  We consider a test particle moving in a random distribution of obstacles in
the plane, under the action of a uniform magnetic field, orthogonal to the
plane. We show that, in a weak coupling limit, the particle distribution
behaves according to the linear Landau equation with a magnetic transport term.
Moreover, we show that, in a low density regime, when each obstacle generates
an inverse power law potential, the particle distribution behaves according to
the linear Boltzmann equation with a magnetic transport term. We provide an
explicit control of the error in the kinetic limit by estimating the
contributions of the configurations which prevent the Markovianity. We compare
these results with those ones obtained for a system of hard disks in
\cite{BMHH}, which show instead that the memory effects are not negligible in
the Boltzmann-Grad limit.
