How can I calculate the magnetic field of a relativistic muon?

[magphys]

I know this is basic stuff but my maths is truly terrible. I hope someone can help.

Assuming you have a muon moving at near light speed, it will generate a magnetic field due to its movement. I'm assuming there is no external magnetuc field present. How can I calculate the field produced please?

 

[nirax]

look up a good text .. it is not as straightforward as it seems

 

[magphys]

look up a good text .. it is not as straightforward as it seems

Probably explains why I can't find it on the web. I don't have a text with me. I was hoping someone might know ...

 

[Bob S]

IAssuming you have a muon moving at near light speed, it will generate a magnetic field due to its movement. I'm assuming there is no external magnetuc field present. How can I calculate the field produced please?

First, the magnetic field due to the negative muon current is the same as an electron at the same speed.
Second, calculate the field due to 1 Coulomb of electrons per second.
Third, multiply this result by 1.6 x 10^-19 Coulombs per electron.
Fourth (this is the hard part), considering relativistic contraction of the EM field of a relativistic charged particle, what is the observed magnetic field of a single charged particle as a function of time?

 

[magphys]

That will be fun!

What I am really interested is knowing whether you could detect a stream of energetic muons purely by the magnetic field they produce and, if so, what kind of flux density to expect. I'm guessing picoTesla (wild guess) or less?

Anyone guess what sort of magnetic field a cosmic ray muon might produce, for instance?

 

[Vanadium 50]

This is a classic lesson in making a problem too hard. You have a current element of qv, where q is the charge of a muon and v is the velocity. Calculate the magnetic field from that and you're done.

 

[Bob S]

In order to completely understand the time-dependent field of a single relativistic muon, one way is first to consider a muon at rest, and then transform it to a relativistic reference frame using the Lorentz EM transformations. See the last four lines in:
http://pdg.lbl.gov/2009/reviews/rpp2009-rev-electromag-relations.pdf
The last four equations deal with the relativistic transformation of electric and magnetic fields. At rest, the muon has no external magnetic field. So only the last equation can transform an electric field of the muon at rest to a magnetic field of a relativistic muon.

[Added note] If you are 1 cm away from a muon with gamma = 10, the magnetic field pulse is picoseconds wide.