Puzzle 2

Here’s the second puzzle I found in the August AJP, specifically in this article. (I describe the first puzzle in another post.) I’d never seen this one before, and I found the answer to be very counterintuitive.

Suppose you have a point charge located somewhere near a perfect conductor with zero net charge. We’re doing good old electrostatics here — nothing’s moving. Intro physics students learn what generically happens in this situation: the presence of the point charge induces negative charge on the near side of the conductor and positive charge on the far side (assuming the point charge is positive). Because the negative charge is closer, you get a net attraction:

Here’s the puzzle: is there any arrangement (i.e., any choice of shape for the conductor and location for the point charge) that leads to a repulsive force between the two?

Figure (b) above shows one way to define “repulsive” more precisely, although pretty much any way will do. Suppose that there is some plane (dashed line in the figure) with the point charge on one side and the whole conductor on the other side. Is there any situation in which the force on the point charge points away from the plane?)