Frequency dependence of the polarizability and susceptibility of a circular hole in a thick conducting wall

We calculate a generalized polarizability and susceptibility of a circular hole in a thick metallic plate as a function of hole dimensions and wavelength. In particular, we construct a variational form which allows us to obtain accurate numerical results with a minimum of computational effort. Numerical results are obtained for a variety of hole dimensions relative to the wave length. In addition, analytic results are obtained and shown to be accurate to second order in the ratio of the hole dimension to the wavelength for a vanishingly thin wall