Finally, plugging in the relations ∇ ∇ ( 1 | r − − ℓ ℓ | ) = − − ∇ ∇ ℓ ℓ ( 1 | r − − ℓ ℓ | ) , ∇ ∇ 2 ( 1 | r − − ℓ ℓ | ) = − − 4 π π δ δ ( r − − ℓ ℓ ) (where δ is the Dirac delta function), using the fact that the divergence of J is zero (due to the assumption of magnetostatics), and performing an integration by parts, the result turns out to be ∇ ∇ × × B = μ μ 0 J i.e. Ampère's circuital law. (Due to the assumption of magnetostatics, ∂ ∂ E / ∂ ∂ t = 0 , so there is no extra displacement current term in Ampère's law.)