14.3.4 Velocity Selector

In many applications such as electron microscopy and mass spectrometers, it is necessary to filter the ions based on their velocity. The device to do such a thing is called a velocity selector.

The working principle of the velocity selector is rather straightforward (pun intended). All the ions (with different velocities) are made to pass through a region of uniform electric and magnetic field. Each ion thus experience both a magnetic force $\displaystyle {{F}_{b}}=Bqv$ and an electric force $\displaystyle {{F}_{e}}=qE$ .

Here comes the crucial bit. The directions of the B and E fields are arranged in such a manner that F_b and F_e are always in opposite directions. Then, by choosing the magnitude of B and E, we can select the velocity at which F_b and F_e are equal in magnitude (but opposite in direction).

$\displaystyle \begin{aligned}{{F}_{b}}&={{F}_{e}}\\Bqv&=qE\\v&=\frac{E}{B}\end{aligned}$

Only ions travelling at the chosen speed of $\displaystyle v=\frac{E}{B}$ can travel along a straight line (since net force is zero) to be collected at the exit. Ions travelling at other speeds will be deflected either upward or downward, away from the exit point and thus filtered away.