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We know that $D=\epsilon_0 E+P$ where'D' is the electric displacement field and takes into account the field due to free carriers.'P' is the polarization and takes into account the field due to bounded charges and 'E' is the fundamental electric field and accounts for both effects of free carriers and bounded charges.

So, shouldn't the 'P' be subtracted from 'E' rather than adding ? Also what is the value of 'D' in vacuum and in a conductor and why ?

Also is displacement current the time rate of change of electric field(E) or electric displacement field(D) ?

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Flux of polarization vector P over a closed surface is negative of the bound charge so there is positive sign instead of negative sign. Susceptibility of vacuum is zero so D in vacuum is permittivity of vacuum times electric field. In conductor electric field is zero so electric displacement D is also zero. Displacement current density is the time derivative of electric displacement vector.

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