  Various electromagnetic systems can carry an angular momentum in their {\bf
E} and {\bf B} fields. The electromagnetic field angular momentum (EMAM) of
these systems can combine with the spin angular momentum to give composite
fermions or composite bosons. In this paper we examine the possiblity that an
EMAM could provide an explanation of the fractional quantum Hall effect (FQHE)
which is complimentary to the Chern-Simons explanation. We also examine a toy
model of a non-BCS superconductor (e.g. high $T_c$ superconductors) in terms of
an EMAM. The models presented give a common, simple picture of these two
systems in terms of an EMAM. The presence of an EMAM in these systems might be
tested through the observation of the decay modes of a charged, spin zero
unstable particle inside one of these systems.
