Experimentally, under the application of an external perpendicular magnetic field, we observe a change in the longitudinal resistance. However, in the theoretical development starting from the Drude model and applying Newton's law, we end up with a resistivity tensor whose longitudinal components don't depend on the magnetic field. So, what's the origin of such a change in the longitudinal resistance in the experiments? Is this misunderstanding due to the approximations of Drude's model that lead to such a simplification?
I understand that the application of a magnetic field somehow hinders the movement of electrons, but at the end what you get is an orbital movement, a circular motion. This means to me that the magnetic field produces always a perpendicular correction to the motion of the electron, meaning that it relates the direction of the current with the perpendicular one. Consequently, in the resistivity tensor , only the transverse components (off-diagonal) should depend on the field and not the longitudinal ones. So, what's the reason?