Toroidal Multipole Moments in Classical Electrodynamics: An Analysis of Their Emergence and Physical Significance

Stefan Nanz investigates the necessity for three multipole families in classical electrodynamics. He shows that by imposing symmetry and parity constraints, it is sufficient to deal with only two multipole families. This implies that the toroidal multipole moments do not represent an independent multipole family, and they only emerge in the long-wavelength limit.