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# HW12 - Physics 3122 Fall 2010 Homework Set 12 Solutions...

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Physics 3122, Fall 2010: Homework Set 12 Solutions. 5.13 B d = μ 0 I enc B = B ( s ) ˆ ϕ (a) s < a I enc = 0 B = 0 s > a I enc = I B 2 π s = μ 0 I B = μ 0 I ˆ ϕ /2 π s (b) J = ks I = Jda = ks 2 π sds 0 a = 2 π ka 3 /3 k = 3 I /2 π a 3 s < a I enc = k ʹஒ s 2 π ʹஒ s d ʹஒ s 0 s = 2 π ks 3 /3 = Is 3 / a 3 B 2 π s = μ 0 Is 3 / a 3 B = μ 0 Is 2 ˆ ϕ /2 π a 3 s > a same as (a) 5.22 (a) A ( r ) = μ 0 4 π Id r = s ˆ s + z ˆ z ʹஒ r = ʹஒ z ˆ z d = d ʹஒ z ˆ z = [ s 2 + ( z ʹஒ z ) 2 ] 1/ 2 A ( r ) = μ 0 I ˆ z 4 π d ʹஒ z [ s 2 + ( z ʹஒ z ) 2 ] 1/ 2 z 1 z 2 = μ 0 I ˆ z 4 π ln ( z ʹஒ z ) + s 2 + ( z ʹஒ z ) 2 { } Ρਟ Σਿ ΢ਯ Τ੏ Φ੯ Υ੟ z 1 z 2 A ( r ) = μ 0 I ˆ z 4 π ln ( z z 1 ) + s 2 + ( z z 1 ) 2 ( z z 2 ) + s 2 + ( z z 2 ) 2 Ρਟ Σਿ ΢ਯ ΢ਯ Τ੏ Φ੯ Υ੟ Υ੟ 5.25 B = B ( s ) ˆ ϕ In B 2 π s = μ 0 ( I / π R 2 )( π s 2 ) B = μ 0 Is /2 π R 2 Out B 2 π s = μ 0 I B = μ 0 I /2 π s A = A ( s z A = A ( s )/ z = 0 B = × A = [ A ( s )/ s ϕ In A ( s )/ s = μ 0 Is /2 π R 2 A ( s ) = μ 0 Is 2 /4
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