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If a conducting material is placed in an external electric field, the free electrons respond to the field. There is a charge redistribution due to the field. The free electrons inside the conductor move opposite to the direction of the external field. As a result one face gets negatively charged and the opposite face positively charged. Such charge redistribution produces an extra electric field ( inside the conductor) which is equal and opposite to the external field. The net electric field inside the conductor is then zero. Thus, a steady state is reached in which some positive and negative charge appear at the surface and there is no electric field inside the plate.
Now we can say 'According to Gauss's law since the electric field inside the conductor is zero, the charge enclosed by the Gaussian surface should also be zero."
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