The filamentary current loop of magnetostatics is naturally associated with toroidal topology rather than the usual cylindrical or spherical topology. The field near the wire is best explored in toroidal coordinates, but even the far magnetic dipole field may be found this way. The loop field becomes infinite near the wire just as does the endless straight wire field, but another, not well‐known logarithmic infinity occurs that is proportional to the curvature. We demonstrate these facts and, in addition, mention a certain duality with the electric field of a ring of charge.

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