Charge distribution in two-dimensional electrostatics

TL;DR

This paper investigates the stability and equilibrium charge distributions of ringlike configurations in a 2D electrostatic system, combining a shell model with numerical simulations to analyze systems of up to 100 particles.

Contribution

It introduces a shell model to interpret equilibrium distributions and validates it through numerical simulations for systems with up to 100 particles.

Findings

Shell model effectively predicts charge distributions.

Numerical simulations confirm model accuracy.

Stable ringlike configurations identified.

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.