I have read there are two ways to express the force caused by a variable magnetic field over a magnetic moment depending on the source of the magnetic moment since it can come from a dipole or a loop of electric current.

A dipole would be a pair of magnetic charges with opposite sign aligned over an axis, the magnetic field exerts a force over the magnetic charges similar to the force that electric field exerts over “normal” charges. A loop of electric current is just a loop with electric charges moving through it.

The force suffered for the magnetic momentum has different expression on each case.

For the dipole it is:

$F_{dipole} = (\mathbf{\mu} \cdot \triangledown) \mathbf{B}$

And for a loop of current:

$F_{loop} = \triangledown(\mathbf{\mu} \cdot \mathbf{B})$

The relation between them is:

$F_{loop} = F_{dipole} + \mathbf{\mu}\times (\triangledown \times \mathbf{B})$

Which means that, as long as there are no currents or time-varying electrical fields both expressions are the same.

My question is: does the electron spin obey any of these two expressions?

I have read some explanations about the Stern - Gerlach experiment in which a gradient in a magnetic field deviates electrons but I could not find how the magnetic field was or how much the electrons were deviated.


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