Problem 3.61

A very long straight thread is oriented at right angles to an infinite conducting plane; its end is separated from the plane by a distance $l$. The thread carries a uniform charge of linear density $\lambda .$ Suppose the point $O$ is the trace of the thread on the plane. Find the surface density of the induced charge on the plane (a) at the point $O$; (b) as a function of a distance $r$ from the point $O$.