Field and Wave Electromagnetics 2nd Edition by David Cheng

Exercise 38

A uniform current density J = a x J 0 flows in a very large rectangular block of homogeneous material of a uniform thickness having a conductivity . A hole of radius b is drilled in the material. Find the new current density J ' in the conducting material. ( H int: Solve Laplace's equation in cylindrical coordinates and note that V approaches - ( J 0 r / )cos as r , where is the angle measured from the x -axis.)