In electrodynamics, the retarded potentials are the electromagnetic potentials for the electromagnetic field generated by time-varying electric current or charge distributions in the past. The fields propagate at the speed of light c, so the delay of the fields connecting cause and effect at earlier and later times is an important factor: the signal takes a finite time to propagate from a point in the charge or current distribution (the point of cause) to another point in space (where the effect is measured), see figure below.

The starting point is Maxwell's equations in the potential formulation using the Lorenz gauge:

where φ(r, t) is the electric potential and A(r, t) is the magnetic vector potential, for an arbitrary source of charge density ρ(r, t) and current density J(r, t), and ${\displaystyle \Box }$ is the D'Alembert operator. Solving these gives the retarded potentials below (all in SI units).

For time-dependent fields, the retarded potentials are:

where r is a point in space, t is time,

is the retarded time, and d³r' is the integration measure using r'.

From φ(r, t) and A(r, t), the fields E(r, t) and B(r, t) can be calculated using the definitions of the potentials:

and this leads to Jefimenko's equations. The corresponding advanced potentials have an identical form, except the advanced time