In this paper we develop an equation for Io's electric field/electric potential which includes Io's inhomogeneous and anisotropic conductances and treats Io's far-field interaction in both limits: the unipolar inductor and the Alfv¿n wing models. We solve this equation for constant conductances within an elliptically shaped Ionian ionosphere, which leads to useful analytic expressions for properties of Io's local interaction, specifically, the total electric current driven by Io's interaction. Several previous calculations underestimated the total electric current by a factor of two. Oversimplifications of the Alfv¿nic current system might be one of the reasons. Our expressions also show that it is not the voltage across Io's ionosphere, as often assumed, that is physically related to the electric current; but it is the electric field and the extensions of the ionosphere in both directions. We show in addition that the Alfv¿nic and unipolar inductor models lead to different properties of Io's local interaction, e.g., the maximum plasma speed up around Io is higher in the Alfv¿nic coupling case.