In a region between the planes and , a material that moves in the direction with velocity has the…

In a region between the planes32991e18 66f5 4873 9c63 8cac9abcf834and d7769d2d 99ab 4988 8a22 231c2ff94b95, a material that moves in the d2f3ed9f 6cd2 414f 9ab9 ab98f0401d3d direction with velocity 30d43f25 814b 4a2e 89e4 1f72ab50dd24 has the magnetization density bf09fad3 2a47 427e 9453 a2af44eb6f89 cos 16ea9206 851f 4c60 b88b 1d93fbd35391 as shown in Fig. P9.2.2. The regions above and below are constrained so that dfc283ae 8ca4 4447 ae1c c1150545d1a9 = 0 there and so that the integral of 56f6c1a8 5564 41e7 9950 304c2b8de6a8· ds between d7769d2d 99ab 4988 8a22 231c2ff94b95 and 013a2292 6549 4c34 868a a9d843f287d6 is zero. (In Sec. 9.7, it will be clear that these materials could be the pole faces of a highly permeable magnetic circuit.)

(a) Show that Amp`ere’s law and (9.2.2) are satisfied if b327ccc1 f280 438f 881a 673d1890bdf4 throughout the magnetizable layer of material.

(b) A one-turn rectangular coil is located in the 590eca51 086a 4b59 b217 b04414d29ca20 plane, one leg running in the 7de73629 a44f 4154 8635 0cae78cf9afb direction at ce44156c 630f 4e9d 9c5d 3a7b1c20d9fd (from de69c4be 9ccb 46f0 9981 69615a70fba8 to 3c3f1cad b646 490f 917c 6128e60af2be) and another running in the 79e55b98 8941 4bef b7fb 2a69241896ae direction at b1d58dd3 ff27 4eec a051 b9fe34b8df19 (from 0aefcb75 b005 4295 9046 cfed7b405d86tob711c995 3406 466f 8ab6 f9aa221ec407). What is the voltage induced at the terminals of this coil by the motion of the layer?

Fig. P9.2.2

90afe535 a324 456c be5a e820745fd391

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