The Paradox of Two Charged Capacitors -- A New Perspective

Abstract

It is shown that the famous paradox of two charged capacitors is successfully resolved if all the energy changes in the system are properly considered when some of the charges are transferred from one capacitor to the other. It happens so even when the connecting wire has an identically zero resistance, giving rise to no Ohmic losses in the wire. It is shown that in such a case the "missing energy" goes into the kinetic energy of conducting charges. It is shown that radiation plays no significant role in resolving the paradox. The problem can be formulated and successfully resolved in a novel form, where the capacitance of the system is increased by stretching the plates of the original capacitor, without involving any connecting wires in a circuit. There is an outward self-force due to mutual repulsion among charges stored within each capacitor plate, and the work done by these self-forces during an expansion is indeed equal to the missing energy of the capacitor system.