The Feynman paradox and hidden momentum

Abstract

Though it is generally accepted that electromagnetic radiation fields possess energy and linear and angular momentum, the adscription of these properties to static and quasi-static fields rises some doubts. Some authors consider that in electrostatics the concept of field is superfluous, or that action-at-a-distance and field are equivalent views. However, the interpretation of Poynting´s vector divided by c2 as a momentum density is consistent and necessary for the conservation laws to hold, even in static conditions. The Feynman paradox exhibits the necessity of assigning linear and angular momentum to static and quasi-static fields, showing in this way that the points of view of action-at-a-distance and field are not equivalent. In the present work we do not intend to present a revision of the literature on this subject, but to show that the concept of hidden momentum is useful to solve the paradox, and we show that it is part of a momentum balance equation derived directly from the macroscopic Maxwell equations. Another consequence of this balance equation is that, in static conditions, the momentum associated to Poynting´s vector equals the hidden momentum and cancels it. Graduate students and researchers interested in conceptual problems of electromagnetism will find a firm foundation of the concept of hidden momentum and an alternative view of the paradox.