Chemical Sciences: A Manual for CSIR-UGC National Eligibility Test for Lectureship and JRF/Velocity selector

A velocity selector is used in accelerator mass spectrometry to select particles based on their speed. The velocity selector is composed of orthogonal electric and magnetic fields, such that particles with the correct charge to mass ratio and speed will be unaffected, and other particles will be deflected.

Theory
Any charged particle in an electric field will feel a force proportional to the charge and field strength such that $$ \vec{F} = q \vec{E} $$, where F is force, q is charge, and E is electric field. Similarly, any particle moving in a magnetic field will feel a force proportional to the velocity and charge of the particle. The force felt by any particle is then equal to $$ \vec{F} = q \vec{v} \times \vec{B}$$, where F is force, q is the charge on the particle, v is the velocity of the particle, B is the strength of the magnetic field, and $$\times$$ is the cross product. In the case of a velocity selector, the magnetic field is always at 90 degrees to the velocity and the force is simplified to $$F = qvB$$ in the direction described by the cross product.

Setting the two forces to equal magnitude in opposite directions it can be shown that $$ \frac{E}{B} = v$$. Which means that any combination of electric ($$\vec{E}$$) and magnetic ($$\vec{B}$$) fields will allow charged particles with only velocity $$\vec{v}$$ through.