I tried to understand by my own couldn't do so.
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2$\begingroup$ Your "If" is in the case of electroSTATICS. Conducing electricity is electroDYNAMICS. There is an electric field inside metals when they keep a constant and steady DC flow of electricity. $\endgroup$– naturallyInconsistentCommented Apr 12 at 7:39
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1$\begingroup$ Also relevant: "How is electric current possible if no electric field exists inside a conductor?", "Is the electric field zero inside an ideal conductor carrying a current?", "Is there no electric field inside a conductor?", "Why is current through the short circuited wire not zero?", …. $\endgroup$– David BaileyCommented Apr 12 at 13:52
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Well you mentioned in your question already that the electrons will be moving to cancel out an electric field. That means an electric field applied to a metal will cause a current in the metal. I am not quite sure what else you would mean with “conducting electricity”.
Now if you have a time constant external electric field the charge transport of your current will eventually screen the inside of the metal from the outside electric field. A voltage source on the other hand can cause a constant electric field inside a metal. But to do so it will have to constantly supply new charge to counter the charge movement inside the metal, so it will not be an equilibrium system.
You actually can easily calculate the electric field inside a conductor with homogeneous resistance connected to a voltage source. All you need to do is differentiate the voltage-drop with respect to the position inside your conductor, which in this trivial Ohms-law-example just means dividing the voltage through the conductor length. Then integrating back the electric field over your conductor you will restore the Voltage.
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$\begingroup$ How can electron flow without having an electric field, as my book says electric field can't go through conductors , even electric charge of a conductor resides entirely on the outer surface. $\endgroup$ Commented Apr 12 at 8:38
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$\begingroup$ @AaravRaj That statement of yours is only true, if the electrons in the metal have enough time to react on the field. In a static or slowly changing situation this will be the case, in a dynamical situation this will not necessarily be the case. $\endgroup$– ZaphCommented Apr 12 at 12:00
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$\begingroup$ Can you please explain a bit, how things go in dynamic situation or atleast tell me any resource where can i learn more about it. $\endgroup$ Commented Apr 14 at 7:09
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$\begingroup$ @AaravRaj Well the easiest way to think of it is, that the movable charges need some time to react to a perturbation of the equilibrium configuration caused by an external field change. As a result of the reaction, there will be some currents and if the perturbing fields then stay constant and you have some damping effects in your system you will eventually end up in a new static equilibrium situation, where no forces act on your charges, which means your charges are screened form the fields. $\endgroup$– ZaphCommented Apr 14 at 11:18
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$\begingroup$ @AaravRaj As for the details, that stuff is really complicated and an active field of science. To get an idea of how complicated it is, you might take a look at “Quantum Theory of the Electron Liquid” by Gabriele F. Giuliani, Giovanni Vignale. That thing surely will contain all the available information you might be interested in, when it comes to systems of charges reacting to external perturbations, and a lot more. $\endgroup$– ZaphCommented Apr 14 at 11:20