Do the two-dimensional analogue of the problem in Example 1. A ``point charge'' in a plane means physically a uniform charge along an infinite line perpendicular to the plane; a ``circle'' at zero potential means an infinitely long circular cylinder perpendicular to the plane. However, since all cross sections of the parallel line and cylinder are the same, the problem is a two-dimensional one. Hint: The potential must satisfy Laplace's equation in charge-free regions. What are the solutions of the two-dimensional Laplace equation?