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1、计算题25道1.andaretwovectorsatpointand,respectively.Determine(a),(b),(c),(d)theunitvectorperpendiculartoand(e)theanglebetweenand题2.202.Iftheelectricfieldintensityinspaceisgivenas,findand.题2.421.Given,verifythedivergencetheoremwhentheregionisboundedbyacylinderandtheplanesatand.题2.441.I
2、nelectromagneticfields,wewilldefinetheelectricfieldintensityasanegativegradientofascalarfunction;i.e..Wewillalsodefinethevolumechargedistributionas,whereisthepermittivityoffreespace.Determineandif(a)incylindricalcoordinates,whereandareconstants,(b)insphericalcoordinates,andinspher
3、icalcoordinates.题2.38解：（a）在柱坐标下1.3.6Anelectroniscirclingaroundnucleusofahydrogenatomataradiusof0.05nm.Determinetheangularvelocityandthetimeperiodoftheelectron.题3.62.Twostraightuniformlychargedlinesareextendingalongthezaxisfromto.Onelinecarriesachargedistributionofandissituatedat,a
4、ndtheotherlineisatandhasachargedistributionof.DeterminetheEfieldatappointonthexaxisat.题3.133.Threeinfiniteelectricsheetscarryinguniformchargedensitiesof2,-3and0.5areeachseparatedbya1-mmairgap,asshowninfigure.Findtheelectricfieldintensityeverywhereinspace.题3.144.3.16Afinitelineexte
5、ndsfromtoandcarriesachargedistributionof.Determinethefieldatapoint2metersawayfromthelineintheplane.题3.161.Asphericalvolumeofradiusbsupportsachargedistributionofeverywhereexceptat.Determinetheelectricfluxdensityintheregion(a),and(b)题3.251.Alongcoaxialcableconsistsofaninnerconductor
6、ofradiusaandanouterconductorofinnerradiusbandouterradiusc.Theinnerconductorcarriesauniformsurfacechargedistributionρs.FindtheEfieldatanypointinspacewhen(a)theouterconductorisnotgrounded,and(b)theouterconductorisgrounded.题3.412.FindthemagneticfluxdensityatpointP.题5.51.Ametalsphereo
7、fradiusahasuniformsurfacechargedistribution.Thepermittivityofthesurroundingregionvariesas.Find(a)D,E,andPeverywhereinspace,(b)theboundchargedensities,and(c)theenergydensity,and(d)showthatthepotentialinthedielectricregionis,whereQisthetotalchargeonthesphere.题3.451.Themagneticfluxde
8、nsityinaregion1,,is.Ifmarksthebou
