Then substituting J by σ σ ( E v a c + E r a d ) , using the fact that ∇ ∇ ⋅ ⋅ E r a d = 0 we obtain, ∇ ∇ 2 E r a d = ∂ ∂ ∂ ∂ t ( μ μ 0 σ σ E v a c + μ μ 0 σ σ E r a d + ϵ ϵ 0 μ μ 0 ∂ ∂ E r a d / ∂ ∂ t )