Electric field inside a conductor not zero (1 Viewer)

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1. The problem statement, all variables and given/known data
Is it possible to create an electric field such that a neutral conductor will experience a net electric field inside?

2. Relevant equations

3. The attempt at a solution
The definition of perfect conductor is that there are an infinite amount of charges free to move so that electric fields will cancel on the inside. How about the case for the not ideal conductor? Will there be a point where the electric field is so strong that the finite amount of free charge to distribute will not cancel it on the inside of the conductor? What are such examples in the physical world?
What are your thoughts?
Griffiths says that charge will continue to flow to the surface of the conductor until the cancellation of the field is complete. However, if there are not enough charges (which may be the case in a real conductor), the total cancellation may not be complete, resulting in a net E field inside. If there's a net E-field, the charges inside the conductor will keep moving around, perhaps forever. Does this violate some sort of conservation law?
In that case, uncanceled electric field's direction is the same of external electric field.
Which means there's no eternal flow of charges inside the unideal conductor.
As a result, the conductor will experience the force which is attempting to destroy
the conductor cuz (-)charges on one side of conductor are heading opposite to
external EF and (+) charges on the other side of conductor are heading to the same direction
of external EF.

Is there any wrong point in my reply? I'm not sure about this explanation, so plz
other people to explain this problem in the right way. :-)

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