The process whereby magnetic flux is removed from the day side region of the magnetosphere and transferred to the magnetotail has been referred to as 'erosion' of the day side magnetosphere. Observations have suggested that the occurrence of this erosion process is related to increases in the southward component of the interplanetary magnetic field and hence by inference to increases in the rate of field line reconnection at the day side magnetopause. Similarly, the inverse of the erosion process (i.e., the net transfer of flux from the magnetotail to the day side magnetosphere) is associated with decreases in the southward component of the interplanetary magnetic field and hence to decreases in the magnetopause reconnection rate. A quantitative theory of the day side erosion process (and its inverse) is developed here in terms of an electrical circuit analogy, in which the ionosphere acts as a resistance with a voltage generator connected in parallel and the closed magnetosphere acts as a set of inductances and a capacitance. Changes in the rate of day side field line reconnection lead directly to changes in the potential drop across the magnetospheric capacitor, and after a characteristic time delay, to changes in the voltage applied by the generator. The response of the coupled ionosphere-magnetosphere circuit to such changes is studied in some detail, and a quantitative estimate for the rate of erosion is obtained. In addition to describing the mean motion of the magnetopause associated with erosion the theory predicts oscillations of the magnetopause about this mean with characteristic periods of several minutes. Such oscillations have frequently been observed by spacecraft.