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Suppose a dielectric with no free charges is placed in an electric field (E). Once polarized, the total "volume bound charge " equals total "surface bound charge" right ? In this condition, the external field (E) is exactly equal and opposite to internal field (-E) right?

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The field inside is not equal and opposite to the external field, since it is only a dielectric. A conductor can cancel the field inside totally, a dielectric can only partially cancel it. You will have to solve the problem of finding the electric field by solving boundary conditions of laplace's equation

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