  Radiation from magnetic and electric dipole moments is a key subject in
theory of electrodynamics. Although people treat the problem thoroughly in the
context of frequency domain, the problem is still not well understood in the
context of time domain, especially if dipole moments arbitrarily vary in time
under action of external forces. Here, we scrutinize the instantaneous power
radiated by magnetic and electric dipole moments, and report findings that are
different from the conventional understanding of their instantaneous radiation
found in textbooks. In contrast to the traditional far-field approach based on
the Poynting vector, our analysis employs a near-field method based on the
induced electromotive force, leading to corrective terms that are found to be
consistent with time-domain numerical simulations, unlike previously reported
expressions. Beyond its theoretical value, this work may also have significant
impact in the field of time-varying metamaterials, especially in the study of
radiation from subwavelength meta-atoms, scatterers and emitters that are
temporally modulated.
