Contribution of electric self-forces to electromagnetic momentum in a moving system

Abstract: In moving electromagnetic systems, electromagnetic momentum calculated from the vector potential is shown to be proportional to the field energy of the system. The momentum thus obtained is shown actually to be the same as derived from a Lorentz transformation of the rest-frame electromagnetic energy of the system, assuming electromagnetic energy-momentum to be a 4-vector. The energy-momentum densities of electromagnetic fields form, however, components of the electromagnetic stress-energy tensor, and their transformations from rest frame to another frame involve additional contributions from stress terms in the Maxwell stress tensor which do not get represented in the momentum calculated from the vector potential. The genesis of these additional contributions, arising from stress in the electromagnetic fields, can be traced, from a physical perspective, to electric self-forces contributing to the electromagnetic momentum of moving systems that might not always be very obvious. Such subtle contributions to the electromagnetic momentum from stress in electromagnetic fields that could be significant even for non-relativistic motion of the system, lead in fact, to resolution of some curious riddles in the electromagnetic momentum of such systems, e.g., the apparent paradox of a {\em nil} electromagnetic momentum in a charged parallel-plate capacitor, moving perpendicular to the plate orientations, in spite of the moving system carrying finite electromagnetic energy within it. Such contributions from stress in electromagnetic fields also provide a natural solution to the famous, century-old, enigmatic factor of 4/3, encountered in the electromagnetic momentum of a moving charged sphere.