Accelerating charges can generate electromagnetic fields that carry energy away to large distances. For a localized source much smaller than the emitted wavelength, the leading time-dependent contribution is often electric-dipole radiation.

Let the source have dipole moment $$\mathbf p(t)=\int \mathbf r'\rho(\mathbf r',t),d^3r'.$$ Far from the source, at distance $r$ much larger than its size, the radiation fields depend on the dipole acceleration evaluated at retarded time. Their magnitudes scale as $$E_{\rm rad}\propto\frac{|\ddot{\mathbf p}(t-r/c)|\sin\theta}{cr},$$ $$B_{\rm rad}=\frac{E_{\rm rad}}{c},$$ where $\theta$ is the angle from the dipole axis.

The $1/r$ falloff distinguishes radiation fields from near electrostatic dipole fields, which decay more rapidly. Because energy flux is proportional to $E^2$, radiation intensity falls as $1/r^2$, so the total power through a sphere remains finite.

The angular dependence is $$\frac{dP}{d\Omega}\propto\sin^2\theta.$$ Radiation is strongest perpendicular to the dipole axis and vanishes along it.

For a harmonically oscillating dipole $\mathbf p(t)=\mathbf p_0\cos\omega t$, the average radiated power scales as $$\langle P\rangle\propto p_0^2\omega^4.$$ High-frequency acceleration can therefore radiate much more strongly than slow motion of the same amplitude.

Dipole radiation underlies elementary antennas and provides the classical counterpart of many atomic electric-dipole transitions. The key mechanism is time-varying source structure producing far fields that transport energy irreversibly away from the source.