Low-frequency induction in a homogeneous sphere by line sources 1. Formulation and line current excitation

The problem of low-frequency induction in a sphere by an external line sour ce is amenable to analytic solution by Stevenson's method. This first of tw o parts develops the complete electromagnetic field solution through first order in frequency, for (magnetic) excitation by zeroth- and first-order li ne current sources. The solutions can all be expressed in terms of elementa ry functions. The result serves as a useful test solution for low-frequency electromagnetic modeling codes involving nonuniform sources, and in partic ular for applications involving power lines. The solution is also applicabl e to a small sphere in the extreme near field of a linear antenna element.