chap19(西爾斯當代大學物理)

1、Welcome you here for University Physics Meng Da MinMeng Da MinHeFei University of TechnologyHeFei University of Technology 2013 fall 2013 fall緒論對標準問題的標準答案的記誦 重燃求知欲 思維訓練 三件東西至為重要：圖書館、好的老師、互聯(lián)網(wǎng) 獨立而有尊嚴的生活 自我意識與公共精神-有穩(wěn)定的價值觀，有獨立思考能力，有積極的行為方式，做一個直立行走的人，大寫的人祝愿年輕的朋友們：祝愿年輕的朋友們：努力學習，努力學習， 勇于探索，勇于探索， 大膽創(chuàng)新，大膽創(chuàng)新，

2、 為我們美好的明天為我們美好的明天 付出今天的辛勞和付出今天的辛勞和汗水！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學家用中子散射觀測科學家用中子散射觀測到了到了“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學科學雜志雜志上，德國亥姆霍茲材料與能源中心的上，德國亥姆霍茲材料與能源中心的喬納森喬納森莫里斯莫里斯(Jonathan Morris)領(lǐng)領(lǐng)導(dǎo)的團隊和法國導(dǎo)的團隊和法國Laue-Langevin研究研究所湯姆所湯姆芬內(nèi)爾芬內(nèi)爾(Tom Fennell)領(lǐng)導(dǎo)的領(lǐng)導(dǎo)的團隊分別報告團隊分別報告: 在自旋冰晶體中觀察在自旋冰晶體中觀察到了類似磁單極子

9、的到了類似磁單極子的“準粒子準粒子”。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（明確的） 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霍耳系數(shù)霍耳系數(shù)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*磁流體發(fā)電磁流體發(fā)電氣體在氣體在3000K高溫下將高溫下將發(fā)生電離，成為正、負離子，發(fā)生電離，成為正、負離子，將 高 溫 等 離 子 氣 體 以將 高 溫 等 離 子 氣 體 以1000m/s的速度進入均勻磁的速度進入均勻磁場場B中中+ + + 高溫高溫等離等離子氣子氣B+vmfmfvI 正電荷聚集在上板，負正電荷聚集在上板，負電荷聚集在下板，因而電荷聚集在下板，因而可向外供電?？上蛲夤╇姟?yōu)點：無機械損耗，可以提高效率，優(yōu)點：無機械損耗，可以提高效率，缺點：尚存在技術(shù)問題有待解決。缺點：尚存在技術(shù)問題有待解決。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有源場有源場保守力場保守力場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磁場是有旋磁場是有旋/無源場無源場(非保守場非保守場)； 電場是有源場，保守場電場是有源場，保守場 磁極磁極成對出現(xiàn)成對出現(xiàn)，不存在磁單極不存

19、在磁單極； 但單獨存在正負電荷但單獨存在正負電荷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特點：不對運動電荷做功，不改變特點：不對運動電荷做功，不改變 的大小，只改的大小，只改變方向；即不改變帶電粒子的速率和動能。變方向；即不改變帶電粒子的速率和動能。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與與v無關(guān)，只與無關(guān)，只與v/成正比，若各成正比，若各粒子的粒子的v/相同，則其螺距是相同的，每相同，則其螺距是相同的，每轉(zhuǎn)轉(zhuǎn) 一周粒子都相交于一點，利用這個一周粒子都相交于一點，利用這個原理，可實現(xiàn)原理，可實現(xiàn)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地磁場，兩極強，中地磁場，兩極強，中間弱，能夠捕獲來自間弱，能夠捕獲來自宇宙射線的的帶電粒宇宙射線的的帶電粒子，在兩極之間來回子，在兩極之間來回振蕩。振蕩。1958年，探索者一號年，探索者一號衛(wèi)星在外層空間發(fā)現(xiàn)衛(wèi)星在外層空間發(fā)現(xiàn)被磁場俘獲的來自宇被磁場俘獲的來自宇宙射線和太陽風的質(zhì)宙射線和太陽風的質(zhì)子層和電子層子層和電子層Van Allen輻射帶輻射帶37Example:

26、Mass spectrometerMass spectrometer221mvqV qmVBrx222mqVqBmqBmvr2qmVB21VqxBm822若每個離子所帶電量相等，由譜線若每個離子所帶電量相等，由譜線的位置可以確定同位素的質(zhì)量。的位置可以確定同位素的質(zhì)量。由感光片上譜線的黑度，可以確定由感光片上譜線的黑度，可以確定同位素的相對含量。同位素的相對含量。鍺的質(zhì)譜鍺的質(zhì)譜38cyclotrons and synchrotrons 391. cyclotronfrequency:mqBtf221qBmvR radius:Time in Dee:qBmvRtresonance condit

27、ion:oscmfqB240mqBRv0 Kinetic energy:mRBqmBqRmmvEk221212022202 Speed (max radiusR0):理論理論增大電磁鐵截面及增大電磁鐵截面及D形盒半徑，以增大粒子的能量形盒半徑，以增大粒子的能量實際實際比較困難比較困難41蘭州重離子加速器蘭州重離子加速器北京正負電子對撞機北京正負電子對撞機合肥同步輻射加速器合肥同步輻射加速器我國最大的三個加速器我國最大的三個加速器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結(jié)果表明：結(jié)果表明：

38、半圓形載流導(dǎo)線上所受的力與其兩個半圓形載流導(dǎo)線上所受的力與其兩個端點相連的直導(dǎo)線所受到的力相等。端點相連的直導(dǎo)線所受到的力相等。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 設(shè)任意形狀的平面載設(shè)任意形狀的平面載流線圈的面積流線圈的面積A，電流強，電流強度度I，定義：，定義：Magnetic Mo

41、ment:nInIA 載流線圈的空間取向用電流右載流線圈的空間取向用電流右手螺旋的法向單位矢量手螺旋的法向單位矢量 描述。描述。n 可以證明，上式不僅對矩形線圈成立，對于均可以證明，上式不僅對矩形線圈成立，對于均勻磁場中的任意形狀的平面線圈也成立，對于帶電勻磁場中的任意形狀的平面線圈也成立，對于帶電粒子在平面內(nèi)沿閉合回路運動以及帶電粒子自旋所粒子在平面內(nèi)沿閉合回路運動以及帶電粒子自旋所具有的磁矩，在磁場中受到的力矩都適用。具有的磁矩，在磁場中受到的力矩都適用。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線圈平面與磁場方向相互平行，力矩最大，這一力矩有使線圈平面與磁場方向相互平行，力矩最大，這一力矩有使減減小的趨勢。小的趨勢。 =0， =BA，力矩，力矩=0，平衡，平衡 (穩(wěn)定穩(wěn)定)線圈平面與磁場方向垂直，力矩為零，線圈處于平衡狀態(tài)。線圈平面與磁場方向垂直，力矩為零，線圈處于平衡狀態(tài)。 = ， =-BA，力矩，力矩=0，平衡，平衡(不穩(wěn)定不穩(wěn)定) 綜上所述綜上所述，任意形狀不變的平面載流線圈作，任意形狀不變的平面載流線圈作為整體在均勻外磁場中，受到的合力為零，合力為整體在均勻外磁場中，受到的合力為零，合力矩使線圈的磁矩轉(zhuǎn)到磁感應(yīng)強度的方向。矩使線圈的

43、磁矩轉(zhuǎn)到磁感應(yīng)強度的方向。線圈平面與磁場方向相互垂直，力矩為零，但為不穩(wěn)定平衡線圈平面與磁場方向相互垂直，力矩為零，但為不穩(wěn)定平衡, 與與 反向，微小擾動，磁場的力矩使線圈轉(zhuǎn)向穩(wěn)定平衡狀態(tài)反向，微小擾動，磁場的力矩使線圈轉(zhuǎn)向穩(wěn)定平衡狀態(tài)。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