物理课件30_Lecture_Outline

1、Chapter30,Inductance电感,Introduction,Howdoesacoilinduceacurrentinaneighboringcoil?Asensortriggersthetrafficlighttochangewhenacararrivesatanintersection.Howdoesitdothis?,InductionLoopSignals,AddsoftironcoretoelectromagnetincreasesBfield,AddcaraboveburiedcoilchangesBfieldVbc0Vab0,Vbc0Vab0WHY?Currentinc

2、reasessuddenly,soinductorresistschange,CurrentdecayinanR-Lcircuit,Testyourself!SignsofVabandVbcwhenS1isclosed?Vab0;Vbc0WHY?CurrentstillflowsaroundthecircuitcounterclockwisethroughresistorEMFgeneratedinLisfromctobSoVbVc!,CurrentdecayinanR-Lcircuit,Testyourself!SignsofVabandVbcwhenS2isclosed,S1open?Va

3、b0;Vbc0Vab0,Vbc0Vab0Vab0,Vbc0WHY?Currentstillflowscounterclockwisedi/dt0;EMFgeneratedinLisfrombtoc!SoVbVc!,磁场能,1、线圈加电的过程中，由于自感两端出现电势差，要继续加电，外电源需要克服这个势差做功。2、外电源做功的功率为：P=Vi3、V=Ldi/dt4、P=Lidi/dt5、dU=Pdt=Lidi6、,56,自感线圈磁能,57,磁场能量密度,磁场能量,Magneticfieldenergy,Inductorsstoreenergyinthemagneticfield:U=1/2LI2U

4、nits:L=Henrys(fromL=NB/i)NB/i=B-fieldFlux/currentthroughinductorthatcreatesthatfluxWb/Amp=Tesla-m2/AmpU=HenrysxAmps2U=Tesla-m2/AmpxAmps2=Tm2AmpButF=qvxBgivesusdefinitionofTeslaB=Teslas=Force/Coulomb-m/s=Force/Amp-m,Magneticfieldenergy,Inductorsstoreenergyinthemagneticfield:U=1/2LI2U=Tesla-m2/AmpxAmp

5、s2=Tm2AmpU=Newtons/Amp-mm2Amp=Newton-meters=Joules=Energy!,Magneticfieldenergy,TheenergystoredinaninductorisU=1/2LI2.Theenergydensityinamagneticfield(Joule/m3)isu=B2/20(invacuum)u=B2/2(inamagneticmaterial)Recalldefinitionof0(magneticpermeability)B=0i/2pr(forthefieldofalongwire)0=Tesla-m/Ampu=B2/20=T

6、2/(Tm/Amp)=T-Amp/meter,Magneticfieldenergy,TheenergystoredinaninductorisU=1/2LI2.Theenergydensityinamagneticfield(Joule/m3)isu=B2/20(invacuum)u=B2/20=T2/(Tm/Amp)=T-Amp/meterU=Tm2Amp=JoulesSoenergydensityu=Joules/m3,62,例如图同轴电缆，中间充以磁介质，芯线与圆筒上的电流大小相等、方向相反.已知，求单位长度同轴电缆的磁能和自感.设金属芯线内的磁场可略.,63,解由安培环路定律可求H,

7、则,64,单位长度壳层体积,Calculatingself-inductanceandself-inducedemf,ToroidalsolenoidwithareaA,averageradiusr,Nturns.AssumeBisuniformacrosscrosssection.WhatisL?,Calculatingself-inductanceandself-inducedemf,ToroidalsolenoidwithareaA,averageradiusr,Nturns.L=NB/iB=BA=(moNi/2pr)AL=moN2A/2pr(selfinductanceoftoroid

8、alsolenoid)WhyN2?IfN=200Turns,A=5.0cm2,r=0.10mL=40mH,TheL-Ccircuit,AnL-Ccircuitcontainsaninductorandacapacitorandisanoscillatingcircuit.Initiallycapacitorfullycharged;closeswitchChargeflowsFROMcapacitor,butinductorresiststhatincreasedflow.Currentbuildsintime.Atmaximumcurrent,chargeflownowdecreasesth

9、roughinductorInductornowresistsdecreasedflow,andkeepspushingchargeintheoriginaldirection,i,TheL-Ccircuit,AnL-Ccircuitcontainsaninductorandacapacitorandisanoscillatingcircuit.Initiallycapacitorfullycharged;closeswitchChargeflowsFROMcapacitor,butinductorresiststhatincreasedflow.Currentbuildsintime.Cap

10、acitorslowlydischargesAtmaximumcurrent,nochargeisleftoncapacitor;currentnowdecreasesthroughinductorInductornowresistsdecreasedflow,andkeepspushingchargeintheoriginaldirection,i,TheL-Ccircuit,AnL-Ccircuitcontainsaninductorandacapacitorandisanoscillatingcircuit.,TheL-Ccircuit,AnL-Ccircuitcontainsanind

11、uctorandacapacitorandisanoscillatingcircuit.Nowcapacitorfullydrained;InductorkeepspushingchargeintheoriginaldirectionCapacitorchargebuildsuponothersidetoamaximumvalueWhilethatsidecharges,“backEMF”fromcapacitortriestoslowchargebuild-upInductorkeepspushingtoresistthatchange.,i,TheL-Ccircuit,AnL-Ccircu

12、itcontainsaninductorandacapacitorandisanoscillatingcircuit.,TheL-Ccircuit,AnL-Ccircuitcontainsaninductorandacapacitorandisanoscillatingcircuit.Nowcapacitorchargedonoppositeside;Currentreversesdirection!Systemrepeatsintheoppositedirection,i,TheL-Ccircuit,AnL-Ccircuitcontainsaninductorandacapacitorand

13、isanoscillatingcircuit.,ElectricaloscillationsinanL-Ccircuit,Analyzethecurrentandchargeasafunctionoftime.DoaKirchoffLooparoundthecircuitinthedirectionshown.Remembericanbe+/-RecallC=q/VForthisloop:-Ldi/dtqC=0,ElectricaloscillationsinanL-Ccircuit,-Ldi/dtqC=0i(t)=dq/dtLd2q/dt2+qC=0SimpleHarmonicMotion!PendulumsSpringsStandardsolution!q(t)=Qmaxcos(wt+f)wherew=1/(LC),ElectricaloscillationsinanL-Ccircuit,q(t)=Qmaxcos(wt+f)i(t)=-wQmaxsin(wt+f)(basedonthisASSUMEDdirection!)w=1/(LC)=angularfrequency,TheL-Ccircuit,AnL-Ccircuitcontainsaninductorandacapacitorandisan