Applications: gear selector, Hall effect, mass spectrometer

The velocity selector

An electric field E and a magnetic field B, which are perpendicular to each other and to the velocity v of the particles, are superimposed. The total Lorentz force is F = qE + q(v x B). For a particular velocity v₀ such that qE and q(v × B) exactly cancel each other out, the particle passes through without deflection:

v₀ = E/B

Only particles travelling at this precise velocity emerge in a straight line; the others are deflected and filtered out. This device selects a velocity independently of mass or charge.

The Hall effect

In a flat conductor through which a current I flows and which is immersed in a perpendicular magnetic field B, the charge carriers are deflected by the magnetic force, which creates a build-up of charge at the edges and thus a transverse voltage U_H (Hall voltage), proportional to I*B and inversely proportional to the thickness and carrier density. The Hall effect enables the measurement of B, the determination of the sign of the charge carriers, and serves as a sensor in many devices (Hall-effect sensors).

The mass spectrometer

After velocity selection, the ions enter a region where only a B field is present. They then follow a circular trajectory with radius r = mv/(qB). By measuring r, one can determine the m/q ratio, which allows isotopes or molecules to be identified based on their mass.

Conventional trap

In the velocity selector, E and B must be correctly aligned so that the forces oppose each other (rather than adding together); otherwise, no specific velocity is filtered out, and all particles are deflected in the same direction.