Do the standard expressions for the electromagnetic field-momentum need any modifications?

Abstract

We investigate here the question raised in literature about the correct expression for the electromagnetic field-momentum, especially when static fields are involved. For this we examine a couple of simple but intriguing cases. First we consider a system configuration in which electromagnetic field momentum is present even though the system is static. We trace the electromagnetic momentum to be present in the form of a continuous transport of electromagnetic energy from one part of the system to another, without causing any net change in the energy of the system. In a second case we show that the electromagnetic momentum is nil irrespective of whether the charged system is stationary or in motion, even though the electromagnetic energy is present throughout. We demonstrate that the conventional formulation of electromagnetic field-momentum describes the systems consistently without any real contradictions. Here we also make exposition of a curiosity where electromagnetic energy decreases when the charged system gains velocity. Then we discuss the more general question that has been raised -- Are the conventional formulas for energy-momentum of electromagnetic fields valid for all cases? Or more specifically, in the case of so-called "bound fields," do we need to change over to some modified definitions which have made their appearance even in standard text books? We show that in all cases it is only the conventional formulas which lead to results consistent with the rest of physics, including the special theory of relativity, and that any proposed modifications are thus superfluous.