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Unformatted text preview: 9. (a) In the region of the smaller loop the magnetic ﬁeld produced by the larger loop may be taken to be uniform and equal to its value at the center of the smaller loop, on the axis. Eq. 30-29, with z = x (taken to be much greater than R), gives B= µ0 iR2 ˆ i 2x3 where the +x direction is upward in Fig. 31-36. The magnetic ﬂux through the smaller loop is, to a good approximation, the product of this ﬁeld and the area (πr2 ) of the smaller loop: ΦB = (b) The emf is given by Faraday’s law: E =− dΦB =− dt π µ0 ir2 R2 2 d dt 1 x3 =− π µ0 ir2 R2 2 − 3 dx x4 dt = 3πµ0 ir2 R2 v . 2x4 πµ0 ir2 R2 . 2x3 (c) As the smaller loop moves upward, the ﬂux through it decreases, and we have situation like that shown in Fig. 31-5(b). The induced current will be directed so as to produce a magnetic ﬁeld that is upward through the smaller loop, in the same direction as the ﬁeld of the larger loop. It will be counterclockwise as viewed from above, in the same direction as the current in the larger loop. ...
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- Fall '08