This result can be plugged into the Ampère–Maxwell equation, ∇ ∇ × × B = μ μ 0 J + 1 c 2 ∂ ∂ E ∂ ∂ t ∇ ∇ × × ( ∇ ∇ × × A ) = ⇒ ⇒ ∇ ∇ ( ∇ ∇ ⋅ ⋅ A ) − − ∇ ∇ 2 A = μ μ 0 J − − 1 c 2 ∂ ∂ ( ∇ ∇ φ φ ) ∂ ∂ t − − 1 c 2 ∂ ∂ 2 A ∂ ∂ t 2 .