By Stokes's theorem, the closed line integral of around a contour is equal to the open surface integral of curl across the surface bounded by the closed contour. Since, from Maxwell's equations, , the closed line integral of evaluates to the total current passing through the surface. This is equal to the excitation, , 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.