The circular cylinder of Fig. P7.9.4a has and and is surrounded by material having and . The…

The circular cylinder of Fig. P7.9.4a has 3c297b06 f93e 4b35 a2a0 67287cf1723b and 83d8d80a f446 402e 979a 4f7d25a86ed5 and is surrounded by material having ef042d2d 1a5c 40c3 b2a3 d36ae1be5bfb and 1cf7f429 2a34 4653 981a 661f94d153e9. The electric field c0766ea9 b1cf 4f28 9596 f796c4cfba46 is applied at d7c0d8d2 1c68 4970 9a27 1ab27c392501

(a) Find the potential in and around the cylinder and the surface charge density that result from applying a step in field to a system that initially is free of charge.

(b) Find these quantities for the sinusoidal steady state response.

(c) Argue that these fields are equally applicable to the description of the configuration shown in Fig. P7.9.4b with the cylinder replaced by a half-cylinder on a perfectly conducting ground plane. In the limit where the exterior region is free space while the half-cylinder is so conducting that its charge relaxation time is short compared to times characterizing the applied field (4d346b62 cdbd 436e a8b1 f3ca532dee67in the sinusoidal steady state case), what are the approximate fields in the exterior and in the interior regions? (See Prob. 7.9.5 for a direct calculation of these approximate fields.)

Fig. P7.9.4a

b98d0fe0 ec61 46c5 83ec 52b2721a8a3d

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