Including both the electric and magnetic fields we get the Hall effect geometry. As in preset 2, the steady state distribution of the electrons is like the equilibrium distribution, but shifted in k-space. However, now the shift is not parallel to the E-field, but in a direction making the "Hall angle" with respect to the drift that would occur in absence of the magnetic field.
Where is the center of rotation of these orbits? Why is it NOT at the green dot (the average k of all the electrons)?
Can you find a value of E_y which gives <k_y> (and hence the y-component of current) = 0? This is the Hall field in the conventional Hall effect experiment.