Problem 3.60

A thin infinitely long thread carrying a charge $\lambda$ per unit length is oriented parallel to the infinite conducting plane. The distance between the thread and the plane is equal to $l$. Find: (a) the modulus of the vector of the force acting on a unit length of the thread; (b) the distribution of surface charge density $\sigma(x)$ over the plane, where $x$ is the distance from the plane perpendicular to the conducting surface and passing through the thread.