Faraday’s law

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The opposing (or induced) emf produced by an inductor is a characteristic of the non-Coulomb electric field (NC) that is proportional to the rate of change in current causing a changing magnetic field. And that is Faraday's Law.
The current is a result of the combination of an opposing Coulomb electric field and the applied field which is changing the current. The opposing Coulomb (C) field is a result of polarization of the inductor by the non-Coulomb (NC) electric field. So, the current is a consequence of the resultant field of the applied field and the Coulomb electric field in the inductance coil and is determined using the governing relation in conductors J = σE_net. If the resistance of the solenoid is very small, the magnitude of the two electric fields is nearly equal (E_C ~ E_NC).
It is not possible in this post to discuss in more detail the formation of the Coulomb field when the current in an inductor is changed.
Before learning Faraday's Law and its application to the operation of inductors, it will be instructive to understand Current, the conduction process and Voltage at the fundamental level as in the following two videos:
i. ruclips.net/video/TTtt28b1dYo/видео.html and
ii. ruclips.net/video/8BQM_xw2Rfo/видео.html
The last frame References in video #1 lists textbooks 3 and 4 which discusses topics on inductance and inductors in more detail using a unified approach and provides an intuitive understanding of inductive reactance.
It also describes with sequential diagrams how an inductor develops the induced emf. Textbook 4 shows how the current lags the voltage across the inductor by 90 degrees for sinusoidal input voltages using sequential diagrams.