Charge distribution in two-dimensional electrostatics.

We examine the stability of ring-like configurations of N charges on a plane interacting through the potential V (z 1 ,. .. , z N) = |z i | 2 − i<j ln |z i − z j | 2. We interpret the equilibrium distributions in terms of a shell model and compare predictions of the model with the results of numerical simulations for systems with up to 100 particles. Determining the distributions of charged particles in a central potential is a classic problem which has been studied since the nature of the electric force was first understood [1]. In two dimensions the Coulomb potential varies logarithmically with distance and describes, for example, the interaction of