Multipole radiation expands radiation from localized time-dependent sources into electric and magnetic multipoles. Electric dipole radiation is the leading electric term, while magnetic dipole radiation and higher electric multipoles contribute when the leading term vanishes or higher precision is needed.
For a localized source whose size is small compared with its radiation wavelength, the radiation fields of its electric dipole moment areTheir total instantaneous power is
For a source of characteristic size and angular frequency , the electric-dipole approximation requiresso the source is much smaller than its radiation wavelength. Observing the pure radiation field additionally requires the radiation zone, and .
If is the angle between the observation direction and , thenIntegrating over solid angle uses and gives the total electric dipole radiation power.
A charge undergoing simple harmonic motion of angular frequency and slowly varying amplitude radiates the averaged powerIts mechanical energy therefore has exponential decay rate and half-life
This is the magnetic-dipole term of the multipole radiation expansion.
If a rigid body's inclined magnetic dipole rotates at angular speed , its radiated power is . Conservation of rotational energy then gives
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Multipole radiation refers to the electromagnetic radiation emitted by a system that can be described by the multipole expansion of its electric or magnetic fields. In classical electrodynamics, charge distributions and currents can be represented by a series of terms that describe their contributions to the electromagnetic field, grouped by their symmetry and decay behavior with distance from the source.