# Measuring the momentum of a charged particle

1. Aug 6, 2013

### Fissi0nable

I am relatively new to particle physics, and I seem to have reached confusion already. I do not seem to comprehend how you could measure the momentum of a charged particle just by exerting force and a magnetic field on it. The formula F = Bqv is mentioned when I hear of this, which does not really help (if anything, it only worsens my confusion). Could anyone please explain in detail how this is done? Much appreciated.

2. Aug 6, 2013

### Staff: Mentor

Let's consider particles moving perpendicular to the magnetic field: they feel a constant force F=Bqv perpendicular to their direction of motion, so they move in a circle with the radius r where F provides the centripetal acceleration: $F=\gamma m\frac{v^2}{r}$ (γ is the relativistic gamma factor). Combining both, $Bqv=\gamma m\frac{v^2}{r}$ or $Bq=\frac{p}{r}$ where p is the relativistic momentum of the particle. B is known from the detector calibration, r can be measured in the detector. q is usually +1 or -1, so you can calculate p.

In high-energy physics, the magnetic field is not large enough to get a full circle for most particles, but you can consider the track as a part of a circle and determine its radius.

If the particle does not move perpendicular to the magnetic field, you have to consider the momentum parallel to the field as well, but the concept is the same.

3. Aug 6, 2013

### Fissi0nable

Thank you very much for your help, mfb. You made it clear. I knew about the circular motion, but I didn't know F played such a big part in calculating the radius. I appreciate your help.