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

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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.
 
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Izzyg said:
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?
 
Indeed it is. So far I have found
{\displaystyle {\boldsymbol {\mu }}={\frac {-e}{2m_{\text{e}}}}\,\mathbf {L} \,,}
from https://en.wikipedia.org/wiki/Electron_magnetic_moment, but I can't see current x area enclosed there.

Cyclotron quantum number must be
{\displaystyle E_{n}=\hbar \omega _{\rm {c}}\left(n+{\frac {1}{2}}\right)+{\frac {p_{z}^{2}}{2m}},\quad n\geq 0~.}
https://en.wikipedia.org/wiki/Landau_levels
 
dlgoff said:
Is this a homework question?
Izzyg said:
Indeed it is.
Thread moved to the advanced physics homework forum.
 
Izzyg said:
So far I have found
{\displaystyle {\boldsymbol {\mu }}={\frac {-e}{2m_{\text{e}}}}\,\mathbf {L} \,,}
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##?
 
TSny, thank you for your message, really helpful. I think I've now found what I need: μ = (-e/2m)L = IA
 

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