The wires comprising the winding shown in cross-section by Fig. P8.6.6 carry current in the…

The wires comprising the winding shown in cross-section by Fig. P8.6.6 carry current in the fb6e13be 0bd8 4d7d bcd2 298ae7f3375e direction over the range eed02059 6ca9 4b54 a7dd 093a20107bd9 and return this current over the range f7674006 619b 46d4 9e36 8d40286573d5. These windings extend uniformly over the range 2e831d63 a21a 4327 afdd 80f8db032433. Thus, the current density in the region of interest is f314b2d2 8e6e 4cd9 9c6e e58308207c19 sind462418c 10bf 4088 b40b 58452b49b884z, where i is the current carried by each wire and 21b3025e 4037 488e a6b8 fb7d1d0659ea is the number of turns per unit area. This region is surrounded by perfectly conducting walls at 365c0afb 1e7c 4940 b267 99c3f226e809 and 46174119 eea7 4dcb 9258 d12a23f77975 and at 159f45eb c3ab 4933 90ff 964c255bfa2a and b576f79b bf71 4e03 8810 3512cdb297a5. The length b9d39b8e 99fe 4e38 a319 199915842beb in the 9807ef95 de7a 4878 93ab ed06fe9f6db9 direction is much greater than either a or b.

(a) Show that

9d93b5f0 6cbc 4899 b60a 7926dfd3343f

(b) Show that the inductance of the winding is

b331f6a8 4615 43c4 8856 1430ee6eed7f

(c) Sketch 3b3f3878 8a1b 428f 977c 5dabfcf76242.

Fig. P8.6.6

1e490931 3191 4b19 bfa9 14aaea0b9b17

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