By Stokes's theorem, the closed line integral of H ·d l around a contour is equal to the open surface integral of curl H ·d A across the surface bounded by the closed contour. Since, from Maxwell's equations, curl H = J, the closed line integral of H ·d l evaluates to the total current passing through the surface. This is equal to the excitation, NI, which also measures current passing through the surface, thereby verifying that the net current flow through a surface is zero ampere-turns in a closed system that conserves energy.