Electric polarizability for two circular apertures in parallel conducting planes

A problem of electrostatic potential penetration into two circular apertures in parallel conducting planes is solved. The Hankel-transform and superposition principle is utilized to represent the scattered potentials in discrete and continuous modes. The boundary conditions are enforced to obtain a set of simultaneous equations for the discrete modal coefficients. The electric polarizability is derived in terms of the discrete modal coefficients. The numerical computation is performed to illustrate the behavior of the polarizability for various aperture geometries.