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 emitted 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. [DOI: 10.1119/1.2990666]