A metal ball of radius a is located at a distance l from an infinite ideally conducting plane. The space around the ball is filled with a homogeneous poorly conducting medium with resistivity p. In the case of a << l find:
(a) The current density at the conducting plane as a function of distance r from the ball if the potential difference between the ball and the plane is equal to V;
(b) The electric resistance of the medium between the ball and the plane.