Epsilon Naught Value: Definition, Formula & Permittivity

Epsilon Naught is the symbol used to represent the vacuum permittivity, which is the value of the absolute dielectric permittivity of a medium. It is also known as epsilon zero and denoted by ε₀. Epsilon Naught is a physical constant that represents the absolute dielectric permittivity of a vacuum. 

• Epsilon Naught value is constant in any part of the universe. 
• It is synonymous with absolute permittivity and is represented by the Greek alphabet ε₀. 
• Epsilon Naught is described as a vacuum’s ability to ease the flow of electric field lines. 
• The dielectric constant of a material is calculated using Epsilon Naught. 
• It can also be pronounced as Epsilon Zero. 

Key Terms: Epsilon Naught, Dielectric Constant, Permittivity, Coulomb's Law, Relative Permittivity, Dielectric Permittivity, Electric Constant, Electric Field, Epsilon

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What is Epsilon Naught?

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Epsilon Naught is defined as the permittivity of free space that is commonly known as Vacuum Permittivity or Electric Constant.

• It may be also referred to as the distributed capacitance of the medium.
• It is the measure of how dense an electric field is permitted in a medium.
• The dielectric or insulating material has a unit of permittivity, and it is known as the Epsilon. 
• A vacuum’s ability to ease the flow of electric field lines can be quantified with Epsilon naught.
• During the formation of an electric field, we receive a measure of the opposition, known as permittivity.
• Free space has dielectric permittivity and is represented by the epsilon naught value.
• The dielectric constant of a material is also calculated using the value of epsilon naught.

Epilson Naught

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Epsilon Naught Value

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The CODATA Value of Epsilon Naught is 

It has relative uncertainty with a value of 1.5 x 10^-10.

The classical vacuum allows the electric field when it receives a capability of permittivity of free space also noted as ε₀.

The defined values of Epsilon Naught are as follows:

• ε₀ = 8.854187817 x 10^-12 F. m^-1 (SI Unit)
• ε₀ = 8.854187817 x 10^-12 C²/N.m² (CGS Unit)

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Epsilon Naught Units

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The permittivity of free space (ε₀ ) is expressed using both the SI unit and CGS unit. The Epsilon Naught units are as follows:

• SI Unit: F.m^-1 or Farad per meter.
• CGS Unit: C²/Nm² or Columb square per Newton meter squared.

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Epsilon Naught Value Formula

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The dimensional formula of Epsilon Naught is M^-1L^-3T⁴A².

Derivation of the Formula of Epsilon Naught

As derived by Coulomb’s law,

F = (1/4π ε₀) q₁q₂/r²

ε₀= (1/4πF) q₁q₂/r²

So, F = M¹L¹T^-2

q = IXT = AxT¹

Then, ε₀ = (1/M¹L¹T^-2)(AT¹ X AT¹)/L²

ε₀ = M^-1L^-3T⁴A²

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Permittivity

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Permittivity of Free Space defines the capability of a vacuum to allow electric fields. It is denoted by ε₀ or epsilon-naught which is also connected to the energy stored within an electric field and capacitance.

The SI unit of the permittivity is F/M (Farad per meter).

F/m = C/V.m = C²/N.m² = A².s⁴/kg.m³ = N/V²

Electric Field Lines

Permittivity is categorized into three different types:

1. Permittivity of Substance (ε)
2. Permittivity of Free Space (ε₀)
3. Relative Permittivity (ϵ_r)

Permittivity of free space is referred to as Epsilon Naught. The free space is a space in which matters do not occupy. The permittivity of free space is used to identify the force using Coulomb's law between the two charged particles. Insulator’s capacitance is also found using the permittivity of free space.

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Things to Remember

• Epsilon Naught helps to quantify the ability of a vacuum to ease the flow of electric field lines.
• Permittivity is the measure of the opposition during the formation of an electric field. 
• The CODATA value of epsilon naught is ε₀ = 8.8541878128(13) x 10^-12 F. m^-1.
• The relative uncertainty of Epsilon Naught is 1.5 x 10^-10.
• Epsilon Naught dimensional formula is given as M^-1L^-3T⁴A². 
• The SI unit and CGS unit express the permittivity of free space. 
• The SI Unit is F. m-1 or Farad per meter and CGS Unit is C²/Nm² or Columb square per Newton meter squared.

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