Measuring the momentum of a charged particle

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SUMMARY

The momentum of a charged particle can be measured using the relationship defined by the formula F = Bqv, where F is the force exerted by a magnetic field B on a particle with charge q moving at velocity v. When particles move perpendicular to the magnetic field, they experience a constant force that causes them to move in a circular path, allowing for the calculation of their relativistic momentum p using the equation Bq = p/r, where r is the radius of the circular path. In high-energy physics, the magnetic field may not allow for a complete circular trajectory, but the radius can still be determined from the particle's track. This method also accounts for momentum components parallel to the magnetic field when necessary.

PREREQUISITES
  • Understanding of Lorentz force and its application in charged particle dynamics
  • Familiarity with the concept of relativistic momentum and the gamma factor (γ)
  • Knowledge of magnetic fields and their effects on charged particles
  • Basic principles of circular motion and centripetal acceleration
NEXT STEPS
  • Study the derivation and implications of the Lorentz force law in particle physics
  • Learn about the relativistic gamma factor and its significance in high-energy physics
  • Explore methods for measuring magnetic field strength in particle detectors
  • Investigate the effects of non-perpendicular motion on charged particle trajectories in magnetic fields
USEFUL FOR

Particle physicists, students of high-energy physics, and researchers involved in experimental physics who seek to understand the measurement of charged particle momentum in magnetic fields.

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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.
 
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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.
 
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.
 

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