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I get it that the free electrons inside the conductor redistribute themselves to make the net field 0 but shouldn't that depend on the material used that how many free e- it has or to what extent the e- can redistribute?

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The net electric field inside a conductor is not always zero. The electric field is 0 inside a conductor if the situation is electrostatic.

Conductors obey Ohm's law $\vec J = \sigma \vec E$ where $\vec J$ is the current density, $\sigma$ is the conductivity of the conductor, and $\vec E$ is the E field. So since the situation is electrostatic then $\vec J=0$. And since $\sigma \ne 0$ for a conductor, we immediately get that $\vec E = 0$.

But this outcome depended both on the material being a conductor, so that it follows Ohm's law, and also on the situation being electrostatic, so that $\vec J=0$. When $\vec J \ne 0$ then $\vec E \ne 0$ by the same logic.

Dale
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