  The zeta function regularization technique is used to study the finite
temperature Casimir effect for a charged and massless scalar field confined
between parallel plates and satisfying Dirichlet boundary conditions at the
plates. A magnetic field perpendicular to the plates is included. Three
equivalent expressions for the zeta function are obtained, which are exact to
all orders in the magnetic field strength, temperature and plate distance.
These expressions of the zeta function are used to calculate the Helmholtz free
energy of the scalar field and the pressure on the plates, in the case of high
temperature, small plate distance and strong magnetic field. In all cases,
simple analytic expressions are obtained for the free energy and pressure which
are accurate and valid for practically all values of temperature, plate
distance and magnetic field.
