Quasi-Static Electric- And Magnetic-Field Penetration of a Spherical Shield through a Circular Aperture

Low-frequency electromagnetic penetration of a closed shielded region through an aperture in the shield is considered by investigating the canonical problems in which the shield is a perfectly conducting spherical shell, the aperture is circular, and the applied field is uniform. Each of these problems reduces to that of solving a set of dual series equations. The solutions of previously solved problems are presented as well as those of heretofore unsolved problems. The penetration of the shielded region is measured by the ratio of the field at the center of the shell to the external applied uniform field. It has been previously shown that these ratios are the same for an applied magnetic field parallel to the symmetry axis and an applied electric field perpendicular to this axis. In this paper it is shown that the ratios are the same for an applied electric field parallel to the axis when the shell is uncharged and for an applied magnetic field perpendicular to the axis. In addition, a new approach to the solution of a certain class of dual series equations is found and exploited in the solution of one of the canonical problems.