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Unformatted text preview: 61. (a) We ﬁnd the ﬁeld by superposing the results of two semiinﬁnite wires (Eq. 309) and a semicircular
arc (Eq. 3011 with φ = π rad). The direction of B is out of the page, as can be checked by referring
to Fig. 306(c). The magnitude of B at point a is therefore
Ba = 2 µ0 i
4πR + µ0 iπ
µ0 i
=
4πR
2R 1
1
+
π2 . With i = 10 A and R = 0.0050 m, we obtain Ba = 1.0 × 10−3 T. The direction of this ﬁeld is out
of the page, as Fig. 306(c) makes clear.
(b) The last remark in the problem statement implies that treating b as a point midway between two
inﬁnite wires is a good approximation. Thus, using Eq. 306,
Bb = 2
This ﬁeld, too, points out of the page. µ0 i
2πR = 8.0 × 10−4 T . ...
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 Fall '08
 SPRUNGER
 Physics

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