Low-Frequency Magnetic Shielding of a Perfectly Electric Conducting Circular Disk: Approximately Analytical Formulation Considering Radius of Emitting Loop

This letter proposes an approximate analytical formulation for the shielding problem of a perfectly electric conducting disk against the low-frequency magnetic field produced by a circular current loop placed coaxially with the disk. First, this problem is related to a complementarity problem: The leakage of the magnetic field through a circular hole on a perfectly magnetic conducting plane of infinite extension. Then, for the complementarity problem, we develop the accurate analytical solution if only the distribution of the normal component of the unshielded magnetic field along the surface of the hole can be expressed as a polynomial function of radial distance. The analytical formulation is verified with finite element simulations and measured results.