This chapter builds the integral solution of Maxwell’s equations using Green’s functions and makes the causal structure of electromagnetism explicit. Starting from the wave equations for E and B, it reduces the problem to a generic scalar wave equation and introduces the Green’s function, G.

G as the response to a spacetime impulse. Solving the three-dimensional wave equation yields the retarded and advanced Green’s functions and leads to retarded integral solutions for arbitrary source distributions. Applying these to charge and current produces the Jefimenko equations, which cleanly separate quasistatic near fields from radiation fields and show how fields at a point depend on sources on its past light cone. A spacetime picture in terms of light cones clarifies retardation and the domain of dependence. The chapter then specializes to moving point charges, deriving compact expressions for their electric and magnetic fields and the associated Jacobian factors. An alternative Fourier–space derivation of the Green’s function connects these classical results to methods used in quantum field theory.