What is the minimum-energy configuration for a system of N equal point charges placed on or inside a circle of radius R? Because the charge on a conductor goes to the surface, you might think the N charges would arrange themselves (uniformly) around the circumference. Show (to the contrary) that for N = 12 it is better to place 11 on the circumference and one at the center. How about for N = 11 (is the energy lower if you put all 11 around the circumference, or if you put 10 on the circumference and one at the center)?