New models for current distributions and scalar potential formulations of magnetic field problems

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Abstract
Given volume distributions of stationary or quasistationary electric current are replaced by equivalent distributions of fictitious magnetization and, eventually, of surface current, on the basis of the Ampèrian model for magnetized media. The fictitious magnetization is subsequently replaced by the equivalent distribution of fictitious magnetic charge. Consequently, the magnetic field due to given volume currents is determined from that produced by the corresponding charges and surface currents. This modeling method is also presented for generalized distributions of current. A scalar potential is introduced to describe the field in the models constructed. This scalar potential is a single-valued function of position when the current distribution is modeled by using a fictitious magnetization and only an equivalent charge distribution within the region considered. The modeling procedure is flexible and the models proposed yield an easier physical interpretation and a substantially reduced amount of computation with respect to vector or combined vector and scalar potential methods used so far. A few illustrative examples are given. This paper relates to stationary or quasistationary magnetic fields, but the modeling technique and the scalar potential presented are applicable to problems relative to any physical fields governed by the same equations.