Multipole radiation fields from the Jefimenko equation for the magnetic   field and the Panofsky-Phillips equation for the electric field
  We show how to obtain the first multipole contributions to the electromagnetic radiation emited by an arbitrary localized source directly from the Jefimenko equation for the magnetic field and the Panofsky-Phillips equation for the electric field. This procedure avoids the unnecessary calculation of the electromagnetic potentials. 
R. de Melo e Souza, M.V. Cougo-Pinto, C. Farina and M. Moriconi