A rare case in which the electrostatic field E for a circuit can actually be calculated...

A rare case in which the electrostatic field E for a circuit can actually be calculated is the following:²⁸ Imagine an infinitely long cylindrical sheet, of uniform resistivity and radius a. A slot (corresponding to the battery) is maintained at and a steady current flows over the surface, as indicated in Fig. 7.51. According to Ohm’s law, then,

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

b) Find the surface charge density on the cylinder.