If a vector field v admits a vector potential A , then from the equality ∇ ∇ ⋅ ⋅ ( ∇ ∇ × × A ) = 0 (divergence of the curl is zero) one obtains ∇ ∇ ⋅ ⋅ v = ∇ ∇ ⋅ ⋅ ( ∇ ∇ × × A ) = 0 , which implies that v must be a solenoidal vector field.