Permittivity

Remarks

For a linear anisotropic material, $D = \varepsilon E$ with a $3 \times 3$ matrix $\varepsilon$, the permittivity tensor. For time-harmonic fields the permittivity depends on the frequency and may be complex, with the imaginary part describing absorption. Example: in a medium of constant permittivity $\varepsilon$, a point charge $q$ at $0$ has $D = q x / (4 \pi \abs{x}^3)$ and $E = q x / (4 \pi \varepsilon \abs{x}^3)$, so the field is weaker than in vacuum by the factor $\varepsilon_r$. Non-example: a ferroelectric material has a polarization that is not proportional to $E$ and shows hysteresis, so it has no permittivity in this sense. In SI units $\varepsilon_0 \approx 8.854 \times 10^{-12}$ farad per metre.