Definition, Types, Units, and Uses of the Epsilon Naught Value

• Eastern Eye Staff
• 25 November, 2020

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By: Eastern Eye Staff

The Epsilon Naught value or ε0 is also called the Epsilon zero. It is the permittivity of the free space. In simple terms, ε0 is used to determine the strength of the electric field in the free space. If the permittivity of any medium is high, then it gets polarised easily when it is subjected to an electrical field. 

So what exactly is the Epsilon value? The Definition of Epsilon Naught Value is simple. It is the permittivity in a vacuum. A vacuum is a space that does not contain any matter.

When permittivity was first discovered, then it was known by several names. The common name used for this constant is the “electric constant.” Some old tests use the term “dielectric constant of free space”, which also means ε0. Earlier, “electric constants” and “dielectric constants” were used interchangeably. However, today, the dielectric constant is used to describe the ratio between ε and ε0. This number is unitless and describes the medium’s relative permittivity to the vacuum.

Understand Epsilon Naught Value

The Epsilon Naught is represented as ε0 and is the value of the absolute dielectric permittivity in an absolute vacuum. It is also called the electric constant. The value of the ε0 is :

• ε0 = 8.8541878128(13)×10−12 F⋅m−1 (farads per meter), with a relative uncertainty of 1.5×10−10. This is in the SI unit. 
• ε0 = 8.854187817 × 10-12 C2/N.m2 (In CGS units)

Many tend to misuse the Epsilon Naught as the value of Epsilon not.

Permittivity refers to the opposition’s measure that is put against the electric field formation. This is the capability of the electric field to permeate through a vacuum. The constant relates the electric charge units to the mechanical quantities like force and length.

Historically, ε0 was referred by various names. The terms vacuum permittivity and permittivity of vacuum were used for it. It was also referred to as the permittivity of space. The standard organization across the world has made electric constant the uniform term to represent this quantity. The earlier terms, however, are still used as a synonym.

The dimension formula of Epsilon naught is:

M⁻¹L⁻³T⁴A²

Types of Permittivity

There are three types of permittivity. They are:

• The permittivity of a substance: It is denoted by ε and is the substance’s ability to let the electric current pass through it. This is dependent on its frequency which is ω.
• The permittivity of free space: This is denoted by ε₀ and is the free space’s ability to let the electric current pass through. It is not dependent on the frequency ω.
• Relative Permittivity: It is denoted by εᵣ and is the ratio of the permittivity of a substance to the permittivity of free space. It is dependent on the frequency ω.

Epsilon Naught is synonymous with the permittivity of free space or absolute permittivity, or electric constant.

ε0 is a constant, and it can present any part of the universe.

• Units:

Farad per meter (Fm-1) is the SI unit of absolute permittivity. 

The formula for absolute permittivity in the free space is derived from Coulomb’s law. Here is Coulomb’s law.

F = (1/4πε₀) q1q2/r²           

Where F is the force formed between two electric charges, which are q1, q2. These are the charges. r is the distance between these two charges. When you rearrange the equation, then you get the value of ε0 as:

ε₀ = (1/4πF) q1q2/r²

The value of ε0 is calculated scientifically, and it is a universal constant. 

The relative permittivity of any material is defined with the permittivity to vacuum. The formula that you use to find relative permittivity is: 

ε = (1 χ)ε0 

X is the electric susceptibility of the material.

Uses of ε0

Let us now discuss the various uses of Epsilon Naught. Going through these points will give you why Epsilon Naught is an important constant in physics. 

• ε0 is used to find out the force that occurs between two electric charges which are kept at a distance. It is also used to find out the dielectric constant of any material. The relative permittivity is determined against the free space permittivity as vacuum is all around.
• ε0 is used to determine capacitance and the formula used is C = εAD

Where A measures the area in between the capacitor plates and D is the distance between the capacitor plates.

• You will also use ε0 in Gauss’ law, which states the relationship between the electric flux that passes through a closed surface and the amount of charge enclosed in that surface. The quantities are proportional to each other directly, and it is expressed as 

EdA = 10Qenclosed

Here E represents the electric field, A  is the area of the enclosed surface, and Qenclsoed is the charge in the enclosed surface.

Key points

• The permittivity of any medium is measured with dielectric spectroscopy. The dielectric spectroscopy is used to determine the dielectric properties, which are measured as a frequency function. The results that are compiled are after observing the interaction between the sample permittivity and the external field.
• In the model of quantum mechanics, permittivity is described as per the molecular and atomic reactions. In low frequency, the polarized molecules perform a periodic rotation. When these molecules are supplied with energy, the field starts to work against the bond. This is the principle that is used in a microwave. 

The frequency of the microwave gives energy to the hydrogen bonds in water. The dielectric field of waterworks again breaks bonds, and this causes the water to get heated. The energy that is thus produced by the microwave and the energy that is expended in bond breaking is used for cooking food. 

At a moderate frequency, the energy gets absorbed as a resonant molecular vibration.

Conclusion

The Epsilon naught value represents the value of dielectric permittivity in free space. Experts use this value to calculate the dielectric constant of any material. Epsilon Naught is the ideal physical constant that is representative of the absolute dielectric permittivity in a vacuum.

In simple terms, the Epsilon naught qualifies the ability of the vacuum to facilitate the electric field lines to flow through it.