Relative Permittivity

The $\textit{relative permittivity}$ of a material under given conditions reflects the extent to which it concentrates electrostatic lines of flux. In technical terms, it is the ratio of the amount of electrical energy stored in a material by an applied voltage, relative to that stored in a vacuum. Likewise, it is also the ratio of the capacitance of a capacitor using that material as a dielectric, compared to a similar capacitor that has a vacuum as its dielectric. Relative permittivity is a dimensionless number that is in general complex. The imaginary portion of the permittivity corresponds to a phase shift of the polarization $P$ relative to $E$ and leads to the attenuation of electromagnetic waves passing through the medium. $$\epsilon_r(w) = \frac{\epsilon(w)}{\epsilon_O}$$, where $\epsilon_r(w)$ is the complex frequency-dependent absolute permittivity of the material, and $\epsilon_O$ is the vacuum permittivity.