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