Dimensional Effects on Electric Potentials and Fields in High-permittivity Thin Films and Interfaces

Abstract

An efiective Lagrange density for electromagnetic flelds in the presence of a high- permittivity thin fllm or interface yields an analytic expression for electromagnetic potentials which interpolates between the two-dimensional logarithmic Coulomb potential at short distances and the three-dimensional Coulomb potential at large distances. It is shown that the analytic expression for the dimensionally hybrid electromagnetic potential is a very good approximation to the inflnite series solution from image charges.