Following the third equation involving the divergence of H ∇ ∇ ⋅ ⋅ H = 0 by vector calculus we can write any divergenceless vector as the curl of another vector, hence ∇ ∇ × × A = H where A is called the magnetic vector potential. Substituting this into the above we get ∇ ∇ × × ( E + j ω ω μ μ A ) = 0 and any curl-free vector can be written as the gradient of a scalar, hence E + j ω ω μ μ A = − − ∇ ∇ Φ Φ where Φ Φ is the electric scalar potential. These relationships now allow us to write ∇ ∇ × × ∇ ∇ × × A − − k 2 A = J − − j ω ω ε ε ∇ ∇ Φ Φ where k = ω ω μ μ ε ε , which can be rewritten by vector identity as ∇ ∇ ( ∇ ∇ ⋅ ⋅ A ) − − ∇ ∇ 2 A − − k 2 A = J − − j ω ω ε ε ∇ ∇ Φ Φ