What basically happens to the electrons, does the magnetic field produced by the electron moving in the inductor affect itself. what are the forces involved? Please elucidate the mathematics.
The question is; Can you take me through the inductor as an electron ?
In an inductor, one has many electrons moving and accelerating in the same direction. In EM theory, lots of same-signed charges accelerating in the same direction means there will be additional electric field near those electrons, called the acceleration field. If this field is due to negatively charged particle such as an electron, it has a component pointing in the same direction as the particle's acceleration.
The acceleration field is proportional to charge and acceleration of the source particle. It also gets weaker with distance and has a particular angular intensity pattern, the same as a dipole antenna.
The acceleration field from a single electron is strongest at points whose radius vector with respect to the source is perpendicular to the line of acceleration. In an inductor, due to the way the wires are wound and fixed, the very electrons producing the acceleration field are at such points. In fact in an inductor, the wires are purposely fixed in space in such a way so that the electrons get under action of their own acceleration field as much as possible.
This field and arrangement of wires has such an effect on the electrons that their resistance to change of their velocity is increased. The resistance force is proportional to their acceleration, thus it increases their effective mass. One can say that inductor manifests great inertia for electric current because of the acceleration field of the electrons opposing their common acceleration. Thus it is all due to mutual interaction of the accelerated electrons.
Neither of the above requires that a single electron acts on itself. It is sufficient to assume that electron is under action of electric fields of different electrons.
EDIT: If you're wondering how emf and magnetic flux arise from this description, here it is: all the acceleration fields of the electrons add up to total electric field that has solenoidal ("curly") nature and is the force causing the presence of emf in an inductor. It so turns out, due to Maxwell's equations, that magnitude of this emf is proportional to rate of change of magnetic flux through the cross section of the inductor and the number of coils ("winding number"). Magnetic field action on the electrons is there as well, but it does not have an important effect on their motion, as opposed to the effect of the acceleration electric field (the magnetic forces push on the electrons to expand the coils out, but this is usually too weak to matter, or, if not, is prevented by robust fixing of the wires in the inductor component). Magnetic flux just quantifies the intensity of the macroscopic induced electric field.
