Computational method in electrostatics based on Monte Carlo energy minimisation

A variational method is presented which uses the Monte Carlo technique to s imulate the evolution of a distribution of discrete charges within a conduc tor towards an equilibrium configuration that is characterised by a minimum of electrostatic energy. Using this approach, the calculation of the capac itance of conductors or complex geometry is presented as a simple problem, as the proposed technique avoids the complex pre-calculations needed in oth er well known classical methods. The technique is also used to calculate ot her parameters of interest, such as the conductor polarisabilities and the calculation of the potential and field distributions from a discrete config uration of charge. The proposed method can be used to help students to deve lop a physical Picture of how the charge distribution on a conductor surfac e is established. It represents a complement to the traditional numerical t echniques in electrostatics for an approximate evaluation of fields and ele ctrical parameters in problems that involve complex conducting shapes.