Quantum, Photo-Electric Single Capacitor Paradox

Abstract

In this work single capacitor paradox (a variation of the remarkable two capacitor paradox) is considered in a new, quantum discrete form. Simply speaking we consider well-known usual, photoelectric effect experimental device, i.e. photo electric cell, where cathode and anode are equivalently charged but non-connected. It, obviously, represents a capacitor that initially, i.e. before action of the photons with individual energy equivalent to work function, holds corresponding energy of the electrical fields between cathode and anode. Further, we direct quantum discretely photons, one by one, toward cathode where according to photo-electrical effect electrons discretely, one by one, will be emitted and directed toward anode. It causes discrete discharge of the cell, i.e. capacitor and discrete decrease of the electrical field. Finally, total discharge of the cell, i.e. capacitor, and total disappearance of the electrical field and its energy will occur. Given, seemingly paradoxical, capacitor total energy loss can be simply explained without any dissipative effects (Joule heating or electromagnetic waves emission can be neglected as high order small corrections) by work done by the electrical field by movement of the electrons from cathode to anode. (Remarkable two capacitors paradox can be, obviously, formulated and explained in the completely analogous way.)