Rearranging the cross products above leads to z ^ ^ × × B ⊥ ⊥ = ∇ ∇ A − − ( z ^ ^ ⋅ ⋅ ∇ ∇ A ) z ^ ^ = ∇ ∇ A , and j ⊥ ⊥ × × B z z ^ ^ = B z μ μ 0 ( z ^ ^ ⋅ ⋅ ∇ ∇ B z ) z ^ ^ − − 1 μ μ 0 B z ∇ ∇ B z = − − 1 μ μ 0 B z ∇ ∇ B z .