New model for the computation of quasi-stationary fields due to arbitrary distributions of magnetic dipoles

The quasi-stationary field of a magnetic dipole in free space is modeled by using the field due to a succession of dipoles oriented along any line between the poles of the original. Dipole, the two fields being identical everywhere except for the points on that line. By choosing appropriately the path of the equivalent string of dipoles, the resultant field due to the original dipole can be obtained from the superposition of fields with a simpler structure. In this paper, the proposed modeling method is illustrated for the quasi-stationary ac field of an arbitrarily located and oriented dipole in the presence of a conducting spherical shell, with the analytic expression of the field quantities derived in terms of single series, which are much more convergent than the double series in the expressions available in the literature. The model presented can be applied efficiently for analyzing eddy-current problems and electromagnetic shielding by various spherical, cylindrical, and planar structures in the presence of arbitrary distributions of electric current.