Maxwell's equations can directly give inhomogeneous wave equations for the electric field E and magnetic field B. Substituting Gauss's law for electricity and Ampère's law into the curl of Faraday's law of induction, and using the curl of the curl identity ∇ × (∇ × X) = ∇(∇ ⋅ X) − ∇ X (The last term in the right side is the vector Laplacian, not Laplacian applied on scalar functions.) gives the wave equation for the electric field E : 1 c 2 ∂ ∂ 2 E ∂ ∂ t 2 − − ∇ ∇ 2 E = − − ( 1 ε ε 0 ∇ ∇ ρ ρ + μ μ 0 ∂ ∂ J ∂ ∂ t ) .