  We study the validity of the so-called Smoluchowski-Kramers approximation for
a two dimensional system of stochastic partial differential equations, subject
to a constant magnetic field. As the small mass limit does not yield to the
solution of the corresponding first order system, we regularize our problem by
adding a small friction. We show that in this case the Smoluchowski-Kramers
approximation holds. We also give a justification of the regularization, by
showing that the regularized problems provide a good approximation to the
original ones.
