An extension of the magnetostatic image theory for a permeable sphere

Abstract

A curious property of a magnetically permeable sphere in the field of a static circular current loop whose axis goes through the centre of the sphere is pointed out: the field outside the permeable sphere is independent of its permeability by a combination of the original current loop exterior and an embedded current loop interior to the sphere. The current inclusion coincides with the image of the original current loop in the ideal diamagnetic (superconducting) sphere. This result is derived following a formal analogy between electrostatics and magnetostatics, and it is checked by finding the corresponding magnetic scalar potential. A detailed analysis of the sources of the magnetic field is presented, leading to interesting insights. © 2006 IOP Publishing Ltd.