Chapter 26 Sources of Magnetic Field The number of turns per unit length of the solenoid(单位长匝数)n. As vertical cross section (纵剖面)sh0wn,(,n,R,L,B1B2) ∞ OOOOOOOOCOOXO. ①A中
Chapter 26 Sources of Magnetic Field The number of turns per unit length of the solenoid(单位长匝数) n. As vertical cross section (纵剖面) shown, (I, n, R, L, 1,2 ) + + + + + + + + + + + + p R + + * o x dx x
Chapter 26 Sources of Magnetic Field 解由圆形电流磁场公式B=_3 (x2+R 2 2\3/2 Qo。 OOOXXOOOO 2 dB=lo R2Indx x= RcotB 2 3/2 R<+x 2 dx=-Rcsc B Bf YoI cx r dx 2 2 R+x R+x'=R cSC B
Chapter 26 Sources of Magnetic Field 2 2 3/ 2 2 0 （2 x R ） IR B + = 解 由圆形电流磁场公式 o p x1 x x2 + + + + + + + + + + + + + + + ( ) 3/ 2 2 2 2 0 d 2 d R x R In x B + = x = Rcot 2 2 2 2 R + x = R csc ( ) + = = 2 1 3/ 2 2 2 2 0 d 2 d x x R x nI R x B B d csc d 2 x = −R 2 1
Chapter 26 Sources of Magnetic Field B uonl rB2 rcsc dB sin Bd B 2 JB, R csc'BdB 2 JBI B (cos B,-cos B,) 2 Fora“ infinitely long” solenoid, The b at the axial line B1=丌,/2=0 B=10n
Chapter 26 Sources of Magnetic Field = − 2 1 sin d 2 0 nI = − 2 1 csc d csc d 2 3 3 3 2 0 R nI R B ( ) 2 1 0 cos cos 2 = − nI B For a “infinitely long” solenoid, The at the axial line: B 1 = , 2 = 0 B nI = 0
Chapter 26 Sources of Magnetic Field Summary of the application of Biot-Savart Law A Long Straight Wire B=/0(cos 0, -cos0,) B 4πr A Circular Arc of wire R B 2(x2+R2)2 2R A Stretched-out solenoid B (cosB,, )B=Lonl 2COS
Chapter 26 Sources of Magnetic Field Summary of the Application of Biot-Savart Law: A Long Straight Wire （ 1 2 ） 0 0 cos cos 4 π = − r I B 0 0 2π r I B = A Circular Arc of Wire 2 3 2 2 2 0 （2 x R ） IR B + = A Stretched-out Solenoid ( ) 2 1 0 cos cos 2 = − nI B B nI = 0 R I B 2 0 =
Chapter 26 Sources of Magnetic Field 26-4&26-5. Ampere's Loop Law p607-613 “安培分子环流假说”: The source of magnetism of all natural-matter come from current(一切磁性的根源是电流) 1. Ampere’ s Loop Law安培环路定理(P607-611): Any line integral of B around a closed path was proportional to the current encircled by the path. 即在真空的稳恒磁场中,磁感应强度B沿任 闭合路径的积分的值,等于/乘以该闭合路径 所包围的各电流的代数和
Chapter 26 Sources of Magnetic Field 26-4&26-5. Ampere’s Loop Law p607-613 “ 安 培 分 子 环 流 假 说 ” : The source of magnetism of all natural-matter come from current（一切磁性的根源是电流）. 1. Ampere’s Loop Law 安培环路定理 (P607-611): Any line integral of around a closed path was proportional to the current encircled by the path. B 即在真空的稳恒磁场中，磁感应强度 沿任 一闭合路径的积分的值，等于 乘以该闭合路径 所包围的各电流的代数和. B 0