1、静电场的标势及其微分方程静电场的标势及其微分方程0EtBEEddzzdyydxxedzedyedxezeyexl dl dEzyxzyx第1页/共47页 Pl dEP 122121PPdl dEPPPP第2页/共47页 rQP04 iiirQP04 rdVxP04EED12第3页/共47页l dEd1221012EEn1122lElE21第4页/共47页1122112212nnEnEnDDnnndnnl ddnn1122nconst.第5页/共47页111122221122WE DdVDdVD dVD dVD dSdV VdVdVW2121 18VVxxWdV dVr第6页/共47页21DE2
2、121dVW21第7页/共47页rEl dEOPPO0)()(rEP0)(22020220ln4144)(zRRzRzdzRdzP第8页/共47页 202202022022220220220220220022000/11/11/11/11ln4ln4ln4ln4ln4)()()()()()(MRMRMRMRMRMMRMMRMMRMzRzzRzzRzzRzPPPPMMMMMM第9页/共47页002020202202020220200ln2ln4/11/11lnlim4/11/11/11/11lnlim4)()(RRRRRRMRMRMRMRMRMRPPMM00ln2)(RRPRRER02第10页/
3、共47页 SSn第11页/共47页,22ii 02,ijijijijijijnnnnjjiijinn第12页/共47页iiiiiviiviiviiviisiidvdvdvdvsd222iviiiSiiiidvsd2jisdsdSisiiSdsdi 第一种情形：第一种情形：0SSS 第二种情形：第二种情形：0SSSnnn第13页/共47页20.iiiVdVconst 第一类：第一类：iin或 第二类：第二类：iQ第14页/共47页iSiiSiQSdQSdEiiiSQdSni20 iiiSiSQdSnQdSn0iSdSn第15页/共47页222VVVVdSdVdVdVdV constiSiiiii
4、SSSSSSdnSdSd0)(0eS00)(2VdVrrAErrAE3231第16页/共47页rrQErrQE3212321122rrQDDrrQEDrrrr321222223211111122QAaaAaaASdESdESdDSS21222221221122221212QA第17页/共47页0222222222sin1sinsin11rrrrrrmnmnnnmnnmmnmnnnmnnmmPRdRCmPRbRaR,1,1sincoscoscos,.),2,1,0,(mncosmnP第18页/共47页nnnnnnPRbRaRcos,1cosnP.)cos3cos5(21)(cos)1cos3(2
5、1)(coscos)(cos1)(cos232210PPPP第19页/共47页)()(12231RRRRdcRRRba00121RdcR321232RbaRdcRR021221212323232QdRRdRRdSRdSRSdSdSdERRRRRR第20页/共47页0a)(114)(41210123011RRRRRQRRRQQ1001101004444QQabQQcdR 131111123RQQRRR 11112111100RRRRQQE dSdSdSR dRR 1QQ第21页/共47页nnnnnnnnnnnnRRPRdRcRRPRbRa)(cos)(cos01201110cos0101naEa
6、REn0ndnnnnnnnnPRcPRbREcoscoscos2101第22页/共47页nn21021nnnnnnnnnnnnnnnnPRncPRbnPEPRcPRbPRE10200100010100)1(00013000011301010001201002322EcREbcRbERcRbRE第23页/共47页nnnnnnnnnnnnnncnnRbcRbcnRRbncRRb)1()1(0120120102000100nnbc)(cos23)(cos2cos00002023000001RRRERRRRERE第24页/共47页)sin(cos23sin23cos23cos23sin11000000
7、0000002eeEeEeEREReReReERRRcossinsincosxzxzReeeeeecossinsinsincossincoscos22xzxzReeeeeezReeesincos0000002323EeEEz第25页/共47页00000032)()(EEEPe030000003042)()(34EREEPRdVPpdpeVVcos2)(420300030RERRRp实际运用：实际运用：03000042)(ERp)()()()(121212leEplEplEEl qlEEqlEEqF第26页/共47页011222222Zrrrrr011222rrrrr)()(rR0122rRrr
8、Rr22221rRrrRr02222222RrRrrRr000000lnDCrBARsincosDCrBrARvv第27页/共47页VCACB000)0(0000BBsin00rDADAV.,3,2,120)2(sin00nnDnnnnnrFVsin)sincos)()(ln(000000DCrBrADCrBARR第28页/共47页)2(2cos)0()2()0(1111011100001211rFrFEEEDDnn211rF21011sin1rFV zererezr111111111cos1sin11rFrErFrEr第29页/共47页考察空间考察空间：镜像电荷镜像电荷：QQ 014QQPr
9、r第30页/共47页考察空间考察空间：镜像电荷镜像电荷：01()04QQPrrrQrQ.rQconstrQ OQ POPQ0.RrconstraaRRb00200RbaRQQa 第31页/共47页0022002214142cos2cosR QQrarQRaRaR Qa RbRb第32页/共47页00QdSE0QQQ000014R QQR QQararR第33页/共47页 231,21.2!1.2!iijii jiijf xxf xxf xx xf xxx xf xxf xxf x xx 00()()4114VVxxdVrxdVxxRxx2,011111()().42!iji jijVxxxx
10、xdVRRx x R 第34页/共47页()()3VVijijVQx dVpxx dVDx xx dV iiixqp Vpxx dV 3VDx xx dV zzyyxxzzyyxxeBeBeBBeAeAeAA第35页/共47页zzzzzyzyzxzxyzyzyyyyyxyxxzxzxyxyxxxxzzyyxxzzyyxxeeBAeeBAeeBAeeBAeeBAeeBAeeBAeeBAeeBAeBeBeBeAeAeABAzzzzzyzyzxzxyzyzyyyyyxyxxzxzxyxyxxxxeeDCeeDCeeDCeeDCeeDCeeDCeeDCeeDCeeDCDCDCBA:xyyxxxxyyx
11、xyyxxyyxxyxyyxyxDCBAeeDCBAeeeeDCBAeeDCeeBA)()(:)()(:)(.0)()(:)()(:)(xyxxxyxxxyxxxyxxxxxyxyeeDCBAeeeeDCBAeeDCeeBA第36页/共47页.1:61141.161141.)(0,20)2()1()0(RDRpRQRxxDRpRQxjijiijRQ0)0(4Rp1410)1(第37页/共47页RpRRpRlQRlRlRQRlRlRlRlRQlRlRlRlRQrrQ1414cos4cos21cos21441cos141cos14)2/(cos1)2/(cos141140302002/122/12
12、0222200第38页/共47页jijiijRxxD,20)2(16141第39页/共47页 3ijijVDx xx dV 22332236666VDz zx dVb Qa QQ baQ baba baabal22plD633RzpRepRpzm1414141000rrzpmm1140第40页/共47页3030204cos4cos4RzzplRRzplRlzpmm32/32222/12221RzzyxzzyxzRzRzplRzzplmm14142200RzplRzDRxxDjijiij14161411614122022330,20)2(,412RR,0R。012R第41页/共47页)(0)(1
13、jijiij01,2jijiijRxx 2(2),022,0111346111346iji jijVijiji jijVx xx dVx x Rx xrx dVx x R 23ijijijVDx xrx dV 23Dx xr Ix dV 0332211DDDjiijDD 第42页/共47页 222213xx dVyx dVzx dVrx dV00332211332211DDDDDDji 3ijijVDx xx dV iixx 0ijD 223zx dVrx dV 223330Dzrx dV0332211DDD021332211DDD第43页/共47页122222azbyx234ab2043ab
14、QVijjiijdVrxxD2030312312DDD222syx154221214/1022222/122abdsssdzdVsdVydVxazbaa154232badVzQbadVxzdVrzDVV)(522232222022033第44页/共47页221122331125DDDabQ 22(2)2250340QzRabR522220cos31014RRbaRQ 331,100331,100(0)10.2!10.6100:0.6eeieijeii jiijxxeieijeii jiijxxeeeWdVxxxx xxdVxx xQpxDxxx xQpDW (1)(2).WW第45页/共47页)()0()1(eeEppWFfgfggfgfgf)()()()()(eeeeEpEpEpEpF)()()(sin)cos()1(eepEpEWL)0(eEpL第46页/共47页感谢您的观看！感谢您的观看！第47页/共47页
