西南交通大学：《大学物理》课程教学资源（讲稿，双语）CHAPTER 20 Magnetic Forces and Magnetic Field

UNIVERSITY PHYSICS II CHAPTER 20 Magnetic Forces and Magnetic Flel 820.1 The magnetic field and its application 1. The magnetic field and its features Gravitational field FG = mg -gravitational force caused by mass Electric field Fe=gE electric force caused by electric charge Magnetic field-- While the magnetic field has similarities to the other fields, it also has some unique features that distinguish it from the others

1 1. The magnetic field and its features While the magnetic field has similarities to the other fields, it also has some unique features that distinguish it from the others. Gravitational field —gravitational force caused by mass Electric field —electric force caused by electric charge Magnetic field--? F mg r r G = F qE r r e = §20.1 The magnetic field and its application

820.1 The magnetic field and its application @Magnets and magnetic poles: Unlike poles attract each other, like poles repel each other The magnetic forces of attraction and repulsion of magnetic poles on each other are similar to the electrical force interactions between electric charges, but they are not at all the same thing. with magnets, no magnetic monopoles ever have been discovered 820.1 The magnetic field and its application It is impossible to isolated either a north or a south magnetic pole hence we say that magnets and the magnetic field always are dipolar Magnetic poles always occur in north-south pairs that produce a dipolar magnetic field B in the surrounding space

2 §20.1 The magnetic field and its application 1Magnets and magnetic poles: Unlike poles attract each other, like poles repel each other. The magnetic forces of attraction and repulsion of magnetic poles on each other are similar to the electrical force interactions between electric charges, but they are not at all the same thing. With magnets, no magnetic monopoles ever have been discovered. It is impossible to isolated either a north or a south magnetic pole; hence we say that magnets and the magnetic field always are dipolar. Magnetic poles always occur in north-south pairs that produce a dipolar magnetic field in the surrounding space. B r §20.1 The magnetic field and its application

820.1 The magnetic field and its application ② magnetic field lines The direction of the magnetic field at any point is tangent to the field line at that point; The number density of the magnetic field lines in a region is a measure of the magnitude of the magnetic field there. 820.1 The magnetic field and its application Othe differences of the magnetic field and the electric field (A charge q placed at rest magnetic field experiences zero force (i)Move the charge along a magnetic field line, the moving charge again experiences zero force; (ii)If the charge is moved at speed v at angle 0 with the direction of a uniform magneti field. a nonzero magnetic force exists on the charge. The force depends on both the speed and the direction of the velocity

3 2magnetic field lines The direction of the magnetic field at any point is tangent to the field line at that point; The number density of the magnetic field lines in a region is a measure of the magnitude of the magnetic field there. §20.1 The magnetic field and its application 3the differences of the magnetic field and the electric field (i)A charge q placed at rest magnetic field experiences zero force; (ii)Move the charge along a magnetic field line, the moving charge again experiences zero force; (iii)If the charge is moved at speed v at angle θ with the direction of a uniform magnetic field, a nonzero magnetic force exists on the charge. The force depends on both the speed and the direction of the velocity. §20.1 The magnetic field and its application

820.1 The magnetic field and its application iv The magnetic force varies with the magnitude of the magnetic field B(as determined from the number of the magnetic field lines): vThe direction of the force on g depends on the sign of the moving charge. In every case the force is perpendicular to both the velocity of the charge and the field direction qv×B The si unit of magnetic field: 1 tesla(T)=104 gauss 820.1 The magnetic field and its application 2. applications A velocity selector/J Fm=φ×B=gn6q B F=￠E=-E v=vi88888oE Fe= qE=gvoB E ν>v,Fm> Fe deflect up B ν<v,Fn< f. deflect down v, depends only on the magnitude of the field vo is independent of the identical charge; Vo is independent of the mass of the particle

4 (iv)The magnetic force varies with the magnitude of the magnetic field B (as determined from the number of the magnetic field lines); (v)The direction of the force on q depends on the sign of the moving charge. In every case the force is perpendicular to both the velocity of the charge and the field direction. F qv B r r r m = × The SI unit of magnetic field: 1 tesla(T)=104 gauss §20.1 The magnetic field and its application 1 A velocity selector F qE qEj F qv B qv Bj ˆ ˆ e m 0 = = − = × = r r r r r B E v qE qv B F F = = + = 0 0 m e 0 r r 0 m e 0 m e , , v v F F v v F F > deflect up deflect down depends only on the magnitude of the field; is independent of the identical charge; is independent of the mass of the particle. 0 v 0 v 0 v 2. Applications + + + + + + − − − − − − ⊗ ⊗ ⊗ ⊗ ⊗ q v v i ˆ = 0 r E r x y ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ B r §20.1 The magnetic field and its application

820.1 The magnetic field and its application ② A mass spectrometer Fn=qv×B F=ma B= R mmV R the speed by B a velocity selector If the beam is composed of the ions of different isotopes of the same element, all with the same charge, each isotope moves in a circle with a different radius 820.1 The magnetic field and its application te hall effect B= Bk negative x××××x cha <> V=-L Positive charge v=L

5 2 A mass spectrometer q B mv R R v q vB m F ma F qv B = = = = × 2 m r r r If the beam is composed of the ions of different isotopes of the same element, all with the same charge, each isotope moves in a circle with a different radius. Choose the speed by a velocity selector §20.1 The magnetic field and its application 3 The Hall effect B Bk ˆ = r v v i ˆ = r Positive charge v v i ˆ =− r negative charge Fm r Fm r Fm r Fe r Fe r r r r i ˆ j ˆ i ˆ j ˆ I I I I I I §20.1 The magnetic field and its application

820.1 The magnetic field and its application (negative charge carriers Fm=gixB=(a)i)x Bk=-a Bj F=(-0)(-E)=E (positive charge carriers Fm=vxB=a(v>i)xBk=-aBj F=qEj=gej Equilibrium state:aE=aB E≤B 820.1 The magnetic field and its application ④ Hall voltage V2-1=∫E==一E let V=v-v=El=Bl B T=nga <> nqe Hall Bl= hB1B「q>0,vmn>0 ngA ngd 1q<0,Hall <0 6

6 (i)negative charge carriers F q Ej q Ej F qv B q v i Bk q v Bj ˆ )ˆ ( )( ˆ ˆ )ˆ ( )( e m = − − = = × = − − × = − r r r r F q Ej q Ej F qv B q v i Bk q v Bj ˆ ˆ ˆ ˆ )ˆ ( e m = = = × = × = − r r r r (ii)positive charge carriers Equilibrium state: E v B q E q v B = = §20.1 The magnetic field and its application 4 Hall voltage V V E r E y El l l B A B − A = − ⋅ = − ⋅ = − ∫ ∫− 2 2 j ˆ j d ˆ d r r nqA I v I nqA v = = nqd IB nqA IlB VHall = Bl = = 0, 0 0, 0 Hall Hall > q V q V x y z B r • • • • • • • • • • • • • • • B A l d A − + + + + + − − − − − v I r q §20.1 The magnetic field and its application V V V El v Bl let Hall = A − B = =

820.1 The magnetic field and its application 5 discovery of the electron and the ratio of mass and charge of electron Thomson’ s experiment B Screen 1 gE L e m BL 2 m B 9 2DE 820.1 The magnetic field and its application 6 magnetic focus. magnetic mirror and magnetic bottle F=qvB=欣 R R The radius of the circular motion X my R= B The period of the circular motion 2 2T 2 q/b It is independent v

7 5 discovery of the electron and the ratio of mass and charge of electron —Thomson’s experiment yE B L q m B E v v L m qE y 2 , 2 1 2 2 2 2 = = ⇒ = §20.1 The magnetic field and its application 6 magnetic focus, magnetic mirror and magnetic bottle R v F q vB m 2 m = = q B mv R = The radius of the circular motion ××××× ××××× × × × ×× ××××× R v r m B r §20.1 The magnetic field and its application q B m v R T 2π 2π = = The period of the circular motion It is independent v

820.1 The magnetic field and its application The radius of the helical motion n y sIn R=2上 B gb The screw--pitch B h= Ty,= 27m y COS gB For small o 274 h B D 820.1 The magnetic field and its application The magnetic focus a)量象管电子束磁聚焦原理图 b)电子束运动截面投影图 TThe magnetic mirror 8

8 φ π cos 2 // v qB m h = Tv = The screw--pitch For small φ v qB m h 2π ≈ qB mv qB mv R sinφ = = ⊥ The radius of the helical motion φ v r // v r ⊥ v r B r h q v r B r r §20.1 The magnetic field and its application The magnetic focus The magnetic mirror §20.1 The magnetic field and its application

820.1 The magnetic field and its application Magnetic bottle B -Particle Spiral path 820.1 The magnetic field and its application The Van Allen radiation belts and aurora Electron path d lines north pole Auroral oval

9 Magnetic bottle §20.1 The magnetic field and its application The Van Allen radiation belts and aurora §20.1 The magnetic field and its application

Aurora 820.1 The magnetic field and its application OThe cyclotron Dee R B 2R2元m T v aB Beam\ Can this process Deflector persist infinitely? plate Oscillator 10

10 Aurora 7The cyclotron q B mv R = q B m v R T 2π 2π = = §20.1 The magnetic field and its application Can this process persist infinitely?