The particular solution, π π e , p ( r , t ) and therefore, E p ( r , t ) , is found using a time dependent Green's function method on the inhomogeneous wave equation for π π e , p which produces the retarded integral π π e , p ( r , t ) = 1 4 π π ϵ ϵ 0 ∫ ∫ d 3 r ′ P ( r ′ , t − − | r − − r ′ | / c ) | r − − r ′ | .