A rare case in which the electrostatic field E for a circuit can actually be calculated is the following Imagine an infinitely long cylindrical sheet, of uniform resistivity and radius a. A slot (corresponding to the battery is maintained at + V0/2, at Ф = + π, and a steady current flows over the surf:ace, as indicated in Fig. 7.51. According to Ohm's law, then,

(a) Use separation of variables in cylindrical coordinates to determine V(s, Ф) inside and outside the cylinder.

(b) Find the surface charge density on the cylinder.

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V(a.p) = Vod 2π (π < < +).