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?
 A: 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.
$$\vec{\tau}=\vec{\mu}\times\vec{B}$$
A: Just as said in the other quite exhaustive answers, I would remark that the image 
is physically meaningless! Electrons and elementary particles don't rotate! They can be thought as very tiny balls and so comes the missleading idealization that they can rotate but actually they can't because they must be thought as point-like particles!
By the way, and that's actually another possible source of confusion, Spin is one of two types of angular momentum in quantum mechanics, the other being orbital angular momentum. The orbital angular momentum operator is the quantum-mechanical counterpart to the classical angular momentum of orbital revolution: it arises when a particle executes a rotating or twisting trajectory (such as when an electron orbits a nucleus).
The existence of spin angular momentum is inferred from experiments, such as the Stern–Gerlach experiment, in which particles are observed to possess angular momentum that cannot be accounted for by orbital angular momentum alone. Remeber that there is not a classical analogue of the spin and it must be considered as an intrinsic quantum property of matter!
