The spherical cavity problem

For a time-harmonic electromagnetic field incident on a thin, perfectly conducting spherical shell with a circular aperture, methods for the exact determination of the interior fields are discussed. The advantages of the direct E-field integral equation are pointed out. The unknowns are then the tangential components of the currents induced in the shell, and two alternative versions of the resulting coupled integral equations are developed. The one found most convenient is particularized to the case of a plane wave incident symmetrically upon the aperture.