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We show how to obtain the first multipole contributions to theelectromagnetic radiation emited by an arbitrary localized source directly fromthe Jefimenko equation for the magnetic field and the Panofsky-Phillipsequation for the electric field. This procedure avoids the unnecessarycalculation of the electromagnetic potentials.

Multipole radiation fields from the Jefimenko equation for the magnetic field and the Panofsky-Phillips equation for the electric field