We study the effect of magnetic field on the properties of a high mobility gated two-dimensional electron gas in a field effect transistor with the Hall bar geometry. When approaching the current saturation when the drain side of the channel becomes strongly depleted, we see a number of unusual effects related to the magnetic field induced re-distribution of the electron density in the conducting channel. The experimental results obtained in the non-linear regime have been interpreted based on the results obtained in the linear regime by a simple theoretical model, which describes quite well our observations.
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