靜電場的標(biāo)勢及其微分方程ppt課件

1、0EtBEEddzzdyydxxedzedyedxezeyexl dl dEzyxzyx Pl dEP 122121PPdl dEPPPP rQP04 iiirQP04 rdVxP04EED12l dEd1221012EEn1122lElE211122112212nnEnEnDDnnndnnl ddnn1122nconst.111122221122WE DdVDdVD dVD dVD dSdV VdVdVW2121 18VVxxWdV dVr21DE2121dVW21rEl dEOPPO0)()(rEP0)(22020220ln4144)(zRRzRzdzRdzP 20220202202222

2、0220220220220022000/11/11/11/11ln4ln4ln4ln4ln4)()()()()()(MRMRMRMRMRMMRMMRMMRMzRzzRzzRzzRzPPPPMMMMMM002020202202020220200ln2ln4/11/11lnlim4/11/11/11/11lnlim4)()(RRRRRRMRMRMRMRMRMRPPMM00ln2)(RRPRRER02SSn(反證法反證法 ) 假設(shè)存在兩個(gè)不同的解假設(shè)存在兩個(gè)不同的解, 22ii 02,ijijijijijijnnnnjjiijinniiiiiviiviiviiviisiidvdvdvdvsd222i

3、viiiSiiiidvsd2jisdsdSisiiSdsdi 第一種情形：給定外外表上電勢第一種情形：給定外外表上電勢 0SSS 第二種情形：給定外外表處法向微商第二種情形：給定外外表處法向微商 0SSSnnn20.iiiVdVconst 第一類：給定導(dǎo)體外表上的第一類：給定導(dǎo)體外表上的iin或 第二類：給定導(dǎo)體上的電荷第二類：給定導(dǎo)體上的電荷 iQiSiiSiQSdQSdEiiiSQdSni20 iiiSiSQdSnQdSn0iSdSn222VVVVdSdVdVdVdV constiSiiiiiSSSSSSdnSdSd0)(0eS00)(2VdVrrAErrAE3231rrQErrQE321

4、2321122rrQDDrrQEDrrrr321222223211111122QAaaAaaASdESdESdDSS21222221221122221212QA0222222222sin1sinsin11rrrrrrmnmnnnmnnmmnmnnnmnnmmPRdRCmPRbRaR,1,1sincoscoscos,.), 2, 1, 0,(mncosmnPnnnnnnPRbRaRcos,1cosnP.)cos3cos5(21)(cos) 1cos3(21)(coscos)(cos1)(cos232210PPPP)()(12231RRRRdcRRRba00121RdcR321232RbaRdcR

5、R021221212323232QdRRdRRdSRdSRSdSdSdERRRRRR0a)(114)(41210123011RRRRRQRRRQQ1001101004444QQabQQcdR 131111123RQQRRR 11112111100RRRRQQE dSdSdSR dRR 1QQnnnnnnnnnnnnRRPRdRcRRPRbRa)(cos)(cos01201110cos0101naEaREn0ndnnnnnnnnPRcPRbREcoscoscos2101nn21021nnnnnnnnnnnnnnnnPRncPRbnPEPRcPRbPRE10200100010100) 1(0001

6、3000011301010001201002322EcREbcRbERcRbREnnnnnnnnnnnnnncnnRbcRbcnRRbncRRb) 1() 1(0120120102000100nnbc)(cos23)(cos2cos00002023000001RRRERRRRERE)sin(cos23sin23cos23cos23sin110000000000002eeEeEeEREReReReERRRcossinsincosxzxzReeeeeecossinsinsincossincoscos22xzxzReeeeeezReeesincos0000002323EeEEz00000032)()

7、(EEEPe030000003042)()(34EREEPRdVPpdpeVVcos2)(420300030RERRRp實(shí)踐運(yùn)用：靜電選礦實(shí)踐運(yùn)用：靜電選礦 03000042)(ERp)()()()(121212leEplEplEEl qlEEqlEEqF011222222Zrrrrr011222rrrrr)()(rR0122rRrrRr22221rRrrRr02222222RrRrrRr000000lnDCrBARsincosDCrBrARvvVCACB000)0(0000BBsin00rDADAV., 3, 2, 120)2(sin00nnDnnnnnrFVsin)sincos)()(ln

8、(000000DCrBrADCrBARR)2(2cos)0()2()0(1111011100001211rFrFEEEDDnn211rF21011sin1rFV zererezr111111111cos1sin11rFrErFrEr調(diào)查空間：導(dǎo)體板上部空間導(dǎo)體板接地，調(diào)查空間：導(dǎo)體板上部空間導(dǎo)體板接地，所以電場僅存在于導(dǎo)體板上部空間。所以電場僅存在于導(dǎo)體板上部空間。 鏡像電荷：用等效電荷替代導(dǎo)體板上的鏡像電荷：用等效電荷替代導(dǎo)體板上的感應(yīng)電荷。感應(yīng)電荷。 且分布在對稱位置。且分布在對稱位置。 QQ 014QQPrr調(diào)查空間：導(dǎo)體球外部空間。調(diào)查空間：導(dǎo)體球外部空間。鏡像電荷：用位于對稱軸上的等

9、效替鏡像電荷：用位于對稱軸上的等效替代導(dǎo)體球面上的感應(yīng)電荷。代導(dǎo)體球面上的感應(yīng)電荷。 01( )04QQPrrrQrQ .rQconstrQ OQ POPQ0.RrconstraaRRb00200RbaRQQa 0022002214142cos2cosR QQrarQRaRaR Qa RbRb00QdSE0QQQ000014R QQR QQararR 231,21.2!1.2!iijii jiijf xxf xxf xx xf xxx xf xxf xxf x xx 00( )( )4114VVxxdVrxdVxxRxx2,011111( )( ).42!iji jijVxxxx xdVRRx

10、 x R ( )( )3VVijijVQx dVpxx dVDx xx dV iiixqp Vpxx dV 3VDxxx dV zzyyxxzzyyxxeBeBeBBeAeAeAAzzzzzyzyzxzxyzyzyyyyyxyxxzxzxyxyxxxxzzyyxxzzyyxxeeBAeeBAeeBAeeBAeeBAeeBAeeBAeeBAeeBAeBeBeBeAeAeABAzzzzzyzyzxzxyzyzyyyyyxyxxzxzxyxyxxxxeeDCeeDCeeDCeeDCeeDCeeDCeeDCeeDCeeDCDCDCBA:xyyxxxxyyxxyyxxyyxxyxyyxyxDCBAeeD

11、CBAeeeeDCBAeeDCeeBA)()( : )()( : )(.0)()( : )()( : )(xyxxxyxxxyxxxyxxxxxyxyeeDCBAeeeeDCBAeeDCeeBA.1:61141.161141.)(0,20)2()1()0(RDRpRQRxxDRpRQxjijiijRQ0)0(4Rp1410)1(RpRRpRlQRlRlRQRlRlRlRlRQlRlRlRlRQrrQ1414cos4cos21cos21441cos141cos14)2/(cos1)2/(cos141140302002/122/120222200jijiijRxxD,20)2(16141 3iji

12、jVDx xx dV 22332236666VDz zx dVb Qa QQ baQ baba baabal22plD633RzpRepRpzm1414141000rrzpmm11403030204cos4cos4RzzplRRzplRlzpmm32/32222/12221RzzyxzzyxzRzRzplRzzplmm14142200RzplRzDRxxDjijiij14161411614122022330,20)2( ,412RR,0R。012R)(0)(1jijiij01,2jijiijRxx 2(2),022,0111346111346iji jijVijiji jijVx xx dVx

13、 x Rx xrx dVx x R 23ijijijVDx xrx dV 23Dxxr Ix dV 0332211DDDjiijDD 222213xx dVyx dVzx dVrx dV00332211332211DDDDDDji 3ijijVDx xx dV iixx 0ijD 223zx dVrx dV 223330Dzrx dV0332211DDD021332211DDD122222azbyx234ab2043abQVijjiijdVrxxD2030312312DDD222syx154221214/1022222/122abdsssdzdVsdVydVxazbaa154232badVzQbadVxzdVrzDVV)(522232222022033221122331125DDDabQ 22(2)2250340QzRab