Problem 3.59

A point charge \(q\) is located at a distance \(l\) from an infinite conducting plane. Determine the surface density of charges induced on the plane as a function of separation \(r\) from the base of the perpendicular drawn to the plane from the charge.

\sigma=-\frac{q l}{2 \pi\left(l^{2}+r^{2}\right)^{3 / 2}}, \quad q_{i n d}=-q

Conductors and Dielectrics in an Electric Field