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Epsilon Naught

Epsilon Naught (εo)

Epsilon Naught, written ε0 (also called epsilon zero), is the permittivity of free space. It means that the value of ε0 decides the strength of the electric field in the free space. If the permittivity of a medium is high, it will easily get polarized when subjected to an electric field. ε0 specifically describes the permittivity of the vacuum. A vacuum is defined as a region of space devoid of any matter.

When it was first discovered, it was called by several different names. Today, the common name of the constant is ‘electric constant’. Some older texts also used the term ‘dielectric constant of the free space’ to describe epsilon naught. It was at that time; the electric constant was used interchangeably with the term dielectric constant. However, today, the dielectric constant is exclusively used to refer to the value describing ε/ε0 (it is a unitless number that describes the relative permittivity of a medium with respect to the vacuum.)

Even the term ‘dielectric constant’ is being rejected by scientists today. They prefer to use a new term for ‘dielectric constant’ called ‘relative static permittivity’. However, even today, some texts can be found that use the term ‘dielectric constant of the free space’.

Formula

The formula for the absolute permittivity of free space can be derived with the help of Coulomb’s law. Coulomb’s law states:

2

Here, F is the force between two electric charges q1, q2 are the two charges r is the distance between the two charges

Rearranging the above equation, we get the value of

3

Value of ε0

The scientifically calculated value of absolute permittivity is a universal constant. The approximate value is: 

4

Units and Dimensions

The SI unit of absolute permittivity is Farad per meter (Fm-1) The dimensions of absolute permittivity can be found by replacing the respective dimensions of all the variables in Eq. 1. On doing so, we get the dimensions of absolute permittivity as, ε0 = [M-1L-3T4A2]

Uses of Absolute Permittivity of Free Space

ε0 is widely used to determine the force between two electric charges kept at a certain distance. It is also used to determine the dielectric constant of a material. The relative permittivity is often determined against the permittivity of free space as vacuum is found all around us.

It is used for determining capacitance as the formula for determining capacitance is: C = εAD

Here, A is the area between the plates of a capacitor D is the distance between the plates of a capacitor

It is also used in Gauss’ law. Gauss’ law states the relationship between the electric flux passing through a closed surface and the amount of charge enclosed by that surface. Both the quantities are directly proportional to each other. This is expressed as: EdA = 10Qenclosed

Here, E is the electric field A is the area of the enclosing surface Qenclosed is the charge enclosed by the enclosing surface.

Recent Developments

In 2019, ‘Ampere’ was redefined in terms of a specific number of Coulombs. This caused the value of the vacuum permittivity to become a measured value rather than a mathematically defined value. The electron was also redefined to having a certain charge. The magnetic permeability μ0 is now also a measured constant.

Relative Permittivity

The relative permittivity of a material is defined with respect to vacuum permittivity. The formula for finding relative permittivity is: ε = (1 + χ)ε0 Here, χ is defined as the electric susceptibility of the material.

Few Key Points

  • The permittivity of a medium is measured using dielectric spectroscopy. In dielectric spectroscopy, the dielectric properties of a medium are measured as a function of frequency. The results are compiled on the observation of interaction between the external field and the permittivity of the sample.
  • In the quantum mechanical model, the permittivity is described by the atomic and molecular interactions. At lower frequencies, the polarized molecules perform periodic rotations. When energy is supplied to such molecules, the field works against the bond. This is also the working principle of the microwave. The Microwave frequency provides energy to the hydrogen bonds of water. The dielectric field of water does work against the breaking of bonds, and the water gets heated. Thus, the energy produced by the microwave and the energy expended in breaking the bonds is both used to cook the food. At moderate frequencies, the energy is absorbed as part of the resonant molecular vibrations.

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