麻省理工电磁学课程lec16_17.pdf

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1、6.013,ElectromagneticsandApplicationsProf.MarkusZahn,November8&10,2005Lecture16&17:ElectroquasistaticandMagnetoquasistaticForcesI.EQSEnergyMethodofForcesa)CircuitPointofViewCourtesyofHermannA.HausandJamesR.Melcher.Usedwithpermission.q=CvdqddvdCi==Cv=Cvdtdtdtd

2、tdvdCd=Cvdtddtddv2dCdP=vi=vinCv=Cvvdtdtddtd122dCd=Cvvdt2ddtd1212dCd=Cvvdt22ddtdWdfdtdtWenergymechanicalpowerstorage(forcevelocity)6.013,ElectromagneticsandApplicationsLecture16&17Prof.MarkusZahnPage1of231212dCW=Cv,f=v22d

3、1q2dC1d1==q22C2d2dCb)EnergyPointofViewdqdWdvi=v=efdtdtdtvdq=dWfddW=vdqfdeeWeWef=;vqqconstantconstantCourtesyofHermannA.HausandJamesR.Melcher.Usedwithpermission.0W=efdvdqq0constantqv=Cq1q2W=dq=eC2CconstantW1d11q2dC

4、e2f==q=2dC2C2dqconstant1dC=v22d6.013,ElectromagneticsandApplicationsLecture16&17Prof.MarkusZahnPage2of23II.ForcesInCapacitorsVE=0xxv=E=(Lowerelectrode)sxxvAq=sA=EA=x=CxvxACx=xCourtesyofKriegerPublishing.Usedwithpermission.6.013,Electromag

5、neticsandApplicationsLecture16&17Prof.MarkusZahnPage3of23a)Coulombicforcemethodonupperelectrode:21121vf=EA=EA=Axsxx2222x1becauseEinelectrode=0,Eoutsideelectrode=Ex2TakeaverageAEnergymethod:Cx=x212dC12d11vAf=v=vA=x22dx2dxx2xqqx1Aqx221q2v==f=x=CxA2x22A2

6、2Ab)CourtesyofHermannA.HausandJamesR.Melcher.Usedwithpermission.111AA=;C=0,C=abCCaCbbb=AA0b=00A12q212d12d1qf=q=0b=2dC0Ad20A6.013,ElectromagneticsandApplicationsLecture16&17Prof.MarkusZahnPage4of231d1dA1v22Af=v2C=v20=0

7、2d2db2b200III.EnergyConversionCyclesf0CourtesyofHermannA.HausandJamesR.Melcher.Usedwithpermission.6.013,ElectromagneticsandApplicationsLecture16&17Prof.MarkusZahnPage5of230vdq=dwfdevdq=fdvdq,fd0Electricenergyin,mechanicalenergyout.vdq,fd

8、0Electricpowerout,mechanicalenergyin.BD1212vdq=vdqvdq=2C0V