chap19(西尔斯当代大学物理)

1、Welcome you here for University Physics Meng Da MinMeng Da MinHeFei University of TechnologyHeFei University of Technology 2013 fall 2013 fall绪论对标准问题的标准答案的记诵 重燃求知欲 思维训练 三件东西至为重要：图书馆、好的老师、互联网 独立而有尊严的生活 自我意识与公共精神-有稳定的价值观，有独立思考能力，有积极的行为方式，做一个直立行走的人，大写的人祝愿年轻的朋友们：祝愿年轻的朋友们：努力学习，努力学习， 勇于探索，勇于探索， 大胆创新，大胆创新，

2、 为我们美好的明天为我们美好的明天 付出今天的辛劳和付出今天的辛劳和汗水！汗水！Introduction on PBL (1) a challenge to greater efforts in your study.1200 pages , 1000 words/page.you should finish reading at least 550pages. (half a million of words ) original English material in two semesters. about 20 min/page at least in average. 180h wi

3、ll be spent in reading the paragraphs my lecture will cover.English is a worry for most learners in China .physics is a difficult subject for most students.ambitious、self-confidence are needed. (2) the goals of PBLequal knowledge in physics.building a suitable environment to promote students convers

4、ion: from English learners into English users. my lectures are the road signs in your study. Try my best to achieve the four: “C”. Complete cover all the knowledge points . Clarification Concise Correct(3) Chapter features on Fundamental of PhysicsOpening puzzlers.Test your understanding: Simple que

5、stions inserted between paragraphs. If you can answer it without any difficulty, you can read on. Otherwise, you should review. Sample problems with key idea_example.Problem-Solving tactics: How to solve problems step by step. How to avoid common errors. Self-Introduction in brief index Part A Mecha

6、nism Part B Electricity Part C Magnetism Part D Wave and Optics Part E Modern Physics10Chap 19 Magnetic Field and Magnetic Forces19-1&2. Magnetism and Magnetic field19-3. Magnetic field Lines and Magnetic Flux19-4. Motion of Charged Particles in a Magnetic field19-5. Applications of Motion of charge

7、d particle (Cyclotrons and Synchrotrons ) 19-6. Magnetic force on a Current-Carrying Conductor19-7. Force and Torque on a current loop19-8. The Hall Effect1119-1&2. Magnetism and Magnetism and Magnetic FieldMagnetic Field1. Analogy between electricity and magnetism (monopoles in magnetism) BElinesBl

8、inesEBE?mqq Fig.19-4Fig.19-4 0qSdEE(or magnetic monopoles) 高斯定理高斯定理科学家用中子散射观测科学家用中子散射观测到了到了“狄拉克弦狄拉克弦”的存的存在在 2009 年年9月月4日出版的日出版的科学科学杂志杂志上，德国亥姆霍兹材料与能源中心的上，德国亥姆霍兹材料与能源中心的乔纳森乔纳森莫里斯莫里斯(Jonathan Morris)领领导的团队和法国导的团队和法国Laue-Langevin研究研究所汤姆所汤姆芬内尔芬内尔(Tom Fennell)领导的领导的团队分别报告团队分别报告: 在自旋冰晶体中观察在自旋冰晶体中观察到了类似磁单极子

9、的到了类似磁单极子的“准粒子准粒子”。131). definition formula:2. Definition of BBvqFBzero-force axis (the direction of )B( , )0)sinBFBv Bqvmagnitude ofBmaximum sideway force whenmaxmax()/2,(),BBFFBqv Bqv0qFEdefinition of electric field:B0BFVq FvBq142). discussright-hand rule:Fig.19-6Fig.19-6 no explicit（明确的） expressi

10、onunit in SI4T (Tesla) =/10N A mGauss always perpendicular to andBFvB isalso a formula for findingBFqvBBF15Example 1:An electron that has velocity An electron that has velocity .)15. 0()03. 0(jTiTBjsmismv)/100 . 3()/100 . 2(66moves through the magnetic fieldmoves through the magnetic fieldFind Find

11、(a)(a) the force on the electron the force on the electron (b)(b) repeat your repeat your calculation for a proton having the same velocity calculation for a proton having the same velocity 163. Crossed Fields: Discovery of the Electron BeFF Self-reading: P7Self-reading: P7171. Hall effect19-8. Cros

12、sed Fields: The Hall Effect (1879)1).1). Hall potential Hall potential difference difference V V and and hall electric field hall electric field E EldvHIBI+_+ + + + +- - - - -EBdl182. Theory of Hall effect HVBAssume: charge carriers are electrons and they drift in the opposite direction of current I

13、. (drift speed is vd).ldnevIdBeveEdHdHBvE dHBvdVneldIvdnelBIVHneRH1lBIRVHH霍耳系数霍耳系数B + + +HEdvIf193. Application of hall effect1). provide a sign judgement of charge carriers in conductors2).measurement of the number of carriers per unit volume of conductor.lBIRnelBIVHHelVBInH3).measurement of B,I,T+

14、B+ + + HEdvfIB + + +HEdvIf20*磁流体发电磁流体发电气体在气体在3000K高温下将高温下将发生电离，成为正、负离子，发生电离，成为正、负离子，将 高 温 等 离 子 气 体 以将 高 温 等 离 子 气 体 以1000m/s的速度进入均匀磁的速度进入均匀磁场场B中中+ + + 高温高温等离等离子气子气B+vmfmfvI 正电荷聚集在上板，负正电荷聚集在上板，负电荷聚集在下板，因而电荷聚集在下板，因而可向外供电。可向外供电。优点：无机械损耗，可以提高效率，优点：无机械损耗，可以提高效率，缺点：尚存在技术问题有待解决。缺点：尚存在技术问题有待解决。21Fast-Readi

15、ng: example 19.12Fast-Reading: example 19.1222Review:Review:1. Magnetic Fields:1. Magnetic Fields:BvqFBMagnitude:direction: right-hand rule FvBq zero-force axis (the direction of )BB0mFVqmaximum sideway force whensinqvFBBqvFBBmax)(200BF232. Hall effect:2. Hall effect:lBIRnelBIVHHelVBInHI+_+ + + + +-

16、 - - - -EBdlHall potential difference V1). provide a sign judgement of charge carriers in conductors2).measurement of the number of carriers per unit volume of conductor.3).measurement of B,I,T19-3. Magnetic Field Lines and Magnetic Field Lines and Magnetic FluxMagnetic Flux1. Magnetic field lines a

17、nd N、S poles2400intl dEqAdEs有源场有源场保守力场保守力场E E lines linesHow about B ?How about B ?25IB262. Magnetic flux BAad .dABdAdBB),(d: .BAbABdcosdBBdAnAdB1).definition of magnetic flux:1).definition of magnetic flux:2).2).calculatingcalculating : :Bthe number of field lines through a surface the number of fi

18、eld lines through a surface in magnetic filedin magnetic filedc. Flux of a c. Flux of a surfacesurfaceABABddAnBAdBB273. Additional problems:1).Gauss law of magnetic field :1).Gauss law of magnetic field :AAdB02).explain2).explain磁场是有旋磁场是有旋/无源场无源场(非保守场非保守场)； 电场是有源场，保守场电场是有源场，保守场 磁极磁极成对出现成对出现，不存在磁单极不存

19、在磁单极； 但单独存在正负电荷但单独存在正负电荷3). note3). noteABBMagnetic field flux through a Magnetic field flux through a closed surface equals to closed surface equals to zero.zero.2819-4. Motion of Charged Particles in a Magnetic field 1. The force on the charged particle qBParticle moves along the Particle moves al

20、ong the direction of magnetic field:direction of magnetic field:qvBFB0BFvqBvFParticle moves perpendicular to Particle moves perpendicular to the direction of magnetic field:the direction of magnetic field:29qvFBin common conditionin common condition，the the direction of velocity and direction of vel

21、ocity and magnetic field makesmagnetic field makes angleangle : :sinqvBF BvqFBmagnetic magnetic force force magnitudemagnitude：directiondirection：the direction of the direction of Bv特点：不对运动电荷做功，不改变特点：不对运动电荷做功，不改变 的大小，只改的大小，只改变方向；即不改变带电粒子的速率和动能。变方向；即不改变带电粒子的速率和动能。v302. The charged particle in uniform

22、 magnetic field 2、force:Bqvf0 RvmmaBqvfm200radius:qBmvR0 + q, m0vfR1、Bv/0Bv0BvBv00path：circular motion with constant speed0v0, 00mfBvpath： uniform liner motion with const speed 0v0vDirection: perpendicular to the vector Bandv031period:qBmqBmvvvRT 222000frequency:mqBTf 21 + q, m0vfRAngular frequency:

23、mqBf 2 do not depend on the speed and radius of the particle but on ., fTBqm,323、sincos/vvvvradius: sinqBmvqBmvR period:qBmvRT 22 pitchthe distance between adjacent turnscos2/vqBmTvp resolve into resolve into two components: two components: vParallel to ： F/=0 ， uniform liner motionPerpendicular to

24、： F=qvBsin，uniform circular motionBBpath：helix，the particle moves in a helical path.),(Bv3334hB B螺距螺距p与与v无关，只与无关，只与v/成正比，若各成正比，若各粒子的粒子的v/相同，则其螺距是相同的，每相同，则其螺距是相同的，每转转 一周粒子都相交于一点，利用这个一周粒子都相交于一点，利用这个原理，可实现原理，可实现磁聚焦磁聚焦。 cos2/vqBmTvp 353. charged particles in nonuniform magnetic field 1 1、 magnetic bottl

25、emagnetic bottleFig.19-17Fig.19-17362 2、 van Allen radiation belts and auroravan Allen radiation belts and aurora地磁场，两极强，中地磁场，两极强，中间弱，能够捕获来自间弱，能够捕获来自宇宙射线的的带电粒宇宙射线的的带电粒子，在两极之间来回子，在两极之间来回振荡。振荡。1958年，探索者一号年，探索者一号卫星在外层空间发现卫星在外层空间发现被磁场俘获的来自宇被磁场俘获的来自宇宙射线和太阳风的质宙射线和太阳风的质子层和电子层子层和电子层Van Allen辐射带辐射带37Example:

26、Mass spectrometerMass spectrometer221mvqV qmVBrx222mqVqBmqBmvr2qmVB21VqxBm822若每个离子所带电量相等，由谱线若每个离子所带电量相等，由谱线的位置可以确定同位素的质量。的位置可以确定同位素的质量。由感光片上谱线的黑度，可以确定由感光片上谱线的黑度，可以确定同位素的相对含量。同位素的相对含量。锗的质谱锗的质谱38cyclotrons and synchrotrons 391. cyclotronfrequency:mqBtf221qBmvR radius:Time in Dee:qBmvRtresonance condit

27、ion:oscmfqB240mqBRv0 Kinetic energy:mRBqmBqRmmvEk221212022202 Speed (max radiusR0):理论理论增大电磁铁截面及增大电磁铁截面及D形盒半径，以增大粒子的能量形盒半径，以增大粒子的能量实际实际比较困难比较困难41兰州重离子加速器兰州重离子加速器北京正负电子对撞机北京正负电子对撞机合肥同步辐射加速器合肥同步辐射加速器我国最大的三个加速器我国最大的三个加速器422. synchrotronsqBmvr BoscfmqBf2oscf43Review:Review:1. Magnetic Fields:1. Magnetic

28、Fields:BvqFBMagnitude:direction: right-hand rule FvBq zero-force axis (the direction of )BB0mFVqmaximum sideway force whensinqvFBBqvFBBmax)(200BF442. Hall effect:2. Hall effect:lBIRnelBIVHHelVBInHI+_+ + + + +- - - - -EBdlHall potential difference V1). provide a sign judgement of charge carriers in c

29、onductors2).measurement of the number of carriers per unit volume of conductor.3).measurement of B,I,T453. The force on the charged particle:3. The force on the charged particle:BvqFBqBqvBFB0BFvqBvFqvFBBvqFB464. The motion of charged particle in 4. The motion of charged particle in uniformuniform ma

30、gnetic fieldmagnetic field due to magneticdue to magnetic force :force :A、Bv/00, 00BfBvpath： uniform liner motion with const speed 0v0vB、+ q, m0vfRBv0BvBv00path：circular motion with constant speed0vradius:qBmvR0 period:qBmT 247C、sincos/vvvvradius: sinqBmvqBmvR period:qBmvRT 22 Pitch:cos 2/vqBmTvpPar

31、allel to ： F/=0 ， uniform liner motionPerpendicular to ： ，uniform circular motionBBpath：helix，the particle moves in a helical path.),(BvhBsinFqvB483. The motion of charged particle in 3. The motion of charged particle in nonuniformnonuniform magnetic fieldmagnetic field : :magnetic bottlemagnetic bo

32、ttle van Allen radiation belts and aurora van Allen radiation belts and aurora4. cyclotrons and synchrotrons4. cyclotrons and synchrotrons49The force on the charged The force on the charged particle :particle :19-6. Magnetic Force on a Current-Carrying Conductor1. Force on charge carriers in current

33、 sinqvBF BvqFmagnitudemagnitude：directiondirection：the direction of the direction of Bv50BvefdBMagnetic force acting on Magnetic force acting on one charge carriersone charge carriers：In a time In a time t t, total charges:, total charges:dvLiitqacting on a length of L:acting on a length of L:BqvBvq

34、FddBiLBBvviLddBevd51BFiLBBdFidLBBBFdFidLBlIdBFdLBdliBFsindirectiondirection：BlidsiniLB52Note:)d(dyZLxxzByBIdFF)d(dzxLyyxBzBIdFF)d(dxyLzzyBxBIdFFkFjFiFFzyxLIB generally speaking, forces on current elements generally speaking, forces on current elements are different, we can resolve into x,y,z are dif

35、ferent, we can resolve into x,y,z components and then sum up it:components and then sum up it:F53Example 1: yxFjFiFddIn uniform magnetic field In uniform magnetic field B B，a current a current I I goes goes through a hemicycle wire with radius through a hemicycle wire with radius R. R. if the if the

36、 plane of the wire is perpendicular to the field, plane of the wire is perpendicular to the field, find the force on the wirefind the force on the wire. . IFdFdxFdxFdyFdyFdxyF r o m s y m m e t r y F r o m s y m m e t r y distribution of the current, distribution of the current, we can get the symme

37、try we can get the symmetry of the force acting on it:of the force acting on it: yFFdS S：54 IFdFdxFdxFdyFdyFdxyddRl From geometrical relation:From geometrical relation:then:then:sinsinlBIFFydddFrom eqs 29-28:From eqs 29-28: yFFd0sindBIRBIR2DirectionDirection：along y( ) axisalong y( ) axisj结果表明：结果表明：

38、半圆形载流导线上所受的力与其两个半圆形载流导线上所受的力与其两个端点相连的直导线所受到的力相等。端点相连的直导线所受到的力相等。55exercise：Find the force on current I in magnetic fieldBII1IIoRIRBIF2 To the right0F0F561. Force equilibrium :19-7. Force and Torque on a Current LoopForce: 21BIlF22BIlFBF4F3F1l1l2MNOPF2Isinsin113BIlBIlFsin14BIlFA torque is formed by F

39、1&F2B)(OP)(NM2F1FneF F3 3& &F F4 4 have the same magnitude have the same magnitude and on the same line of action,but and on the same line of action,but the opposite direction, thus their the opposite direction, thus their net force & torque are force & torque are zero.572. torque on a current loop

40、:The net torque on the loop by The net torque on the loop by B B：B)(OP)(NM2F1Fnegeometrical relation of geometrical relation of & & : :2/Replace Replace with with ，we get the net torque:we get the net torque:cos12LFsinBIAcos21LBILcosBIA58 设任意形状的平面载设任意形状的平面载流线圈的面积流线圈的面积A，电流强，电流强度度I，定义：，定义：Magnetic Mo

41、ment:nInIA 载流线圈的空间取向用电流右载流线圈的空间取向用电流右手螺旋的法向单位矢量手螺旋的法向单位矢量 描述。描述。n 可以证明，上式不仅对矩形线圈成立，对于均可以证明，上式不仅对矩形线圈成立，对于均匀磁场中的任意形状的平面线圈也成立，对于带电匀磁场中的任意形状的平面线圈也成立，对于带电粒子在平面内沿闭合回路运动以及带电粒子自旋所粒子在平面内沿闭合回路运动以及带电粒子自旋所具有的磁矩，在磁场中受到的力矩都适用。具有的磁矩，在磁场中受到的力矩都适用。Torque on a current loop due to magnetic field：B59Discussion： = /2，磁

42、通量，磁通量 =0，力矩，力矩max=IAB线圈平面与磁场方向相互平行，力矩最大，这一力矩有使线圈平面与磁场方向相互平行，力矩最大，这一力矩有使减减小的趋势。小的趋势。 =0， =BA，力矩，力矩=0，平衡，平衡 (稳定稳定)线圈平面与磁场方向垂直，力矩为零，线圈处于平衡状态。线圈平面与磁场方向垂直，力矩为零，线圈处于平衡状态。 = ， =-BA，力矩，力矩=0，平衡，平衡(不稳定不稳定) 综上所述综上所述，任意形状不变的平面载流线圈作，任意形状不变的平面载流线圈作为整体在均匀外磁场中，受到的合力为零，合力为整体在均匀外磁场中，受到的合力为零，合力矩使线圈的磁矩转到磁感应强度的方向。矩使线圈的

43、磁矩转到磁感应强度的方向。线圈平面与磁场方向相互垂直，力矩为零，但为不稳定平衡线圈平面与磁场方向相互垂直，力矩为零，但为不稳定平衡, 与与 反向，微小扰动，磁场的力矩使线圈转向稳定平衡状态反向，微小扰动，磁场的力矩使线圈转向稳定平衡状态。B60Example 2:241RQrdrorrRQqd2d2 rrRQTdqId22d2 rrd rrrIddd32Rrr03dd241RQ Charge Q distributes uniformly on a disk and the Charge Q distributes uniformly on a disk and the disk rotated with velocity disk rotated with velocity .Prove the magnetic .Prove the magnetic dipole moment of this disk isdipole moment of this disk is61Assignment: P32-34 Assignment: P