Cartesian coordinates A rectangular metal tube (its height extends from z = 0 to infinity) is placed on the XY plane. See Fig. 1. The side faces of the tube are kept at zero potential, V = 0, and the face of the base, supported on the XY plane, is maintained at a potential Vo (x.y). 

a) Calculate the potential inside the tube.
b)Assume that the base plate, the one that rests on the XY plane, is conductive and maintained at a constant potential, that is, Vo (x,y) = V. Calculate the potential inside the tube and determine the density of load o (x, y) on this plate, at z = 0. It might be useful know that: σ = - εo ∂V / ∂n

 

V.0