Comparison of magnetic fields computed by finite element and classical series methods

The reduced scalar potential technique is applied, in conjunction with the field analogy technique of NASTRAN (the NASA Structural Analysis program), to two problems for which classical series solutions have also been obtained. The first problem involves a thick spherical ferromagnetic shell with an inner radius of 10 m and an outer radius of 12 m surrounded by an infinitely thin current band of 16-m radius, 20 arc-degrees wide. The second problem is similar, except that the thin spherical shell has an inner radius of 10 m and an outer radius of 10.1 m, and the current band is of 12.1-m radius. In both cases, the area surrounding the shell has the permeability of vacuum, and the current band carries a current of 1 amp per meter of cross-sectional length. A comparison of the magnetic fields, both in air and within the ferromagnetic shell, shows generally good agreement between the two methods.