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.