Electric polarizability and magnetic susceptibility of small holes in a thin screen

It is found that the fields inside a cavity with a hole can be written in terms of a coupling integral involving the tangential electric field in the plane of the hole. For a hole whose dimensions are small compared to the wavelength, this coupling integral is separated into an electric term, proportional to the (scalar) polarizability of the hole, and a magnetic term, proportional to the (vector) susceptibility of the hole. Integral equations are developed for the determination of these static geometrical parameters. These equations can be solved exactly for circular and elliptical shapes but only approximately for other shapes. The derivation of what appears to be a relation between the electric polarizability and the (diagonalized) magnetic susceptibility for a hole of general shape is given