or that the circulation of the electric field around a loop is equal to the negative rate of change of the magnetic field flux through any surface spanned by the loop, by Stokes' theorem ∮ ∮ ∂ ∂ S E ⋅ ⋅ d l = ∬ ∬ S ∇ ∇ × × E ⋅ ⋅ d S = − − d d t ∫ ∫ S B ⋅ ⋅ d S .