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# HW11 - Physics 3122 Fall 2010 Homework Set 11 Solutions 5.1...

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Physics 3122, Fall 2010: Homework Set 11 Solutions. 5.1 ( R s ) 2 + a 2 = R 2 R 2 2 Rs + s 2 + a 2 = R 2 R = ( s 2 + a 2 )/2 s F = qvB = mv 2 / R mv = qBR = qB ( s 2 + a 2 )/2 s 5.4 B = ( kz )/ x = 0 OK Bottom F 1 = I ˆ ydy × k ( a /2) ˆ x a / 2 a / 2 = 1 2 Ika 2 ˆ z Right F 2 = I ˆ z dz × kz ˆ x a / 2 a / 2 = 1 4 Ika 2 ˆ y Top F 3 = I ( ˆ y ) dy × k ( a /2) ˆ x a / 2 a / 2 = 1 2 Ika 2 ˆ z Left F 4 = I ( ˆ z ) dz × kz ˆ x a / 2 a / 2 = 1 4 Ika 2 ˆ y F = F 1 + F 2 + F 3 + F 4 = Ika 2 ˆ z 5.8( a ) B = μ 0 I ˆ z 4 π y ( x a ) ( x a ) 2 + y 2 ( x b ) ( x b ) 2 + y 2 Ρਟ Σਿ ΢ਯ ΢ਯ Τ੏ Φ੯ Υ੟ Υ੟ x = 0 a = R b = R y = R B 1 = μ 0 I ˆ z 4 π R R R 2 + R 2 ( R ) R 2 + R 2 Ρਟ Σਿ ΢ਯ Τ੏ Φ੯ Υ੟ = 2 μ 0 I ˆ z 4 π R B = 4 B 1 = 2 μ 0 I ˆ z π R or B = μ 0 I (sin θ 2 sin θ 1 ) ˆ n /4 π s s = R θ 1 = π /4 θ 2 = π /4 B 1 = μ 0 I 1/ 2 ( 1/ 2 ) [ ] ˆ n /4 π R = 2 μ 0 I ˆ n /4 π R B = 4 B 1 = 2 μ 0 I ˆ n / π R 5.11 d B = μ 0 dIa 2 /2[ a 2 + ( z ʹஒ z ) 2 ] 3/ 2 dI = nId ʹஒ z α
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