Plasma pp 71-73

# Electric Drift

• D. A. Frank-Kamenetskii
Chapter

## Abstract

As our first example we consider the case in which the force F is due to an electric field:
$${F_ \bot } = Ze{E_ \bot }.$$
Therefore,
$$\left| {{v_E}} \right| = \frac{{{E_ \bot }}}{B}.$$
The quantity E⊥is the component of the electric field perpendicular to the magnetic field. Since the electrons have a negative charge Z = -1. The general expression for the drift velocity contains the charge number Z in the denominator. Therefore, if the force F E⊥ acts in a similar way on electrons and ions, the effect is a drift of electrons in one direction and ions in the other. We note, however, that the electric field has an opposite effect on electrons and ions; the force is proportional to the charge number Z. Therefore, the charge cancels out of the drift velocity when ZeEE⊥is inserted for FE⊥. The drift caused by an electric field is called the electric drift. The velocity of the electric drift is the same for electrons and ions, both in magnitude and direction. In vector form it is expressed as
$${{\text{v}}_{\text{E}}} = \frac{{{\text{E}} \times {\text{B}}}}{{{B^2}}}.$$