How to Calculate the Cyclotron Magnetic Dipole Moment in a Penning Trap?

[Izzyg]

Hello, this is a question regarding Penning trap design.

I need to calculate the magnetic dipole moment of the cyclotron motion, as a function of the cyclotron quantum number. The result needs to be given in terms of Bohr's magnetron.

The magnetic dipole moment is defined as current x area enclosed by current.

 

[dlgoff]

I need to calculate the magnetic dipole moment of the cyclotron motion, as a function of the cyclotron quantum number. The result needs to be given in terms of Bohr's magnetron.

Just curious. Is this a homework question?

 

[Izzyg]

Indeed it is. So far I have found

from https://en.wikipedia.org/wiki/Electron_magnetic_moment, but I can't see current x area enclosed there.

Cyclotron quantum number must be

https://en.wikipedia.org/wiki/Landau_levels

 

[PeterDonis]

Is this a homework question?

Indeed it is.

Thread moved to the advanced physics homework forum.

 

[TSny]

So far I have found

from https://en.wikipedia.org/wiki/Electron_magnetic_moment, but I can't see current x area enclosed there

Consider a particle of mass $m$ and charge $q$ moving in uniform circular motion of radius $r$ and speed $v$.

Can you express the angular momentum $L$ in terms of $m$, $r$ and $v$?

Can you express the current $I$ due to the motion of the charge in terms of $q$, $r$ and $v$?

 

[Izzyg]

TSny, thank you for your message, really helpful. I think I've now found what I need: μ = (-e/2m)L = IA