I am looking at this brief derivation of the E cross B drift for a plasma, starting at the top of page 3: link. I am a bit confused as to the justification that the drift velocity is perpendicular to the magnetic field, as stated at the top of page 3. Is this an ansatz, which just happens to work out? One can immediately check that this velocity solves the equation preceding (5), and if I am not mistaken the solution is linear in components of drift velocity so it must be the unique solution. Or am I missing something and is there a reason why the drift velocity is perpendicular to B?