We investigate the dielectric response of a planar Fermi plasma in the
presence of a constant external magnetic field. The conductivity tens
or is derived in the random-phase approximation taking into account th
e effects of the spin of the electron. This proper inclusion of spin m
akes a significant difference to the results compared with all previou
s studies, which ignored the intrinsic spin of the electron. In studyi
ng the dispersion relations for the electrodynamic modes of the plasma
in an external magnetic field, it is necessary to observe that the lo
ngitudinal and transverse modes are coupled. These coupled modes are i
nvestigated in some detail.