Electric Displacement

#Physics

$\displaystyle \vec{D}\equiv {\varepsilon}{0}\vec{E}+\vec{P}={\varepsilon}{0}(1+\chi_{e})\vec{E}=\varepsilon \vec{E}$

• Electric displacement for a linear media
• $\displaystyle \varepsilon$ is the permittivity of the substance
• $\displaystyle \vec{P}$ is the polarization of an atom
• $\displaystyle \chi_{e}$ is the electric susceptibility of the substance

$\displaystyle \nabla \cdot \vec{D}=\rho_{f}$

• Gauss's law for electric displacement
• $\displaystyle \rho_{f}$ is the free charge density

$\displaystyle \oint D\cdot d\vec{a}=Q_{f_{\text{enc}}}$

• $\displaystyle Q_{f_{\text{enc}}}$ is the total enclosed free charge in the volume