# Spin and its connection to magnetic field

How the intrinsic spin of an electron results in a magnetic field? How does spin couples to the magnetic field? I mean to ask how does the phenomenon of Spin orbit coupling happens physically? Is the electron really spinning or not?

• In order to understand what you mean by "how" here - "how" does the magnetic field couple to ordinary classical angular momentum, in your understanding? – ACuriousMind Oct 17 '17 at 15:31
• @AndreiGeanta : Can you kindly update the link. It seems to be broken. – user35952 Jul 8 at 10:20

The electron is not spinning. Elementary particles are considered to be point-like particles, meaning that they do not have an internal structure. The spin is, as you say, an intrinsic property of particles. It is a pure quantum mechanical property that particles just have. The spin induces a spin magnetic moment: $$\vec{\mu_{s}}=g\frac{q}{2m}\vec{S}$$ So if an external magnetic field is applied, it will exert a torque on the particle's magnetic moment depending on its orientation with respect to the field. $$\vec{\tau}=\vec{\mu}\times\vec{B}$$