P30_059 - r > a , so this along with the result...

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59. (a) For the circular path L of radius r concentric with the conductor I L ~ B · d~s =2 πrB = µ 0 i enc = µ 0 i π ( r 2 b 2 ) π ( a 2 b 2 ) . Thus, B = µ 0 i 2 π ( a 2 b 2 ) µ r 2 b 2 r . (b) At r = a, the magnetic ±eld strength is µ 0 i 2 π ( a 2 b 2 ) µ a 2 b 2 a = µ 0 i 2 πa . At r = b, B r 2 b 2 = 0. Finally, for b =0 B = µ 0 i 2 πa 2 r 2 r = µ 0 ir 2 πa 2 which agrees with Eq. 30-22. (c) The ±eld is zero for r<b and is equal to Eq. 30-19 for
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Unformatted text preview: r &gt; a , so this along with the result of part (a) provides a determination of B over the full range of values. The graph (with SI units understood) is shown below. 0.0002 0.0004 0.0006 0.0008 0.001 B 0.01 0.02 0.03 0.04 0.05 0.06 r...
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