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I have often seen that the relationship between magnetic dipole moment $\vec \mu$ and angular momentum $\vec{L}$ expressed as $$\vec{\mu}=\gamma \vec{L} $$

But consider a current loop of a charged particle in this diagram:enter image description here

The magnetic moment $\vec \mu$ and angular momentum $\vec{L}$ points in different directions. How then is $\vec{\mu}=\gamma \vec{L} $ still valid?

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  • $\begingroup$ Wrong radius. It means angular momentum respect to the axis, not respect to a point. Because you can choose the origin anywhere you want, that's not giving information. In contrast, w.r.t the axis is an objective manner. $\endgroup$ – FGSUZ Feb 28 at 0:33
  • $\begingroup$ @FGSUZ what would be the correct expression for $\vec{L}$ then? $\endgroup$ – TaeNyFan Feb 28 at 0:36
  • $\begingroup$ r is the radius from the axis to the particle. It is perpendicular to the axis. $\endgroup$ – FGSUZ Feb 28 at 0:39
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    $\begingroup$ you could define the origin to be at the particle and then $L=0$...if you were choosing arbitrary origins. $\endgroup$ – JEB Feb 28 at 1:23

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