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

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The discussion focuses on calculating the magnetic dipole moment of cyclotron motion within a Penning trap, specifically as a function of the cyclotron quantum number and expressed in terms of Bohr's magnetron. Participants clarify that the magnetic dipole moment is defined as the product of current and the area enclosed by that current. The inquiry is confirmed as a homework question, prompting further exploration of relevant physics concepts, including angular momentum and current due to charged particle motion. A key formula derived in the discussion is μ = (-e/2m)L = IA, which relates the magnetic dipole moment to angular momentum and current. The thread emphasizes the importance of understanding these relationships in advanced physics contexts.
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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
 

Thread 'Help with derivation of electric field of a moving charge'

At first, I derived that: $$\nabla \frac 1{\mu}=-\frac 1{{\mu}^3}\left((1-\beta^2)+\frac{\dot{\vec\beta}\cdot\vec R}c\right)\vec R$$ (dot means differentiation with respect to ##t'##). I assume this result is true because it gives valid result for magnetic field. To find electric field one should also derive partial derivative of ##\vec A## with respect to ##t##. I've used chain rule, substituted ##\vec A## and used derivative of product formula. $$\frac {\partial \vec A}{\partial t}=\frac...
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