Under steady state conditions and in the absence of parallel electric fields, ionospheric convection is a direct map of plasma and magnetic flux convection in the magnetosphere, and quantitative estimates can be obtained from the mapping along magnetic field lines of electrostatic ionospheric electric fields. The resulting magnetospheric electrostatic potential distribution then provides the convection electric field in various magnetospheric regions. We present a quantitative framework for the investigation of the applicability and limitations of this approach based on an analytical theory derived from first principles. Particular emphasis is on the role of parallel electric field regions and on inductive effects, such as expected during the growth and expansive phases of magnetospheric substorms. We derive quantitative estimates for the limits in which either effect leads to a significant decoupling between ionospheric and magnetospheric convection and provide an interpretation of ionospheric convection which is independent of the presence of inductive electric fields elsewhere in the magnetosphere. Finally, we present a study of the relation between average and instantaneous convection, using two periodic dynamical models. The models demonstrate and quantify the potential mismatch between the average electric fields in the ionosphere and the magnetosphere in strongly time-dependent cases that may exist even when they are governed entirely by ideal MHD.