We use a global MHD simulation to compute the distribution of E∥ on the face of the magnetopause as represented by the last closed field line surface. In MHD codes, E∥ is a proxy for magnetic reconnection. Integrating E∥ along the topological separator line between open and closed magnetic field lines gives the global reconnection rate at the magnetopause. In the case studied here, where the interplanetary magnetic field (IMF) is precisely duskward, we find the global reconnection rate to be ~49 kV, comparable to potentials inferred from measurements made in the polar cap. The exercise demonstrates an application of a general reconnection theorem that, in effect, equates reconnection with E∥. It prepares the way for MHD imaging of reconnection in terms of contours of E∥ on the magnetopause. The result also illustrates a property of parallel potentials in the global context that is not generally recognized. Nearly the full magnetopause reconnection voltage exists on some closed field lines between the northern and southern polar caps, so that they leave the dawn, southern hemisphere with a sizable positive polarity and enter the dusk, northern hemisphere with a sizable negative polarity. An unexpected finding is a substantial parallel potential (between 10 and 15 kV) between the magnetopause and the ionosphere in northern dawn and southern dusk sectors. (Interchange dawn and dusk for dawnward IMF.) This potential has the polarity that accelerates electrons into the ionosphere in the dusk sector and, so, might be the origin of the hot spot seen there in precipitating electrons. ¿ 2001 American Geophysical Union