7 Lorentz 7.1 Ampère I 1 I 2 I 2 I 1 L I 1 I 2 21 12 L r 21 = 12 = µ 0 2π I 1 I 2 r L. (7.1) 7.1 µ 0 =4π 10 7 N A 2 (7.2) magnetic permiability I 1 I 2 I 1 I 2 12 21 12 21 7.1: 1m 95
96 7 1m =2 10 7 N 1A 7.1 7.2 a C (1) I (2) A C I A A a A a A A a C C C 7.2: C A C A = = µ 0 2π (1) A C 7.2 AC C A 3 3 µ0 I 2 = 2πa. (2) A C C 7.2 A A = µ 0 I2 2πa. I 2 a.
7.2 97 7.2 (7.1) I 1 I 2 r Coulomb Coulomb q 1 q 2 q 2 E 2 q 1 I 2 I 1 magnetic field Coulomb I ds d d = I ds (7.3) leming leming s left-hand rule d Ids 7.3: E I I ds d (7.1) I d = I ds
98 7 7.1 d I ds xx xy xz = yx yy yz zx zy zz d x d y = xx xy xz yx yy yz I ds x I ds y d z zx zy zz I ds z ij (7.1) I ds d z z = 0 0 0 0 0 0 0 d I ds d x = I ds y, d y = I ds x, d z =0 z =(0, 0, ) I ds y z I ds z y d = I ds = I ds z x I ds x z I ds x y I ds y x z z
7.3 Lorentz 99 7.3 Lorentz q v m = q v (7.4) Lorentz Lorentz s force Lorentz v =0 Lorentz (7.3) S n v 7.4 I I = n ( e) Sv (7.3) I ds d = nes ds v v ds ns ds ds = e v ds I e v S 7.4: Lorentz q (7.4) E e = qe Lorentz = q ( E + v ). (7.5)
100 7 Lorentz Lorentz (7.5) v K v Lorentz (7.5) E v K q K u K Lorentz (7.5) = q ( E + v ) v K E K Lorentz E E E p = E p, E t = p = p, t = 1 1 (u/c) 2 ( E + u ) t 1 1 (u/c) 2 ( 1 c 2 u E ) t (7.6) p u t u 7.2 v 0 q m q r v 7.5: Lorentz = q v v 7.5 r
7.3 Lorentz 101 m dv dt =0, m v2 r = qv v = v 0 = r = mv 0 q = r = mv 0 /(q) v 0 cyclotron motion ω c = v r = q m cyclotron frequency q/m 7.3 Hall (a) (b) 7.6 (a) y y v 7.6 (b) x Lorentz m =( e ) v v y x Lorentz z Lorentz z (c) z z E h Hall Hall effect field Hall e =( e )E h z Hall = m + e =( e ) v +( e )E h.
102 7 z (a) I y x z (b) I y x z (c) E h I y x 7.6: Hall Hall z m e y Hall z z z Hall y z x z Hall Hall Hall effect Hall Hall electromotive force
7.4 103 7.4 Ampère I C E, θ b D a E C,D S 7.7: 7.7 θ 7.7 C DE C DE C = I C = Iasin(π θ) k = Iasin θ k, DE = Iasin θ k k CD E CD E CD = I CD = Ibn, E = I E = Ibn n Ib N = CD CE cos θ k = Iabcos θ k = IS S ab S IS magnetic moment IS θ π/2 N
104 7 IS IS S N N S 7.4 a I I ds a θ θ ds ds d ds d 7.8: θ I ds ds θ + π/2 ( d = I ds = I ds sin θ + π ) n = Iacos θ dθ n 2 n a ds a dθ θ = π θ I ds d = Iacos θ dθ n = Iacos θ dθ n d 2a cos θ dn = Iacos θ 2a cos θ dθ =2Ia 2 cos 2 θ dθ θ π/2 π/2 N = π/2 π/2 2Ia 2 cos θ dθ = πa 2 I.
7.5 105 7.5 Coulomb Coulomb N +q m S q m m = 1 4πµ 0 q m q m r 2 (7.7) µ 0 Wb = J/A Coulomb P q m m H H H N/Wb = A/m m = q m H. (7.8) = µ 0 H (7.9) ±q m magnetic dipole 7.9 L q m z +q m +q m L/ 2 O L p m = q m L L/ 2 q m q m 7.9: q m +q m L p m = q m L. (7.10) magnetic dipole moment 7.9
106 7 z q m +q m z z r θ (3.11) H r (r, θ) = 2p m cos θ 4πµ 0 r 3 H θ (r, θ) = p m sin θ 4πµ 0 r 3 (7.11) 7.10 H N N = p m H. (7.12) N 7.10 +q m H N +q m H q m q m H 7.10: H p m θ p m H = p m H sin θ = q m LH sin θ