  I investigate the finite temperature Casimir effect for a charged and
massless scalar field satisfying mixed (Dirichlet-Neumann) boundary conditions
on a pair of plane parallel plates of infinite size. The effect of a uniform
magnetic field, perpendicular to the plates, on the Helmholtz free energy and
Casimir pressure is studied. The zeta-function regularization technique is used
to obtain finite results. Simple analytic expressions are obtained for the zeta
function and the free energy, in the limits of small plate distance, high
temperature and strong magnetic field. The Casimir pressure is obtained in each
of the three limits and the situation of a magnetic field present between and
outside the plates, as well as that of a magnetic field present only between
the plates is examined. It is discovered that, in the small plate distance and
high temperature limits, the repulsive pressure is less when the magnetic field
is present between the plates but not outside, than it is when the magnetic
field is present between and outside the plates.
