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