I What does the magnetic moment of a particle depend on?

[joegibs]

Every magnetic object has a magnetic moment. From electrons to molecules, to even planets.
But my question is, what determines how much of a magnetic moment a quantum object has? I'm not sure if "how much" is the right word for it. What determines the "quantity" of a magnetic moment of a particle? Still not sure if quantity is the right word. But anyway, does the magnetic moment of a quantum particle depend on mass, charge, ect? Or is it just an intrinsic property that a particle has, and is not dependent on anything?

 

[Khashishi]

It's not a free parameter. The gyromagnetic ratio for an electron has been accurately predicted to 12 decimal places or so, and this is one of the successes of quantum field theory. Sorry, I don't know much more about it.

 

[John Park]

For elementary particles, the magnetic momentum depends on the angular momentum and the mass, though not necessarily in a simple way. For similar particles the magnetic moment increases with the angular momentum*. For particles of the same spin, the magnetic moment is roughly inversely proportional to the mass. (Both the proton and the electron are spin-1/2 particles; the proton is about 2000 times the more massive, while its magnetic moment is about 700 times smaller.) Charge isn't a good indicator. The neutron is an uncharged particle but is has a respectable magnetic moment--about 70% of that of the proton--which can be interpreted as due to a distribution of charge within the neutron).

*Edit. This is simplistic. The magnetic moments of nuclei are roughly of the same order of magnitude but their actual dependence on spin from element to element looks pretty random to the uninformed eye. Nuclei in this respect are not elementary particles and their internal structure causes the relation between angular momentum and magnetic moment to be quite complex.