Deriving the E Cross B Drift Velocity: A Puzzling Explanation

[pierce15]

I am looking at this brief derivation of the E cross B drift for a plasma, starting at the top of page 3: http://www.physics.sfsu.edu/~lea/courses/grad/motion.PDF.

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?

 

[nbryan5]

Yes, there is a reason why the drift velocity is perpendicular to B. This is because of the Lorentz force law, which states that the force on a particle in a magnetic field is proportional to the velocity and perpendicular to both the velocity and the magnetic field. Therefore, the drift velocity must be perpendicular to the magnetic field in order for the Lorentz force to be zero.