Impact of Circular Apertures on Static Shielding Performances of Spherical Magnetic Shields

The magnetic field inside a spherical magnetic shield with infinite permeability and a circular aperture in a homogeneous magnetic field of arbitrary direction is analytically derived. The closed-form formulas for the static shielding factors are theoretical upper limits for real shields. We discuss the magnetic field gradient inside the shield caused by a single aperture, implying that using symmetric aperture pairs is more favorable. Based on the theoretical results for ideal shields, an approximate solution to calculate the shielding factor for shields with finite permeability and/or multiple apertures is developed. The calculations for one aperture pair are compared to finite-element analysis. The basic effects could be guidance for the design of apertures in shields of various shapes.