高等电磁理论复习题

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1、1.DerivethedifferentialformofthecontinuityequationfromMaxwelTsequations.2.DerivetheintegralformsofMaxwelPsequationsandthecontinuityequations,fromthecorrespondingonesindifferentialform3.Theelectricfluxdensityinsideacubeisgivenby(a)D=&(3+x),(b)D=a(4+尹2).F

2、indthetotalelectricchargeenclosedinsidethecubicalvolumewhenthecubeisinthefirstoctantwiththreeedgescoincidentwiththex,y,zaxesandonecornerattheorigin.Eachsideofthecubeislm.4.Theelectricfieldinsideacircularcylinderofradiusaandheighthisgivenbywherecandharec

3、onstants.Assumingthemediumwithinthecylinderisfreespace,findthetotalchargeenclosedwithinthecylinde匚5.Theinstantaneouselectricfieldinsideasource-free,homogeneous,isotropic,andlinearmediumisgivenbyE=5/(x+p)+a.g(x_尹)]cos(血)DeterminetherelationsbetweenAandB.

4、6.Themagneticfluxdensityproducedonitsplanebyacurrent-carryingcircularloopofradiusa=0.1m.placedonthexyplaneatz=0,isgivenby]0-12BF吋叭1500刃)Wb//wherepistheradialdistanceincylindricalcoordinates.(a)Findthetotalfluxinthezdirectionpassingthroughtheloop.(b)Find

5、theelectricfieldatanypointpwithintheloop•7.TheinstantaneousmagneticfluxdensityinfreespaceisgivenbyB=aYBxcos()sin(6ZX-)+arBvcos(2y)cos(et—兀z)whereBxandByareconstants-Assumingtherearenosources,determinetheelectricdisplacementcurrentdensity.1.Thedisplaceme

6、ntcurrentdensitywithinasource-freecubecenteredabouttheoriginisgivenby•八A2A"ajz+ap+a2xyzEachsideofthecubeis1mandthemediumwithinitisfreespace.Findthedisplacementcurrentleaving,intheoutwarddirection,throughthesurfaceofthecube.2.Thetime-harmoniccomplexelect

7、ricfieldradiatedinfreespacebyalinearradiatingelementisgivenbyE=ar£r+a^厂COS&E。丁1+j0O厂wherearand编areunitvectorsinthesphericaldirectionrand仇E°isaconstant,and几=诃角勺)・Determinethecorrespondingsphericalmagneticfieldcomponents.3.Atime-harmonicelectromagneticfie

8、ldtravelinginfreespaceandperpendicularlyincidentuponaflatsurfaceofdistilledwater@=8Is。，“=〃o),asshowninfollowingfigure,createsareflectedfieldonthefree-spacesideoftheinterfaceandatransmittedfieldonthewatersideoftheinterface.Assumin