A similar principle is applied in mass spectrometers, which can be used to detect even the smallest quantities of a substance in the human body.
First, the atoms or molecules to be studied are ionized in an ion source. The charged particles are then accelerated by an electric field and pass through a velocity filter, also called a Wien filter. This filter consists of a capacitor that generates an electric field, together with a magnetic field oriented perpendicular to it.
The charged particles are deflected in opposite directions by the two fields. A particle can only pass through the filter if the two forces cancel out, i.e., if the electric force equals the Lorentz force:
$$
F_\mathrm{el} = F_\mathrm{L}
$$
Substituting the respective formulas and solving for the velocity gives the filter condition:
$$
\boxed{v = \frac{E}{B}}
$$
After passing through an aperture, the ions enter a strong magnetic field and are forced into circular trajectories. Since the radius of the circular path, at constant velocity, is proportional to the particle’s mass, the ratio of charge to mass ($q/m$) can be reconstructed from the point of impact on the detector.