  This paper investigates the density expansion of the thermodynamic properties
of a two component plasma under the influence of a weak constant uniform
magnetic field. We start with the fugacity expansion for the Helmholtz free
energy. The leading terms with respect to the density are calculated by a
perturbation expansion with respect to the magnetic field. We find a new
magnetic virial function for a low density plasma which is exact in quadratic
order with respect to the magnetic field. Using these results we compute the
magnetization and the magnetic susceptibility.
