Static Magnetic Shielding of a Perfectly Electric Conducting Circular Disk: Exact Analytical Solution Considering Radius of Emitting Loop

Abstract

This letter proposes an accurate analytical formulation for the shielding problem of a perfectly electric conducting disk against the static magnetic field of a circular current loop placed coaxially with the disk. The key is to convert this problem into an electric field problem: the circular disk is grounded and is excited by nonuniform line charges distributed on the loop. The latter can be solved through the known Green function. Then, we obtain the accurate solution in integral form for magnetic vector potential at any field point and the accurate analytical solution for the magnetic field on the central axis of the disk. Also, the solution for the magnetic field is extended to the whole space when the loop radius is approaching zero.