  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.
