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 
and 
and is surrounded by material having 
and 
. The electric field 
is applied at 
(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 (
in 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
