Magnetostatic potential penetration into two circular apertures in a thick conducting plane

A boundary value problem of magnetostatic potential penetration into two circular apertures in a thick conducting plane is solved. The Hankel transform and mode-matching is used to represent the scattered potentials in rapidly-convergent series. The magnetic polarizability is rigorously derived and presented in numerically efficient forms. Numerical computations are performed to illustrate the field penetration and coupling behaviors in terms of aperture geometry.