Retarded Potential - Potentials in The Lorenz Gauge

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.