How does electromagnetic induction work on an atomic level? So far I have come to know that changing magnetic field (or flux) creates current. This is also known as Faraday's law of electromagnetic induction. The direction of the current is opposite to the change occurring in the circuit.
But why is the current induced at the atomic level? I don't want to end up accepting it as an unclear phenomenon to me. In fact, I know the reason for the magnetic properties of matter. So I'm interested to know the reason for electromagnetic induction.
 A: 
So far I have come to know that changing magnetic field (or flux) creates current, also known as Faraday's law of electromagnetic induction.

This is a mis-statement of Faraday's law of induction. Faraday's law, $\nabla \times \vec E = -\frac{\partial}{\partial t} \vec B$ says that a changing magnetic field creates a curling E field, not a current. That is purely an EM field phenomenon and has nothing whatsoever to do with atoms, the atomic level, or matter.
Matter can respond to that E field, e.g. by Ohm's law, to produce a current. When that happens the explanation will be related to the matter by whatever principle connects the atomic level to the macroscopic constitutive relationship. For conductive materials that will be something like the Drude model or its various refinements. For other materials it will be different.
But regardless of the type or presence of matter, the induction is a field phenomena that must be understood as a field phenomena and not as some atomic thing.
A: A changing magnetic field induces an electric field not current but even that phrasing is questionable for this induces that is not really in the sense of causality. For example, you do get $\oint_{\mathcal L} \mathbf E \cdot d\ell =-\frac{d\Phi}{dt} \ne 0$ over any closed contour $\mathcal L$ irrespective  whether the contour is representing the filament of a physical conductor or just an idealized locus of integration. Instead, one can only say in full generality that a time varying magnetic (electric) field is always balanced by electric (magnetic) field vorticity. This, I believe, also answers your question to the extent I understand it.
