The Liouville equation with non-constant magnetic field is obtained as a limit in the Planck constant of the Heisenberg equation with the same magnetic field. The convergence is with respect to an appropriate semiclassical pseudo distance, and consequently with respect to the Monge-Kantorovich distance. Uniform estimates both in ǫ and are proved for the specific 2D case of a magnetic vector potential of the form 1 ǫ x ⊥ . As an application, an observation inequality for the Heisenberg equation with a magnetic vector potential is obtained. These results are a magnetic variant of the works [F. Golse and T.