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This paper presents an analysis concerning an inductive system comprised of four sensing coils wound around a nonmagnetic toroidal core that is traversed by a current-carrying primary wire. The primary wire is a rectilinear conductor arbitrarily positioned, off-centered, and tilted. A magnetic vector potential-based approach is developed, aimed at the determination of closed-form expressions for the induced voltages appearing at the open terminals of the four sensing coils, all of them depending on the 3-D position of the primary wire. The inverse problem, that is, the determination of the primary wire position based on the coils-induced voltages, is also formulated, but only exactly solved for the case of an off-centered wire parallel to the core axis.