大学物理双语版奥本汉姆课件Chap27To29-EMagIndu.ppt

Chapter27to29Electro MagneticInductionandField TheLawofElectro MagneticInductionMotional 动生 Induced 感生 EMFSelfandMutualInduction 自感与互感 EnergyStoredinaMagneticFieldDisplacementCurrent Ampere Max LawMaxwell sEquation 27 1 Electro MagneticInduction Law AfterOersted sdiscoveryin1820 asteadycurrentproducedasteadymagneticfield Experimentalistseagerlysoughttodemonstratethereverse asteadymagneticfieldcouldcreateasteadyelectriccurrent MichaelFaraday 1791 1867 Englishphysicistandchemist whoseexperimentscoveredawiderangeofelectrical magnetic opticalandchemicalphenomena Heisbestknownforhisfamousdiscoveryofelectro magneticinduction 1 Faraday slawofinduction P630 Commonpoints Fluxofchangesandelectromotiveforce EMF 电动势 occurs whereismagneticfluxthroughareaA voltage V Faraday slaw ForacoilofNturns thecoiliscloselypacked thesamemagneticfluxpassesthroughalltheturns thetotalEMFinducedinthecoilis coilofNturns SIunit 1weber 1Wb 1T m2 ThestepstodeterminethedirectionofibyFaraday slaw 1 Freelysetapositivenormaldirectionofaloop 2 If 3 If 1 Iftheloop sresistanceisR theninducedcurrentintheloopis 2 Thechargesintheloop 通过回路的电量 is Thechargesqisdirectlyproportionalto andindependentond dt HeinrichFriedrichEmilLenz aGermanphysicist in1834heproposedthislaw original Self loop magneticflux LookatP631 please Example Solution Question a Themagnitude directionof b Thecurrentintheloopatt 10s a b clockwise AsFig aconductingloop r 0 2m Solution Given Question Themagnitude directionof Direction withtime inducedemfiscounterclockwise Example Aconductingloop 27 2 Motional InducedEMF 1 Motionalelectromotiveforce P634 Theconductingrodabisslidingalongthemetalrailsandacross Direction fromatob Microscopicview EMFisinducedbyLorrentz force 3 coincideswithFaraday slaw uniform 1 MotionalEMFis innature theworkdonebyLorentz sforcetotransferaperunitpositivechargefrompointatob 2 ThismotionalEMFisnotpresentinastaticsystem Themovingpartisanalogoustoachemicaldeviceforgeneratingelectriccurrent fromlowelectricpotentialtohigh 5 Relationshipofwork energy tomaintainmotionofconductor requiringappliedforcetodopositivework Theenergytransferedtotheclosedloop magnetsystemviatheforceendsupinthermalenergy外力克服安培力作功 转化为电能 Lookatandworkoutexamples27 3and27 4byyourselfafterclass 4 TheconditioncreatingmotionalEMF movingconductormustcutthemagneticfieldlines So wecanpicturethemotionalEMFasthetimerateofcuttingthemagneticfieldlines AconductingwireoflengthLrotatesaboutOwith inuniformmagneticfieldwhichisperpendiculartorotatingplane Find a b WhichpointhashigherEMF PointOhasahigherEMF Solution WayI WayII MakingupaclosedloopandusingFaraday slaw Example Solution Asthefigure astraightwireoflengthl MN isputhorizontallyandfree fall Whatisthepotentialdifferenceoftwosidethewireattimet 经时间t导线两端电位差 PointMhasahigherEMF Example WorkoutProblem27ofP641afterclass Settingxaxisasthefigure 2 InducedelectricfieldsandEMF P635 Inducedelectricfieldarisingfromthechangingofmagneticfieldwiththetime ConnectwiththelawofFaraday InducedEMFequalsthecirculationofinducedelectricfield 感生电动势等于感生电场场强的环流 Takenotes Achangingmagneticfieldproducesanelectricfieldevenifthereisnoconductingloop 1 Italsohasactingforceonchargedparticleasstaticelectricfielddoes 感生电场对电荷有作用力 2 Itisoriginfromvaryingmagneticfield 3 Comparingwiththelooplawofelectrostaticfield wemayfindthatinducedfieldisanotherkindofelectricfield Thesourceofarechargesandchanging respectively isacurlelectricfield 有旋电场 itslinesareclosed noheadandnotail nonconservativefield andnopotential Solution AlongsolenoidofradiusR findthedistributionofwhenthemagneticfieldinsideofitvarieswithtime dB dt C Fromsymmetry istangentialdirection freelyassumepositivedirectionofandLasthefigure Itcanbecalculatedwhenhassomesymmetrybyusingequation Example27 5 1 Ifr R inside 2 Ifr R outside IfdB dt 0 directionofisthesameasassumed counterclockwise otherwise opposite Notethesign 27 3 Self Induction MutualInduction TheprocessthataninducedEMFappearinanycoilinwhichthecurrentischangingiscalledself induction 由于自己线路中的电流的变化而在自己的线路中产生感应电流的现象 自感现象 1 Self Induction 自感应 P645 IfweestablishacurrentIinthewindings themagneticfluxlinkageN isproportionaltoI Inductancedefined ThenthecoefficientLisdefinedastheinductanceoftheinductor 1henry 亨利 1H 1T m2 A TheinductanceLisameasureofmagneticfluxlinkageproducedbytheinductorperunitofcurrent Itrelatedtothegeometryofthewindingsandmagneticmedium ItsSIunit TheEMFappearsinself inductioniscalledself inducedEMF ItobeysFaraday slawofinduction self inducedEMF Theminussignindicatesthattheself inducedEMFhastheorientationsuchthatitopposesthechangeinI Inductanceofasolenoid Consideringthecaseasfigure N l Magneticfieldinsidethesolenoidoflengthlis Magneticfluxlinkage Theinductanceperunitlengthforalongsolenoidnearitscenter InductanceL likecapacitance dependsonlyonthegeometryofthedevice Hey Calculatingself inductanceofco axiswireinunitlength 同轴电缆单位长度的自感 Solution Example 2 Mutual induction 互感应 P643 Asteadycurrentinonecoilwillsetupamagneticfluxlinkingtheothercoil Ifcurrentchangeswithtime anEMFappearsinthesecondcoil Theprocessiscalledmutualinduction DefinethemutualinductanceM21ofcoil2withrespecttocoil1as 线圈1对2的互感系数 If byexternalmeans wecauseI1tovarywithtime then Bysimilarway interchangingtherolesofcoils1and2 AccordingtoFaraday slaw withaminussigntoindicatedirection compareto TheEMFinducedineithercoilisproportionaltotherateofchangeofcurrentintheothercoil Itcanbeproved TheSIunitforM asforL isalsotheHenry Ingeneral Mshouldbemeasuredinexperiments AcoilofN2turnswoundasshownaroundpartofatoroidofN1turns Thetoroid sinner outerradiusareaandb itsheightish ShowMforthetoroid coilcombination Example Solution Lookatexample28 1ofP644afterclass 27 4 EnergyStoredinaMagneticField P647 Recalltheenergystoredinelectricfield UsingOhm sonit Energyofcapacitor Densityofenergy Togetmagneticenergy considersuchaRLcircuit MultiplyeachtermbyIdtandintegrate wehave Energystoredbyaninductor Ontheotherhand ifUBisknown Lcanbegottenfromthisequation Takelongsolenoidasanexample Theenergystoredperunitvolumeofthefield densityofenergy 能量密度 is magneticenergydensity Ingeneral onecanuse Discussexample28 5inP648asfollows 27 5 DisplacementCurrent MaxwellEquations 1 Displacementcurrent 位移电流 P661 TheintroductionofdisplacementcurrentisthebasisonwhichMaxwell EnglishphysicistJamesClerkMaxwell equationsaresetup UsingAmpere looplawtoS1 andS2 Theyarecontradict Tomakethemcoordinate weneedtoconsiderthecontinuityofcurrent oneget and whenS1farfromplates UsingGauss lawtotheclosedsurfacemadeofS1 S2 Realcurrentinconductingwire changingrateofelectricdisplacementfluxtotimethroughsurfaceS2 From So atnon steadycurrent Amperelawcanberewrittenas Ampere Maxwelllaw 1 Fictitious 假想的 displacementcurrentbetweentheplatesisassociatedwiththatchangingE field 通过某个面积的位移电流为通过该面积的电位移通量对时间的变化率 2 ThedisplacementcurrentgivenbyMaxwellis innature thatachangingelectricfluxwillalwaysinduceamagneticfieldwheneveritoccurs 3 AlthoughIandIdareequivalentatproducingmagneticfield theyaredifferentinthatdisplacementcurrentisvaryingelectricfield位移电流是变化的电场 可以存在于一切物质或真空中而传导电流是导体中电荷的定向运动 LookatExample29 1 please 2 Maxwell sequations P667 Maxwell sEquationswrittenontheassumptionthatnodielectricormagneticmaterialsarepresent Takenotes Theassumptionofdisplacementcurrentandinducedmag