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• Epsilon Naught – Concept, Meaning, Formula, and Examples

Published on November 20, 2021

Physics is an interesting subject as there are many concepts students learn in this subject close to what we experience every day. For instance, the law of gravitation describes why things fall to the ground and do not move up, how a lightbulb generates light and heat energy, etc. One such crucial concept in Physics is that of Permittivity of space.

Permittivity is a physical attribute of any medium, and it denotes how freely the medium allows an electric field to pass through it. For a medium with low permittivity, an electric field can pass through it freely. Vacuum (a space with no matter) has the lowest permittivity, represented by an epsilon symbol, ϵ.

Epsilon Naught Value in Electric Field denotes the permittivity of free space. It appears in many branches of Physics, especially in equations based on James Maxwell’s work and electrostatics. Epsilon naught is a universal constant and stands for absolute dielectric permittivity of space. Its unit is farads/meters or C2N-1m-2.

Permittivity Of a Material and Types of Permittivity

The permittivity of any insulating material tells us the tendency of the atomic charge inside the material to distort when it is around an electric field. In other words, permittivity gives the relation between the electric field inside the material and the electric displacement.

Permittivity of an insulating material – This value is denoted by the Greek letter ϵ. It is the ability of a material to allow an electric current to pass through it and depends on frequency ⍵.

Permittivity of free space – This is denoted by ϵ0, and it is a constant value that denotes the ability of vacuum or free space to allow an electric current to pass through it. It also depends on frequency ⍵.

Relative permittivity is also called the dielectric constant (q.v.) of a material and is the ratio of material permittivity to free space’s permittivity. The symbol for relative permittivity is the Greek letter kappa, κ. So, κ = ϵ/ϵ0. Relative permittivity depends on frequency ⍵.

Understanding the Value of Epsilon Naught

The value of epsilon naught is 8.85* 10-12 F.m-1 (farads per meter) which has a relative uncertainty of 1.5 * 10-10. It is a constant value that can be present anywhere in the universe.

The vacuum permittivity is denoted by ϵ0 and called epsilon zero or epsilon naught.

Experts refer to epsilon naught as electric constant, distributed vacuum capacitance, or free space units’ permittivity.

ϵ0 measures the ability of an electric field to permeate the vacuum and draws relation between electric charge units and mechanical quantities like force and length.

In the CGS unit ϵ0 = 8.85 * 10-12 C2/N.m2

In the past ϵ0 has been called by many names, but now all the standard organisations uniformly call it “electric constant”.

The value of Epsilon naught is used by experts to find the relative permittivity (or dielectric constant, which is the capacity of a material to store electrical energy in an electric field) of any material. For example, the epsilon value of water would give an idea about how much electricity can cross water.

Derivation of Formula of Epsilon Naught From Coulomb’s Law

Coulomb’s law helps in finding the force between two charged bodies (q1,q2). Let us look at how to derive the formula of Epsilon naught based on Coulomb’s law.

As per Coulomb’s law, F(Force) ∝ (q1 * q2)/r2.

We remove the proportionality by using a constant K; F(Force) = k * ((q1 * q2)/r2), where K = 1/4𝝿ϵ0

Hence F(Force) = (1/4𝝿ϵ0) * ((q1 * q2)/r2), where ϵ0 is the permittivity of free space.

So we get  = (1/4𝝿Fϵ0) * ((q1 * q2)/r2)

Derivation of Dimensional Formula of Epsilon Naught

The dimensional formula of a physical quantity is an expression in base quantities which, in the case of Epsilon naught, are M (mass), L (length), A (Ampere), and T (time). Epsilon naught’s dimensional formula is expressed in M, L, A, T, which only depicts the nature of the unit, not its magnitude. The dimensional formula of Epsilon Naught is given by M-1L-3T4A2.

From the above derivation we know that ϵ0 = (1/4𝝿Fϵ0) * ((q1 * q2)/r2).

• Dimensional formula of force = M1L1T-2.
• Dimensional formula of charge = AT1

Hence dimensional formula of ϵ0 = (1/ M1L1T-2) * ((AT1)2/L2) = M-1L-3T4A2

Derivation of Epsilon Naught Formula In Terms of Capacitance

The capacitance of an electric circuit component is its ability to collect and store energy in the form of an electric charge.

The capacitance of a conducting sphere having radius R is given by; C = 4𝝿ϵ0R.

Hence, ϵ0 = C/4𝝿R.

Importance of Absolute Permittivity of Free Space

Epsilon naught or absolute permittivity of space is useful in finding out the force between two electric charges apart by some distance.

Another use of ϵ0 is to find out the dielectric constant of other substances. Since the vacuum is all around us, the relative permittivity is mostly determined against the permittivity of the vacuum.

The capacitance of a capacitor can be determined using epsilon naught in the formula; C = ϵ0 A * D, where A is the area between the capacitor’s place and D is the distance between the plates.

ϵ0 also has used in Gauss’ law. Gauss’ law gives us the relationship between the amount of charge enclosed within a closed surface and the electric flux passing through that surface. These two quantities are directly proportional to each other and expressed as

E · dA = Q. ε0, where E denotes the electric field, Q. ε0 is the charge within the closed surface, and A is the area of the enclosing face.

Final Words

The value of epsilon naught or electric constant has many uses in the world of Physica. Epsilon naught denotes the permittivity of free space i.e. it is the ability of vacuum to allow passage of electric current through it.

Epsilon naught is denoted by the symbol ϵ0, and its value is 8.85* 10-12 F.m-1 (farads per meter). Epsilon naught is used to measure the force between two electric charges which are kept at a distance, the capacitance of a capacitor, and also in Gauss’ law.

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