If metals can’t sustain an electric field inside them (as their electrons move to cancel it out), how do they still conduct electricity?

Question

I tried to understand by my own couldn't do so.

Answer 1

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.