I have a good understanding of how inductors behave in electrical circuits, and a somewhat rough-and-ready understanding of how this behaviour arises from Maxwell's equations. However, what I don't have a good mental picture of is how electromagnetic induction works on the microscopic level, i.e. in terms of forces experienced by individual electrons in the wire. Ideally I would like to be able to understand the operation of an inductor, at least qualitatively, in terms of the statistical mechanics of the electron gas in the coil and the electron spins in the core.
To clarify: in Maxwell's equations there is a term for $I$, the electric current. But current is a macroscopic quantity - it's the expected number of charges passing through a surface, with the expectation taken over an ensemble. So Faraday's law is a macroscopic relation, just like the gas equation. For the gas equation, we can understand how it arises from the microscopic motion of molecules. I want to understand how Faraday's law arises from the microscopic motion of electrons.
Would anyone be able to provide an explanation of how induction works in microscopic terms, or point me towards somewhere I can read up on it?