無(wú)極分子電介質(zhì)有極分子電介質(zhì)2Polarization極化的強(qiáng)弱程度用電極化強(qiáng)度矢量描述。由于每個(gè)分子為偶極子，偶極矩P越大，單位體積內(nèi)偶極子越多，極化越強(qiáng)。3極化電荷與自由電荷的關(guān)系對(duì)無(wú)限大均勻帶電平板：線性各向同性介質(zhì)+++++++++++----------------+++++解：QR例1一點(diǎn)電荷Q被半徑為R的介質(zhì)1包圍，球外是2的介質(zhì)，求空間電場(chǎng)強(qiáng)度。例2平行極板間極化強(qiáng)度矢量，求介質(zhì)表面束縛電荷密度解：選取圓柱形高斯面return110-310-610-910-12FmFF微nF納pF皮1ThecapacitanceofanIsolatedConductorUnit：Farads法拉TheradiusoftheearthR＝6370kmC=7.08×10-4F§3CapacitanceCapacitorCapacitanceisameasureofamountofchargeaconductorholdsatagivenpotentialdifference電容是一個(gè)導(dǎo)體被給定電勢(shì)差時(shí)所能容納的電荷量的測(cè)量2CapacitanceofaCapacitorCapacitor：Itisconsistsoftwoconductorplatesbeingveryclosed（1）電容器分類按形狀：柱型、球型、平行板電容器按型式：固定、可變、半可變電容器按介質(zhì)：空氣、塑料、云母、陶瓷等（2）電容器電容特點(diǎn)：非孤立導(dǎo)體，由兩極板組成4CalculatingtheCapacitanceofaCapacitor(1)AParallel-plateCapacitorThecapacitanceofacapacitordependsontheseparationdistanced,theareaSandthepermittivityεRARBq-qSD=0-QdABQ(2)ASphericalCapacitor(3)ACylindricalCapacitor-取高為h圓柱形高斯面RARBr

hNote：1Thecapacitanceofacapacitordependsonthegeometryofthecapacitorandthepermittivityε,independentof

thepotentialdifferenceandthecharge2ThesphericalcapacitorisastandardcapacitorEx1Aparallel-platecapacitorconsistsoftwosquareplates,eachofsides4.0cmseparatedby2.0mm.(a)Calculatethecapacitance.(b)Howmanyelectronscanbestoredonaplateifthecapacitorischargedto50V?Solution(a)(b)Q=CU=7.1×10-12×50=3.5×10-10CThemagnitudeofthechargeofoneelectronis1.6×10-19C,sothenumberNofelectronsthatcanbestoredis=7.1×10-12F=7.1pF.1EnergystorageinacapacitorElectricpotentialenergyisrelatedtotheworkdowninmovingachargeinanelectricfield.Theamountofworkdonetoassemblethechargeisequaltothepotentialenergystoredinthesystem.Foraparallel-platecapacitor:CStart:Nocharge;End:-Q,+Q.Atamoment:-q,qTheworkisequaltothetotalenergystoredinthecapacitor§4TheEnergyofElectricfieldTheworkdonetomovethechargedqfromAtoBAB2ThedensityofelectricfieldenergyTheenergystoredinacapacitorisintheformofelectricpotentialenergy.Whereistheenergy?Considerthespecificexampleofaparallel-platecapacitorItmeansthattheenergyisstoredintheelectricfield.Althoughthisdiscussionreferstoaparallel-platecapacitor,theconceptofenergydensityisdefinedbythesameequationforcapacitorsofanyshapeEnergydensity:theenergyperunitvolumeForacapacitorofanyshape,theenergystored解1用電場(chǎng)能量公式:在r處取半徑為r,r+dr的球殼,在球殼內(nèi)電場(chǎng)能量:解2導(dǎo)體球電容公式:例求半徑為R,帶電為+Q的導(dǎo)體球所具有的靜電能..B.A問(wèn)題帶電平行板電容器充滿均勻介質(zhì),中間挖去一扁平的圓柱,A點(diǎn)和B點(diǎn)的D和E誰(shuí)大?答案:EA>EBDA=DBreturn§5Application例1無(wú)限長(zhǎng)均勻帶電圓柱面內(nèi)外的場(chǎng)強(qiáng)分布：>0，R面內(nèi)面外方向垂直柱面向外解：電荷分布具有柱對(duì)稱性，電場(chǎng)分布具有柱對(duì)稱性；利用高斯定理求場(chǎng)強(qiáng)分布，選取柱形高斯面rR

例2無(wú)限長(zhǎng)均勻帶電圓柱體內(nèi)外的場(chǎng)強(qiáng)分布：>0，R柱體內(nèi)柱體外方向垂直圓柱體軸線向外方向垂直圓柱體軸線向外rR

例3無(wú)限長(zhǎng)均勻帶電圓柱面，半徑為R，單位長(zhǎng)帶電量為+，試求其電勢(shì)分布。解：電場(chǎng)強(qiáng)度分布：r>R：r<R：

P1P2??電場(chǎng)強(qiáng)度方向垂直于帶電圓柱面沿徑向。若仍選取無(wú)窮遠(yuǎn)處為電勢(shì)零點(diǎn)，則導(dǎo)致電勢(shì)為無(wú)窮大選取距軸線nR處為零電勢(shì)點(diǎn)：

例4如圖，在一電荷體密度為的均勻帶電介質(zhì)球體中，挖出一個(gè)以O(shè)’為球心的球狀小空腔。試證：球形空腔內(nèi)的電場(chǎng)是均勻電場(chǎng)，其表達(dá)式為：證明：用填補(bǔ)法證明。介質(zhì)球在空腔內(nèi)任一點(diǎn)的場(chǎng)為：P點(diǎn)的合場(chǎng)強(qiáng)：??OO’空間任意一點(diǎn)