1、10 10 電磁電磁 IIIIII How is an aurora so How is an aurora so thin yet so tall and thin yet so tall and wide?wide?SectionsSections1.1.磁場磁場2.2.電流與磁場電流與磁場10-1 10-1 磁場磁場vThe The electric electric field field and the and the magnetic magnetic fieldfieldvElectromagnetElectromagnets and s and permanent perman
2、ent magnets magnets 10-1.1 The definition of 10-1.1 The definition of B BBvqFBThe tracks in a The tracks in a bubble chamberbubble chamberThe SI unit for BThe SI unit for B1 tesla=1T=1 N/A m=104 gauss Magnetic Field LinesMagnetic Field Lines lMagnetic vs.electric dipoles Magnetic vs.electric dipoles
3、 lA horseshoe and a C-shaped A horseshoe and a C-shaped magnetsmagnets 例例 1 A 5.3 1 A 5.3 MeVMeV proton proton m/s107.3/N101.6sinm/s102.3/212157mFaqvBFmKvBB10-1.2 Crossed Fields:10-1.2 Crossed Fields:Discovery of the Discovery of the ElectronElectronlA cathode ray tube A cathode ray tube lThomsons p
4、rocedure:Thomsons procedure:l設定設定E=0,B=0,E=0,B=0,並記錄光點並記錄光點位置位置 l開啟電場開啟電場 l開啟磁場開啟磁場,並調至與電場相等並調至與電場相等 yELBqmBEvqvBqEmvqELy2,/,22222CalculationCalculation10-1.3 Crossed Fields:10-1.3 Crossed Fields:The Hall EffectThe Hall EffectlBy the conduction electrons in copper:VleBinneAineJvBeveEEdVdd 例例 2 A cub
5、e generator2 A cube generatormV0.3VdvBVEdVevBeE10-1.410-1.4 A Circulating A Circulating Charged ParticleCharged ParticleqBmvrTqBmvrrmvqvBrmvmaF/2 /2/22lThe frequency and angular frequencylHelical Paths 2 21mqBfmqBTfsin cos11vvvv頻率與軌跡頻率與軌跡極光橢圓圈極光橢圓圈例例 3 The Mass 3 The Mass Spectrometer(Spectrometer(質
6、譜質譜儀儀)221/2212rxqmVBqBmvrmqVvqVmvu93.203822222VqxBmqmVBrx Isotope Separation Centrifuge and diffusion chamber 質譜儀質譜儀u93.203822222VqxBmqmVBrxcm16.92cos11qBmvTvpThe pitch(The pitch(螺距螺距)of the of the helical pathhelical path10-1.510-1.5 Cyclotrons and Cyclotrons and Synchrotrons SynchrotronsFermilabFe
7、rmilab:6.3km:6.3km ringring(迴旋加速器與同步加速器迴旋加速器與同步加速器)lThe resonance condition:The resonance condition:lWhen proton energy 50Mev:When proton energy 50Mev:lOut of resonance(relativistic Out of resonance(relativistic effect)effect)lA huge magnet(4A huge magnet(4 10106 6 m m2 2)is)is needed for high energ
8、y(500Gev)needed for high energy(500Gev)protons protons lThe proton The proton sychrotronsychrotron at at FermilabFermilab can produces 1Tev protoncan produces 1Tev protonoscff SynchrotronsSynchrotrons10-1.610-1.6 Magnetic Force on a Magnetic Force on a Current-Carrying WireCurrent-Carrying WireBLiFi
9、LBBqvFviLitqBdBdsin/For a wire segment:BLidFdBMagnetic ForceMagnetic Force例例 4 A length of wire with 4 A length of wire with a a semicircularsemicircular arc arc)(22sin)(3210231RLiBFFFFiBRdFFRdiBiBdLdFiLBFFCalculationCalculation線圈線圈10-1.710-1.7 Torque on A Torque on A Current LoopCurrent LooplF F2 2
10、 and F and F4 4 cancel cancel lF F1 1 and F and F3 3 form a force couple form a force couple sin)(sin )sin2()sin2(cos)90sin(2BNiANiabBbiaBbiaBibBibBF例例 5 A galvanometer for 5 A galvanometer for analoganalog meters metersdegree/mM102.528)23.0)(10(250)(100=sinsin86-NiABNiAB10-1.810-1.8 The Magnetic Th
11、e Magnetic DipoleDipolelThe magnetic dipole moments The magnetic dipole moments lThe magnetic potential The magnetic potential energy energy):cf(sinEpBBNiA)()(BUEpUBBBU2 )()(磁能磁能10-2 Magnetic Fields 10-2 Magnetic Fields due to Currentsdue to CurrentsConventional Conventional rocket EM Rail rocket EM
12、 Rail GunGun10-2.1 Calculating the 10-2.1 Calculating the Magnetic Field due to a Magnetic Field due to a currentcurrentThe law of The law of BiotBiot and and SavartSavartdEdqrdEdqrrdBidsrdBidsrr 14144402020203sin020020sin2 2sin4rdsidBdBBridsdBMagnetic Field Due to a Magnetic Field Due to a Current
13、in a Current in a Long Straight Long Straight WireWire RiRssRiRsRdsiBRsRRsr2)(2=)(2=sin,002/122002/32202222IntegrationIntegrationRidRiRiRddBBRidsRidsdB44=44=90sin40000202020Magnetic Field Due to a Magnetic Field Due to a Current in a Current in a Circular Arc of Circular Arc of WireWire RiRiBBBrsd8=
14、4)2/(0000321例例 6 What B does the 6 What B does the current produce?current produce?diLiLBiFBLiFdiBbaabbaabbaaa290sin20010-2.210-2.2 Two Parallel Two Parallel CurrentsCurrents例例 7 The Field Between Two 7 The Field Between Two wireswires10-2.310-2.3 Amperes Law Amperes LawencisdB0lComparing GaussCompa
15、ring Gauss law and Amperelaw and Ampere s laws lawlAmperes lawAmperes lawThe Magnetic Field The Magnetic Field OutsideOutside a a Long Straight Wire with Long Straight Wire with CurrentCurrentThe Magnetic Field The Magnetic Field InsideInside a a Long Straight Wire with Long Straight Wire with Curre
16、ntCurrent 例例 7 A hollow conducting 7 A hollow conducting cylindercylinder10-2.410-2.4 Solenoids and Solenoids and ToroidsToroidslMagnetic Field of a Solenoid(Magnetic Field of a Solenoid(螺螺線管線管)lMagnetic Field of a Magnetic Field of a ToroidToroid(螺線螺線環環)inhBhsdBsdBsdBsdBsdBaddccbba0 Magnetic Field
17、of a Magnetic Field of a SolenoidSolenoidiNrB0)2(Magnetic Field of a Magnetic Field of a ToroidToroid磁圍阻核融合反應磁圍阻核融合反應器器TokamakTokamak Fusion Test Fusion Test Reactor Reactor 10-2.510-2.5 A Current Carrying A Current Carrying Coil and a Magnetic Coil and a Magnetic DipoleDipolelA current loop and a bar A current loop and a bar magnetmagnetMagnetic Field of a CoilMagnetic Field of a Coil 敬請期待敬請期待電磁電磁 IVIV
