Charge distribution in two-dimensional electrostatics

Abstract

We examine the stability of ringlike configurations of N charges on a plane interacting through the potential $V(z_1,...,z_N)={\sum }_i|z_i{|}^2-{\sum }_{i<j}ln|z_i-z_j{|}^2$. 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.

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