Fields and radiation of toroidal dipole moments moving uniformly in a medium

Fields and Vavilov-Cerenkov radiation are examined for a toriodal dipole moment moving at constant velocity in a medium with permittivity epsilon and permeability mu; a dipole moment of this sort can be possessed by a current toroid, i.e., a toroidal solenoid with a coil that provides for the absence of current components 'along' the torus. In vacuum the fields outside the toroidal dipole are zero. But fields do appear outside the dipole in a medium; they are proportional to (epsilon)(mu) - 1, and arise as a result of the fact that, according to the macroscopic electrodynamics of a homogeneous medium, the medium should be considered as permeating the dipole itself. Toroidal dipoles, including point dipoles, that are not filled with the medium do not emit during uniform motion. The problems considered are of methodological interest and their study should facilitate an understanding of radiation from magnetic dipole moments.