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1、AsymptoticclosedformforthecapacitanceofanarbitrarilyshapedconductingplateC.H.Liang,L.LiandH.Q.ZhaiAbstract:Closed-formresultsforthecapacitanceofanarbitrarilyshapedconductingplatearepresented.Ifthechargedensitysuitableforfringeconditionsandtheappropriatechargebarycentrearesupposed,theasymptot
2、icclosed-formforthecapacitanceCcanbeachievedwithhighaccuracybysimplecurveintegralsorthesuperpositionofbasictriangles.Sometypicalexamples,suchasanellipticalplate,aregularpolygonalplateandarectangularplate,aregiven.1IntroductionInthispaper,theaboveideaisextendedtodealwiththecapacitanceofanarbi
3、trarily-shapedconductingplate.IftheItisofgreatpracticalapplicationtocalculatethechargedensity,suitableforfringeconditions,andthecapacitanceofanarbitrarily-shapedconductingplateinappropriatechargebarycentrearesupposed,theasymptoticmanyfields,suchascommunicationsandelectricpower.closedformswill
4、beachievedwithhighaccuracybysimpleHowever,mostcasesresorttothenumericalanalysiscurveintegralsorthesuperpositionofbasictriangles.Inthemethod,suchasthemethodofmoments(MoM)[1].Theaboveexampleofthecircularconductingplate,thechargecapacitanceofasquareplatehasbeenstudiedextensivelyinbarycentreisco
5、nsistentwiththegeometrycentre.[2–7].Athinningtechniqueformomentmethodsolutionshasbeenputforwardin[2]andtheclosedformexpressions2Capacitanceofconductingplatewithcurvefortheoff-diagonalmatrixelementshavebeenderivedbyboundaryusingapoint-matchingtechniquein[3],andbyusingGalerkin’sprocedurein[4].
6、TostudythecapacitanceofaconductingplateboundedbyItisknownthataconductingcircularplatehasatrueacurveequation,wefirsttaketheexampleofanellipticalclosedformforcapacitanceC,asshowninFig.1,wherer0plate,whoseequationissatisfiedasistheradiusofacircularplate.x2y2Inthiscase,thechargedensitys(r)isgi
7、venasþ¼1ð3Þabs0sðrÞ¼sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffið1Þandb4aissupposed,asshowinFig.2.2rAnequivalentequationinpolarco-ordinatescanbe1r0expressedaspffiffiffiffiffiffiffiffiffiffiTherefore,thecapacitanceofthecircularconductingplateisr0SðjÞ¼1ð4ÞQ2r09C¼¼8e0r0¼10Fð2ÞV9pybZr0xy
