The electrical surface as centroid of the surface-induced charge

The electrical surface is the `surface where the electric field appears to startʹ; in simple models for flat charged surfaces it often coincides with the image plane. There is a theoretical result, first derived in 1973 by Lang and Kohn, that for a flat surface the electrical surface coincides with the centroid of the induced charge. The work reported here extends and consolidates this result, by offering proofs that this `Electrical Centroid Rule’ applies to all forms of charge distribution considered in the various models that exist for charged, atomically structured, flat metal surfaces. The proofs are set in the context of a revised discussion of some of the associated basic theoretical concepts. The paper also reports results from new array-model calculations of the location of the electrical surface, for the close-packed faces of a range of metals. In all cases the repulsion distance is roughly comparable in size with the atomic radius, as estimated by half the nearest-neighbour distance in the space lattice.