Define the electric displacement vector . Starting from Maxwell's equations, deduce Gauss's law in dielectric media. Explain the physical significance of bound and free charges.
The electric displacement vector (\vec{D}) is defined as [ \vec{D} = \epsilon_0 \vec{E} + \vec{P} ] where (\vec{E}) is the electric field, (\epsilon_0) is the permittivity of free space, and (\vec{P}) is the polarization vector representing the dipole moment per unit volume of the dielectric material. In a linear, isotropic dielectric, (\vec{P} = \chi_e \epsilon_0 \vec{E}), giving (\vec{D} = \epsilon \vec{E}), where (\epsilon = \epsilon_0 (1+\chi_e)) is the permittivity ___ __________ _____ ________ ________ ______ ______ ________ ________ _________ ___ ___.
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