Explain the reason behind electromagnetic induction of closed loop wires Don't mistake me for asking why Faraday's law of induction works fundamentally. (I know there exists duplicates if that was my question). Firstly, I can explain why when a straight infinite wire moved in a magnetic field with a velocity, an E.M.F is generated or basically current is generated with the help of Lorentz force law.
But my teacher told that even when a closed loop of wire is present in a magnetic flux,  and the flux was changed suddenly still tiny amounts of current flow through the wire or current is generated. I'm not able to explain it with lorentz law. What is the reason or math or physics concept behind the generation of this current? 
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... even when a closed loop of wire is present in a magnetic flux, and the flux was changed suddenly still tiny amounts of current flow through the wire or current is generated.

You know the rule of the right hand. The thumb is the magnetic field, the second finger is the moving charge and the resulting deflection occurs in the direction of the third finger. The last one must always point in the direction that is perpendicular to the first two fingers.
In principle this is all you need. A subtlety is that a changing strength of the magnetic field (pictorially the length of the thumb) changes the amount of deflection or displacement of the charges (pictorially the length of the third finger).

I'm not able to explain it with lorentz law.

Now you are able. Than more, you are able to see, why a charge, moving in the direction of the magnetic field, not gets deflected. Simply the length of the third finger, calculated as a vector product is zero in this case.
Even more, now you are able to explain the Hall effect, which is nothing else as some part of a current loop. In other words, making the conductor plate big enough you get a circular current for a changing magnetic field.

What is the reason or math or physics concept behind the generation of this current?

It's a bit tricky. Maybe you know that charges have an electric charge that manifests itself through their intrinsic (inner) electric field around the charge. Less emphasized is the fact that electrons also have an intrinsic magnetic field. These two fields, the external magnetic field and the intrinsic magnetic field, interact and we are talking in these cases about the Lorentz force.
More often - for the electron - it is to talk about its spin, which was discovered exactly in this way; the interaction of these two fields leading to the lateral deflection of a moving charge. Not knowing or not caring too much about electrons magnetic field, the scientists saw the analogy to the gyroscopic effect and the name spin was born.
It’s all about deflection. The Hall effect, the Lorentz force, the electromotoric and so on, they all based on the right hand rule and its derivatives.
