# How can energy in Ev of particles e.g. muons be measured in a cloud chamber?

I have a Wilson thermoelectric cloud chamber and would like to obtaine the energy of cosmic particles e.g. muons. I would greatly appreciate your answer.

You need a magnetic field, then you can measure the curvature of the particle's path. The curvature gives you the momentum, from which you can determine the energy if you know the particle type, and thus the mass.

In a uniform magnetic field of strength $B$, a particle of charge magnitude $q$ and momentum $p$ traveling in the plane perpendicular to the magnetic field travels in a circular path with a radius given by: $$R=\frac{p}{qB}$$

So if you have a uniform field in your cloud chamber charged particles will follow a circular arc. Using simple geometry, you can determine the radius of curvature and thus the momentum. Once you have that, the kinetic energy is simply: $$K=\sqrt{(pc)^2+(mc^2)^2}-mc^2$$

If you have a non-uniform field, you have to map out the field and then probably use a computer to model the problem.

• Muon mass is 200 times the electron mass, and energies are very high. So one would need a large field for sufficient curvature. – Pieter Dec 11 '17 at 7:22
• @Pieter Depends on the granularity with which you can measure the particle's path and the size of the chamber. – Chris Dec 11 '17 at 7:34
• May I have step by step calculations because I am a medical doctor with some physics background and just want to use a cloud chamber to explore their action on biological samples. References for the calculations also will be helpful. I have very dtrong magnets 30 and 60 kg strenght to separate. Thanks. – Evgeni Gabev Dec 11 '17 at 14:01
• Dear Chris, Many thanks for yor detailed and very helpful answer. The vendor told me that the field is homogeneous within about 5-6 cm between the magnets made from neodimium. How can I prove that. Is it is ok if I use metal dust and thus looking at the magnetic lines of force to judge about the homogeneity of the magnetic field. – Evgeni Gabev Dec 11 '17 at 22:16