# What is electric permittivity?

Answering requests, I will explain what is electric permittivity. Many from the area know as a constant, but there is much more behind.

#### Definitions

It is a measure which determines the substances capacity to resist an electrical field from an induced charge. Represented by Greek letter epsilon $\varepsilon$ and measured in farads/meter (F/m). This is the equation of dielectric constant $\kappa$ or $\varepsilon _{r}$, also called relative permittivity.

$\kappa=\varepsilon _{r}=\frac{\varepsilon }{\varepsilon _{o}}$

• $\varepsilon_{o}$ is the electric permittivity of vacuum, which values $8,854\cdot 10^{-12}F/m$;

In the presence of an electric field, the materials molecules form electric dipoles inside it’s structure and are oriented by electric field. Depending on the material, the electric field can modify the dielectrics molecular structure. This is the equation of electric flux density $\vec{D}$ in Coulomb by square meter $[C/m^2]$.

$\vec{D}=\varepsilon \vec{E}$

• $\vec{E}$ is the electric field in V/m.

$\chi _{e}$ is the materials electrical susceptibility and calculated in this way.

$\chi _{e}=\varepsilon _{r}-1$

This is the dielectric constant table of some materials. Other material’s constant can be found in this link.

#### Polarization

Other way to calculate flux density $\vec{D}$:

$\vec{D}=\varepsilon _{o}\vec{E}+\vec{P}$

$\vec{P}$ is the polarization vector in $[C/m^2]$. Polarization is the change of charge distribution in a dielectric (insulating) due to electric field. Can be calculated in this way:

$\vec{P}=\chi _{e}\varepsilon _{o}\vec{E}$

#### Complex permittivity

With alternate current or electromagnetic wave, the polarization don’t change instantly in the presence of an electric charge, producing a phase difference. For that, the dielectric constant has real and imaginary parts.

$\varepsilon =\varepsilon _{o}\varepsilon _{r}=\varepsilon _{o}(\varepsilon '-j\varepsilon '')$

The real part $\varepsilon '$ represents the quantity of stored energy of electrical field in the material, in addition to change the relation between the electric and magnetic fields. While the imaginary part $\varepsilon ''$ represents the material’s losses to an external field. The relative permittivity form an angle with the real part, this angle’s tangent is called loss tangent.

$tan(\delta) =D=\frac{1}{Q}=\frac{\varepsilon'' }{\varepsilon '}$ • $D$ is the dissipation factor.
• $Q$ is the quality factor.

This is the loss tangent table of some materials. Loss tangent of other materials can be found in this link.

#### Changing electric permittivity

The dielectric constant can change with frequency, temperature and other physical properties. The chemical connections in the material determine how relative electric permittivity will change with the frequency. Many materials has a stable relative permittivity until the microwave or megahertz frequency. In transition regions of polarization, the real part (Dk) fall out with the increase of frequency and loss tangent (Df) increases.   