 Electric-cross-magnetic-field drift

In the nonrelativistic Lorentz force model, uniform perpendicular electric field $\mathbf{E}$ and magnetic field $\mathbf{B}\ne 0$ give the guiding-centre velocity ${\mathbf{v}}_D=\mathbf{E}\times \mathbf{B}/|\mathbf{B}{|}^2$, independent of electric charge and mass. For $\mathbf{E}=E{\mathbf{e}}_x$ and $\mathbf{B}=B{\mathbf{e}}_z$, the drift component is $v_y=-E/B$.

The electric drift in crossed uniform fields derivation separates force-cancelling drift from the remaining cyclotron motion and states the nonrelativistic speed restriction and the relativistic magnetic-dominated condition. These conditions matter when using the drift to describe Landau levels in crossed electric and magnetic fields.