The model of the self-consistent interaction between magnetospheric convection and the ionosphere as developed into a general formalism in separate papers by Vasyliunas, Wolf and Southwood leads to a fundamental relationship between the radius b of the ring formed in the ionosphere by the Region 2 Birkeland current system, regarded as a dependent variable, and the cross polar cap potential &PHgr; and polar cap radius a, regarded as independent variables. When the control of &PHgr; on a is taken into consideration in a time dependent model, one finds that a grows much more rapidly than b. This leads to a dilemma, which substorms can be used to resolve by removing magnetic flux from the polar cap. Thinning of the plasma sheet prior to substorms emerges as a simple, geometrical consequence of the model. For a steady potential, the system evolves to a steady state for which the functional dependences of the sizes of the polar cap and the Region 2 ring on &PHgr; are found to be (a/Re)=&agr;&PHgr;3/16, (b/Re)=&bgr;&PHgr;3/16, with &agr; and &bgr; constants which satisfy &bgr;-&agr;≪(1/2)( &bgr;+&agr;). That is, the inter-ring separation is predicted to be much less than the radii of the rings, as is observed.