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A solution is presented for the boundary value problem posed by a current‐carrying coil of arbitrary shape in air above the plane surface of a conductor of semi‐infinite extent. Two special cases are also treated: a circularly‐symmetric coil at an arbitrary tilt angle with respect to the surface normal, and an infinitesimal coil, a magnetic dipole, also at an arbitrary tilt angle. Numerical results are presented for dipole orientations parallel and perpendicular to the surface.