Walker, Halliday & Resnick — Electric Potential: Problem 29

29 Suppose \(N\) electrons can be placed in either of two configurations. In configuration 1, they are all placed on the circumference of a narrow ring of radius \(R\) and are uniformly distributed so that the distance between adjacent electrons is the same everywhere. In configuration 2, \(N - 1\) electrons are uniformly distributed on the ring and one electron is placed in the center of the ring. (a) What is the smallest value of \(N\) for which the second configuration is less energetic than the first? (b) For that value of \(N\), consider any one circumference electron—call it \(e_0\). How many other circumference electrons are closer to \(e_0\) than the central electron is?