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I started studying about how a conductor behaves once placed inside an electric field E0 . The electrons will move inside the conductor according to the electric filed's direction gathering at one side of the conductor leaving the other positive.

This is what that looks like

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After this process the electric field inside the conductor will be zero. How am I sure that the object has enough electrons to create the required field E1 to cancel the outside field E0. That field could be huge and the object definitely has finite electrons.

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Compare the number of electrons in a Coulomb to the number of molecules in a mole. There are a lot of electrons in something like copper.

Any E field that would require more than a tiny fractions of the electronics in a conductor to slosh from one end to the other, the E field would be so strong that it would arc and generally be unsustainable.

As a exercise, calculate the E field required to displace just one Coulomb from one side of a copper penny to the other. You will see it would need to be unrealistically large. Then compare that Coulomb of electrons to the total number of electrons even just in the outer conduction band of all the copper atoms in the penny. You'll see that number is vastly higher then one Coulomb.

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