8 Biot-Svt Ampèe Biot-Svt 8.1 Biot-Svt 8.1.1 Ampèe B B B = µ 0 2π. (8.1) B N df B ds A M 8.1: Ampèe 107
108 8 0 B line of mgnetic induction 8.1 8.1 AB MN ds df (7.1) (7.3) (8.1) df = µ 0 ds, df = ds B = B ds 2π 8.1 8.2 A B P P O s s Q PQ R QP AB θ 0 <θ<π Q ds P db db = µ 0 sin θ ds R 2 n AB n s B Q θ B θ O R P A θ A 8.2: R = dθ, ds = sin θ sin 2 θ
B AB = µ 0 B A sin θ R 2 8.1 Biot-Svt 109 ds n = µ 0 ( cos θ A cos θ B ) n θ A 0 θ B π B = µ 0 2π n 8.2 8.3 n θ 2 O R O θ 1 8.3: n 8.3 n O B 1 = µ 0 R ( cos θ 1 cos θ 2 ) R θ 1 θ 2 R = cos π n, θ 1 = n 2 2n π, θ 2 = n +2 2n π cos n 2 n +2 π cos 2n 2n π = 2 sin π ( 2 sin π ) = 2 sin π n n B 1 = µ 0 2π tn π n n B = nb 1 = nµ 0 2π tn π n.
110 8 8.1.2 Biot-Svt ds Biot Svt Biot-Svt ds ds db db = µ 0 ds 3 (8.2) Biot-Svt Biot-Svt s lw T T =N A 1 m 1 =Wb m 2 (8.3) Wb B P ds Q 8.4: Biot-Svt 8.4 Biot-Svt (8.2) A B P ds Q db db = µ 0 ds 2 sin θ θ ds = PQ db ds ds θ
8.1 Biot-Svt 111 q v B = µ 0 q v 3 (8.4) Biot-Svt S = nqvs n q v ds ds = nqvs ds = ns ds qv ds S ds ns ds qv v ds Biot-Svt (8.2) ds qv ds db B (8.4) 8.3 8.5 O z Q ds z P (8.2) db = µ 0 ds 3 Q P db ds = QP z db z 0 z db z B = db z = µ 0 ds 2 + z 2 cos φ = µ 0 2( 2 + z 2 cos φ. )
112 8 P z P z φ B z z O ds Q O ds Q 8.5: φ db z cos φ = / 2 + z 2 B = µ 0 2 2( 2 + z 2 ) 3/2. n n 8.2 lim n tn π n n = π B = µ 0 2 z =0 8.4 Helmholtz 8.6 x x = /2 x = /2 µ B(x) = 0 2 2[ 2 +(/2+x) 2 ] 3/2 + µ 0 2 2[ 2 +(/2 x) 2 ] 3/2 x Tylo B(x) = k=0 1 k! d k B(x) dx k x k x=0
8.1 Biot-Svt 113 x 8.6: Helmholtz B(x) x 0 d 2 B(x) dx 2 =0 x=0 0 x x 4 B(x) = µ 0 ( 4 5 ) 3/2 + O(x 4 )
114 8 8.2 8.2.1 B = µ 0 p m 2π 3 cos θ e + µ 0 p m 3 sin θ e θ (8.5) p m = π 2 (8.5) 8.7 O xy P yz y z x y z P e θ R e θ x e x O φ dφ Q ds y 8.7: Q ds P db QP = R db = µ 0 ds R R 3 (8.6) ds R = OP e yz e θ x e x ds R ds = dφ ( sin θ cos φ e + cos θ cos φ e θ sin φ e x ) R = OQ=( sin θ sin φ) e cos θ sin φ e θ cos φ e x
8.2 115 e e x = e θ, e θ e = e x, e x e θ = e, e x e x = e e = e θ e θ =0 [ ] ds R = dφ cos θ e +(sin φ sin θ) e θ + cos θ cos φ e x (8.7) R 3 e e = e θ e θ = e x e x =1, e e θ = e θ e x = e x e =0 R 3 = [ ( sin θ sin φ) 2 +( cos θ sin φ) 2 +( cos φ) 2 ] 3/2 = [ 2 + 2 2 sin θ sin φ ] 3/2 (8.8) (8.7) (8.8) (8.6) ds P db db = µ 0 cos θ e +( sin φ sin θ) e θ + cos θ cos φ e x [ 2 + 2 2 sin θ sin φ ] 3/2 dφ dφ 0 2π sin φ P 1/R 3 / Tylo 1 R 3 = 1 [ 2 + 2 2 sin θ sin φ ] 3/2 = 1 3 db = µ 0 [( 3 cos θ + 32 (1+ sin θ cos θ sin φ ) e 3 sin θ sin φ + ). ( ) + sin φ sin θ +3sin θ sin 2 φ 32 sin2 θ sin φ ] ( ) + cos θ cos φ +3sin θ cos θ sin φ cos φ e x dφ e θ φ 0 2π cos φ sin φ sin φ cos φ = 1 2 sin 2φ 0 2π 0 cos φ dφ = 2π 0 cos φ dφ = 2π 0 sin φ cos φ dφ =0.
116 8 e e e θ e x 0 e θ sin 2 φ = 1 2 1 cos 2φ 2 0 e e e θ e x (8.5) (8.5) B = µ 0 p m cos θ 2π 3 e + µ 0 p m sin θ 3 e θ 1 p cos θ E = 2πε 0 3 e + 1 p sin θ ε 0 3 e θ p m p µ 0 1/ε 0 (8.5) Tylo / φ 2 0 3 ds p m = ds (8.5) C ds i 8.8: C 8.8 C S ds i C
8.2 117 ds i C ds i C C 8.2.2 S p m = S 8.9 q m L p m V q 8.9: V S L = m V = mv S = π 2, = qv 2π p m = S = qv 2π π2 = qv 2 p m = q 2m L (8.9) p m L (8.9)
118 8 8.2.3 H p m (7.12) L dl/dt = N dl dt = q 2m L H (8.10) L 8.10 H L 8.10: Plnck 1/2 J p m = gj. (8.11) g 8.9 g = q/(2m) H dj dt = g J H (8.12)