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retarded potential
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.〔McGraw Hill Encyclopaedia of Physics (2nd Edition), C.B. Parker, 1994, ISBN 0-07-051400-3〕
==Potentials in the Lorenz gauge==
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 potential, for an arbitrary source of charge density ρ(r, ''t'') and current density J(r, ''t''), and is the D'Alembert operator. Solving these gives the retarded potentials below (all in SI units).
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