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

Derivation of the linear Landau equation and linear Boltzmann equation from the Lorentz model with magnetic field