In a region with no charges (ρ = 0) and no currents (J = 0), such as in vacuum, Maxwell's equations reduce to: ∇ ∇ ⋅ ⋅ E = 0 , ∇ ∇ × × E + ∂ ∂ B ∂ ∂ t = 0 , ∇ ∇ ⋅ ⋅ B = 0 , ∇ ∇ × × B − − μ μ 0 ε ε 0 ∂ ∂ E ∂ ∂ t = 0.