Surface currents on a perfect conductor, induced by a magnetic dipole

An oscillating magnetic dipole located near a perfect conductor induces a current density on the surface of the metal. We have derived an expression for this current density, and studied its field line patterns for various orientations of the dipole moment. When the dipole moment is perpendicular to the surface, the field lines are circles which run clockwise and counterclockwise. For a linear dipole oriented parallel to the surface, the field line pattern is much more complex, and it contains singular points. When the dipole moment rotates in a plane parallel to the surface, the field lines are spirals. A field line spirals inward from infinity to some given point, after which it spirals outward back to infinity. We have also considered the Poynting vector of the electromagnetic field near the surface, and we found that its field lines can have singular points or exhibit a vortex.