The Ideal Conductor Limit

TL;DR

This paper compares two statistical mechanics approaches for Coulomb systems near an ideal conductor, showing they agree on some quantities like forces but differ on others such as potential correlations.

Contribution

It demonstrates the equivalence of two methods in calculating certain properties of Coulomb systems near conductors, clarifying their differences and similarities.

Findings

Both methods yield the same electric forces on the system.

Quantities depending only on the system's degrees of freedom are identical in both methods.

Electric potential correlations and stress tensor differ between the approaches.

Abstract

This paper compares two methods of statistical mechanics used to study a classical Coulomb system S near an ideal conductor C. The first method consists in neglecting the thermal fluctuations in the conductor C and constrains the electric potential to be constant on it. In the second method the conductor C is considered as a conducting Coulomb system the charge correlation length of which goes to zero. It has been noticed in the past, in particular cases, that the two methods yield the same results for the particle densities and correlations in S. It is shown that this is true in general for the quantities which depend only on the degrees of freedom of S, but that some other quantities, especially the electric potential correlations and the stress tensor, are different in the two approaches. In spite of this the two methods give the same electric forces exerted on S.