Problem 3.158

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 $\rho$. In the case of $a \ll l$ 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.