Computational method in electrostatics based on Monte Carlo energy minimisation

Abstract

A variational method is presented which uses the Monte Carlo technique to simulate the evolution of a distribution of discrete charges within a conductor towards an equilibrium configuration that is characterised by a minimum of electrostatic energy. Using this approach, the calculation of the capacitance of conductors or complex geometry is presented as a simple problem, as the proposed technique avoids the complex pre-calculations needed in other well known classical methods. The technique is also used to calculate other parameters of interest, such as the conductor polarisabilities and the calculation of the potential and field distributions from a discrete configuration of charge. The proposed method can be used to help students to develop a physical Picture of how the charge distribution on a conductor surface is established. It represents a complement to the traditional numerical techniques in electrostatics for an approximate evaluation of fields and electrical parameters in problems that involve complex conducting shapes.