# Electric constant

The electric constant, or vacuum permittivity, earlier called the absolute dielectric permittivity and dielectric permittivity of vacuum, is a physical constant, a scalar quantity that:

The electric constant has the dimension of farad per meter.

## Definition

The electric constant ${\displaystyle \varepsilon _{0}}$  is determined with the help of the speed of light ${\displaystyle c}$  and the magnetic constant ${\displaystyle \mu _{0}}$  : [1]

${\displaystyle \varepsilon _{0}\,{\overset {\underset {\mathrm {def} }{}}{=}}\,{\frac {10^{7}}{4\pi \ c^{2}}}\equiv {\frac {1}{\mu _{0}c^{2}}}\approx 8,854187817620\times 10^{-12}}$  F/m.

## Application

The electric constant appears in Maxwell's equations in vacuum, which describe the properties of electric and magnetic fields, as well as electromagnetic radiation, and relate the fields with their sources.

In the matter the material equations of the electromagnetic field are used, while the electric displacement field D is expressed in terms of the electric constant, the electric field strength vector E and the polarization density vector P:

${\displaystyle \mathbf {D} =\varepsilon _{0}\ \mathbf {E} +\mathbf {P} .}$

As a rule, we can assume that ${\displaystyle \mathbf {P} =\varepsilon _{0}\chi \mathbf {E} }$ , where the quantity ${\displaystyle \chi }$  represents a tensor and is called electric polarizability. This expression means that the polarization density vector as a certain reaction of the matter is generated by the vector of the electric field strength in the matter, while the directions of these vectors may not coincide.

In the weak field, the quantity ${\displaystyle \chi }$  has the special name electric susceptibility and it is almost constant, depending on the type of matter and its state. In this case we can write:

${\displaystyle \mathbf {D} =\varepsilon _{0}\ \mathbf {E} +\varepsilon _{0}\chi \mathbf {E} =\varepsilon _{0}(1+\chi )\mathbf {E} =\varepsilon _{0}\varepsilon _{r}\mathbf {E} =\varepsilon _{a}\mathbf {E} .}$

The product of the electric constant by the relative permittivity ${\displaystyle \varepsilon _{r}}$  in this expression is called the absolute electric permittivity ${\displaystyle \varepsilon _{a}}$ .

The electric constant is included in the formulation of the Coulomb's Law, giving the expression for the force acting between two electric charges:

${\displaystyle \mathbf {F} _{12}={\frac {q_{1}q_{2}}{4\pi \varepsilon _{0}r_{12}^{2}}}{\frac {\mathbf {r} _{12}}{r_{12}}},}$

where ${\displaystyle r_{12}}$  is the distance between the charges ${\displaystyle q_{1}}$  and ${\displaystyle q_{2}}$ . If ${\displaystyle \mathbf {r} _{12}}$  is a vector directed from the charge ${\displaystyle q_{1}}$  to the charge ${\displaystyle q_{2}}$ , then the force ${\displaystyle \mathbf {F} _{12}}$  will be the force acting on the charge ${\displaystyle q_{2}}$  from the charge ${\displaystyle q_{1}}$ . From the expression for the force we can see that the electric constant in the system of physical units SI relates the electric charge with the mechanical units, such as force and distance.

## Expression in terms of the vacuum field parameters

In the concept of the force vacuum field [2] it is assumed that the electrogravitational vacuum is filled with the fluxes of particles that create gravitational and electromagnetic forces between the bodies. In particular, the fluxes of charged particles – praons, moving at relativistic velocities and transferring their momentum to the charged matter, are considered to be responsible for emergence of the Coulomb force.

In the model of cubic distribution of the praons’ fluxes, for the electric constant we obtain the following: [3]

${\displaystyle ~\varepsilon _{0}={\frac {e^{2}}{6p_{q}D_{0q}\vartheta ^{2}}}={\frac {e^{2}}{\varepsilon _{cq}\vartheta ^{2}}}.}$

Here ${\displaystyle ~p_{q}}$  is the momentum of praons, interacting with the charged matter; the fluence rate ${\displaystyle ~D_{0q}}$  denotes the number of praons dN coming per time dt through the perpendicular to the flux area dA of one face of the cube, limiting the volume under consideration; ${\displaystyle ~\vartheta =2.67\cdot 10^{-30}}$  m² is the cross-section of interaction between praons and nucleons; ${\displaystyle ~e}$  is the elementary charge; ${\displaystyle ~\varepsilon _{cq}=4\cdot 10^{32}}$  J/m³ is the energy density of the praons’ fluxes for cubic distribution.

In the model of spherical distribution of the praons’ fluxes in space:

${\displaystyle ~\varepsilon _{0}={\frac {e^{2}}{16\pi p_{q}B_{0q}\vartheta ^{2}}}={\frac {3e^{2}}{2\varepsilon _{sq}\vartheta ^{2}}},}$

where the fluence rate ${\displaystyle ~B_{0q}}$  denotes the number of praons dN coming per time dt from the unit solid angle ${\displaystyle d{\alpha }}$  inside the spherical surface dA; ${\displaystyle ~\varepsilon _{sq}=6\cdot 10^{32}}$  J/m³ is the energy density of the praons’ fluxes for spherical distribution.

Hence it follows that the electric constant is a dynamic variable, depending on the parameters of the vacuum field particles.

## References

1. CODATA Value: electric constant. The NIST Reference on Constants, Units, and Uncertainty. US National Institute of Standards and Technology. June 2015. Retrieved 2015-09-25. 2014 CODATA recommended values.
2. Fedosin S.G. The Force Vacuum Field as an Alternative to the Ether and Quantum Vacuum. WSEAS Transactions on Applied and Theoretical Mechanics, ISSN / E-ISSN: 1991-8747 / 2224-3429, Volume 10, Art. #3, pp. 31-38 (2015).
3. Fedosin S.G. The charged component of the vacuum field as the source of electric force in the modernized Le Sage’s model. Journal of Fundamental and Applied Sciences, Vol. 8, No. 3, pp. 971-1020 (2016). http://dx.doi.org/10.4314/jfas.v8i3.18, https://dx.doi.org/10.5281/zenodo.845357.