Toroidal Multipole Moments in Classical Electrodynamics

Stefan Nanz investigates the necessity for threemultipole families in classical electrodynamics. He shows that by imposingsymmetry and parity constraints, it is sufficient to deal with only twomultipole families. This implies that the toroidal multipole moments do notrepresent an independent multipole family, and they only emerge in the long-wavelength limit.