 Guiding-centre drift

For a constant perpendicular force in a uniform magnetic field, write the particle velocity as $\mathbf{v}={\mathbf{v}}_d+\mathbf{u}$. Choosing $q{\mathbf{v}}_d\times \mathbf{B}=-\mathbf{F}$ leaves the ordinary gyromotion equation for $\mathbf{u}$. The gyroperiod-averaged transverse velocity is therefore the displayed drift. An electric force gives the same drift for both charge signs; a charge-independent applied force gives opposite drifts.