  Using 2D MHD numerical simulations performed with two different finite
difference Eulerian codes, we analyze the effect that a toroidal magnetic field
has on low mass planet migration in nonturbulent protoplanetary discs. The
presence of the magnetic field modifies the waves that can propagate in the
disc. In agreement with a recent linear analysis (Terquem 2003), we find that
two magnetic resonances develop on both sides of the planet orbit, which
contribute to a significant global torque. In order to measure the torque
exerted by the disc on the planet, we perform simulations in which the latter
is either fixed on a circular orbit or allowed to migrate. For a 5 earth mass
planet, when the ratio \beta between the square of the sound speed and that of
the Alfven speed at the location of the planet is equal to 2, we find inward
migration when the magnetic field B_{\phi} is uniform in the disc, reduced
migration when B_{\phi} decreases as r^{-1} and outward migration when B_{\phi}
decreases as r^{-2}. These results are in agreement with predictions from the
linear analysis. Taken as a whole, our results confirm that even a subthermal
stable field can stop inward migration of an earth--like planet.
