Page 315 - Engineering Electromagnetics, 8th Edition

CHAPTER 9 Time-Varying Fields and Maxwell’s Equations 297

Figure 9.4 See Problem 9.1.

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9.3 Given H = 300a z cos(3 × 10 t − y) A/m in free space, find the emf
developed in the general a φ direction about the closed path having corners
at (a) (0, 0, 0), (1, 0, 0), (1, 1, 0), and (0, 1, 0); (b) (0, 0, 0) (2π,0,0),
(2π,2π, 0), and (0, 2π, 0).
9.4 A rectangular loop of wire containing a high-resistance voltmeter has
corners initially at (a/2, b/2, 0), (−a/2, b/2, 0), (−a/2, −b/2, 0), and
(a/2, −b/2, 0). The loop begins to rotate about the x axis at constant
angular velocity ω, with the first-named corner moving in the a z direction at
t = 0. Assume a uniform magnetic flux density B = B 0 a z . Determine the
induced emf in the rotating loop and specify the direction of the current.
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9.5 The location of the sliding bar in Figure 9.5 is given by x = 5t + 2t ,
2
and the separation of the two rails is 20 cm. Let B = 0.8x a z T. Find the
voltmeter reading at (a) t = 0.4s;(b) x = 0.6m.
9.6 Let the wire loop of Problem 9.4 be stationary in its t = 0 position and find
the induced emf that results from a magnetic flux density given by
B(y, t) = B 0 cos(ωt − βy) a z , where ω and β are constants.

Figure 9.5 See Problem 9.5.