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# Permittivity

In electromagnetism, the permittivity ε of a medium is the ratio D / E where D is the electric displacement in coulombs per square metre (C/m2) and E is the electric field strength in volts per metre (V/m).

Permittivity is specified in farads per metre (F/m). It can also be defined as a dimensionless relative permittivity, or dielectric constant, normalized to the absolute vacuum permittivity ε0 = 8.854 10-12F/m.

When an electric field is applied, a current flows. The total current flowing in a real medium is in general made of two parts: a conduction current and a displacement one. A perfect dielectric is a material that shows displacement current only.

The permittivity ε and magnetic permeability μ of a medium together determine the velocity of electromagnetic radiation through that medium.

$\epsilon \mu = \frac{1}{v^2}$

In a vacuum, these are given by

$\epsilon_0\mu_0 = \frac{1}{c^2}$

where μ0 is the magnetic constant, or permeability of free space, equal to 4π × 10-7 N·A-2, and c is the speed of light, 299,792,458 m/s.

In case of lossy medium (i.e. when the conduction currents are not negligible) the total current density flowing is:

$J_{tot}=J_c+J_d=\sigma E + j \; \omega \epsilon_0 \epsilon_d E = j \; \omega \epsilon_0 \epsilon^* E$

where $j = \sqrt{-1}$, σ is the conductivity (responsible for conduction current) of the medium and εd is the relative permittivity (responsible for displacement current).

In this formalism the complex permittivity ε* is defined as:

$\epsilon^* = \epsilon_d - j \frac{\sigma}{\epsilon_0 \omega}$

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