where ϕ ϕ ( x → → , t ) has − − ∇ ∇ → → ϕ ϕ = E → → ( ϕ ϕ is a scalar potential for the irrotational/conservative vector field E → → ) and A → → ( x → → , t ) has ∇ ∇ → → × × A → → = B → → ( A → → is a vector potential for the solenoidal vector field B → → ).