Define electric displacement vector D  and deduce Gauss’s law for dielectrics.

Electric Displacement Vector (D):

In the realm of electricity and magnetism, the electric displacement vector, denoted as \( \mathbf{D} \), plays a crucial role in describing the response of a dielectric material to an electric field. The electric displacement vector is defined as the electric flux density, which is the electric flux per unit area (\( \mathbf{D} = \epsilon_0 \mathbf{E} + \mathbf{P} \)), where:

- \( \mathbf{D} \) is the electric displacement vector,
- \( \epsilon_0 \) is the vacuum permittivity (a fundamental constant),
- \( \mathbf{E} \) is the electric field vector,
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