Why does magnetic dipole moment $\vec{\mu}=\gamma \vec{L}$?

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:

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

• 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. – FGSUZ Feb 28 at 0:33
• @FGSUZ what would be the correct expression for $\vec{L}$ then? – TaeNyFan Feb 28 at 0:36
• r is the radius from the axis to the particle. It is perpendicular to the axis. – FGSUZ Feb 28 at 0:39
• you could define the origin to be at the particle and then $L=0$...if you were choosing arbitrary origins. – JEB Feb 28 at 1:23