Magnetic moment and surface dipole distributions of circular holes in a conducting screen

This paper presents a method to account for the quasi-static magnetic interaction among circular holes in a conducting screen. Employing the oblate spheroidal system of coordinates, we derive expressions for the field arising when magnetic point charges and dipoles of arbitrary orientation are brought close to the hole in the plane of the screen. Using a set of two-dimensional (2-D) integrals for the Legendre polynomials, the "modes" for the potential are interpreted as being due to certain eigenfunctions expressing the density distribution of superficial magnetic dipoles in the plane of the hole. The dipole distributions are applied in discretised form to estimate the coupling of the surface polarizations of two similar circular holes.