E导体与电介质课件

§1ConductorsintheElectrostaticField§2DielectricsandPolarization

intheElectricField§3CapacitanceandCapacitor§4TheEnergyofElectricfield

Chapter6ConductorsandDielectricsintheElectrostaticField§5Application1ElectrostaticEquilibriumInelectricconditionsallthefreeelectronareatrest2ConditionsofElectrostaticEquilibriumTheelectricfieldiszeroinsideaconductorProving1Notangentialcomponentcanexistab－－－++Proving2§1ConductorsintheElectrostaticFieldCorollary1Theconducingsurfaceisanequipotentialsurface,andallpointsintheinteriorareatthesamepotentialasthesurfaceCorollary2Thefieldatthesurfaceoftheconductor(andjustoutside)isperpendiculartothesurface3DistributionofChargea)AllofthechargesisonthesurfaceoftheconductorProve：b)TheelectricfieldonthesurfaceofaconductorsNote:Thefieldatthesurfaceoftheconductor(andjustoutside)c)DistributionofChargeofSphericalConductorRestrictingfactors：theelectricfieldiszeroinsideaconductor.5ElectrostaticScreening静电屏蔽ElectrostaticScreening:InsulatingtheinfluenceofelectricfieldusingconductorshellNomatterthechangeofchargeAtheforceonBchargealwaysiszero.A电荷变化,B电荷受力总是为零。Thechargeinsideshellcanbeshielded壳可以屏蔽内部IfthechargeBischanged,theforceonthechargeAischangedtoo.B电荷变化，A电荷受力会变化。ThechargeAoutsideshellcannotbeshielded壳不能屏蔽外边电荷A。A。BIftheshellistheground,theinfluencebetweenAandBisnotexist.接地导体壳，可以使壳内外的电荷彼此不影响。例：球形壳C，电荷A带＋q,B带＋Q，

r远大于R。求:A，B，C彼此之作用力。解：(1)A、B之间作用力：(2)A、C对B来说是带电量q的点电荷，B受力：(3)静电屏蔽，A受力 F=0+QBA+qCrR(4)A、C之间作用力：(5)B、C之间作用力F＝0(6)C接地，A、B受力为零问题：导体壳是否真的能够屏蔽掉外电场使其不能进入腔内？答：接地导体壳return电介质中不存在自由电荷，在电场中会发生极化现象。极性介质：HCl、SO2、H2O非极性介质：O2H2CO21Dielectricpolarization无外电场时，电偶极矩取向杂乱或为零，整个介质呈电中性。当有外电场时，非极性分子产生极化，极性分子趋向外场排列，介质表面产生束缚电荷。E---2Polarization

极化的强弱程度用电极化强度矢量描述。由于每个分子为偶极子，偶极矩P越大，单位体积内偶极子越多，极化越强。线性各向同性介质§2DielectricsandDielectricPolarization解：QR例1一点电荷Q被半径为R的介质1包围，球外是2的介质，求空间电场强度。例2平行极板间极化强度矢量，求介质表面束缚电荷密度解：选取圆柱形高斯面return110-310-610-910-12FmFF微nF纳pF皮1ThecapacitanceofanIsolatedConductorUnit：Farads法拉TheradiusoftheearthR＝6370kmC=7.08×10-4F§3CapacitanceCapacitorCapacitanceisameasureofamountofchargeaconductorholdsatagivenpotentialdifference2CapacitanceofaCapacitorCapacitor：Itisconsistsoftwoconductorplatesbeingveryclosed3CombinationsofCapacitors电容器的联接(1)ConnectedinSeries串联(2)ConnectedinParallel并联Forcapacitorsconnectedinseriesthechargeoneachcapacitoristhesame.C1C2

C1

C2CapacitorsconnectedinParallelhavethesamepotentialdifferenceacrosstheirplateComparing弹簧的串并联，电阻的串并联，物理中由几个相同量纲量组成另一个同量纲量时，只有上面的组合。(3)ACylindricalCapacitor-取高为h圆柱形高斯面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.Ex2Asphericalcapacitorconsistsoftwothinconcentricsphericalshellsofradiiaandb,witha<b.AchargeQisplacedontheinnershell,and–Qontheoutershell,whichisgrounded.Calculatethecapacitance.InordertouseC=,weneedfirsttocalculatethepotentialdifferencebetweentheshells,whichinturndependsonthefield.Aconcentricsphereofradiusr,wherea<r<b,containschargeqso,byGauss’slaw,theelectricfieldonthisspherehasintensityE=UsingandsubstitutingforE`return2ThedensityofelectricfieldenergyTheenergystoredinacapacitorisintheformofelectricpotentialenergy.Whereistheenergy?Considerthespecificexampleofaparallel-platecapacitorItmeansthattheenergyisstoredintheelectricfield.Althoughthisdiscussionreferstoaparallel-platecapacitor,theconceptofenergydensityisdefinedbythesameequationforcapacitorsofanyshapeEnergydensity:theenergyperunitvolumeForacapacitorofanyshape,theenergystored解1用电场能量公式:在r处取半径为r,r+dr的球壳,在球壳内电场能量:解2导体球电容公式:例求半径为R,带电为+Q的导体球所具有的静电能..B.A问题带电平行板电容器充满均匀介质,中间挖去一扁平的圆柱,A点和B点的D和E谁大?答案:EA>EBDA=DBreturn§5Application例1无限长均匀带电圆柱面内外的场强分布：>0，R面内面外方向垂直柱面向外解：电荷分布具有柱对称性，电场分布具有柱对称性；利用高斯定理求场强分布，选取柱形高斯面rR

例3无限长均匀带电圆柱面，半径为R，单位长带电量为+，试求其电势分布。解：电场强度分布：r>R：r<R：

P1P2••电场强度方向垂直于带电圆柱面沿径向。若仍选取无穷远处为电势零点，则导致电势为无穷大选取距轴线nR处为零电势点：

例4如图，在一电荷体密度为的均匀带电介质球体中，挖出一个以O’为球心的球状小空腔。试证：球形空腔内的电场是均匀电场，其表达式为：证明：用填补法证明。介质球在空腔内任一点的场为：P点的合场强：••OO’空间任意一点的电场强度可看做体电荷密度为的介质球体和一个空腔处