# Epsilon Naught Value: Definition, Formula & More

Epsilon Naught Value is 8.85418782 × 10-12 m-3 kg-1s4 A2. It is also referred to as the permittivity of free space and can easily be understood when tiny electric charges interact with each other across vast distances. Epsilon Naught (ε₀), pronounced “epsilon nought” or “epsilon zero,” is a fundamental constant that defines the measure of how electric fields can easily propagate through a vacuum.

## What is Epsilon Naught?

Imagine the universe filled with invisible threads that carry the power of electricity. These threads are crucial for everything from lightning to the electricity powering your phone. Epsilon naught (ε₀) is a constant value, meaning it’s the same everywhere in the universe (as far as we know) for a perfect vacuum. It’s a fundamental building block for understanding electricity and its behaviour in empty space.

Think of epsilon naught as a measure of how easily these invisible “threads” allow electric fields to form in a perfect vacuum. A higher value of epsilon naught would indicate a stronger electric field for the same amount of electrical charge. It tells us how readily these “threads” let electric forces act between charged particles.

## Value Of Epsilon Naught

The ability of the electric field to pass through the classical vacuum is defined as the permittivity of free space (ε0). This has a fixed, defined value that can be estimated to a close approximation as –

In SI Unit – ε0 = 8.854187817 × 10-12 F.m-1

Or

In CGS units – ε0 = 8.854187817 × 10-12 C2/N.m2

### A further breakdown can be –

Epsilon naught is usually represented by the symbol ε₀. While the formula itself might look complex (ε₀ = 8.854 × 10⁻¹² F/m), we can break it down as –

“F” stands for Farad, the unit of capacitance

“m” for meter, the unit of distance.

This tells us that epsilon naught relates the ability to store electric charge (capacitance) to the distance between charged particles.

## What is the Permittivity?

Imagine a material like air or water. Permittivity (ε) tells us how easily an electric field can pass through that material. The ability of a material to allow the passage of an electric field is measured by its permittivity, which in turn indicates the material’s polarizability. The vacuum’s ability to permit electric fields is referred to as free space permittivity.

Since each medium has a unique ability to pass an electrical field through it, the permittivity also changes when dealing with material media. In contrast, the permittivity remains constant since empty space has no matter or fields.

Therefore, open space has a standard, constant permittivity value with a relative standard uncertainty of 1.5 × 10-10, which is roughly equivalent to 8.854 x 10-12 F/m (farad per meter). The standard unit of capacitance used to evaluate a material’s ability to store an electric charge is the farad.

The formula for permittivity can be written as –

## ε = D/E

where,

ε = Permittivity

D = Displacement Electric Field

E = Electric Field

## What is the Permittivity Of Free Space?

The permittivity of free space is a physical constant that represents the ability of electrical fields to pass through a classical vacuum. Just like every other medium, free space has its own permittivity. This means that the Permittivity of Free Space is also known as the Permittivity of Vacuum. The electric constant, or vacuum permittivity, is yet another name for this constant. In a particular medium, such as a vacuum, permittivity is the constant that establishes the proportionality between electric displacement and electric field intensity. The value of the Permittivity of free space is 8.854 x 10-12 F/m.

The formula of Permittivity of free space is given as –

ε0 = ε/εᵣ

where,

ε = the Permittivity

εᵣ = the Relative Permittivity

## Types Of Permittivity

There are main three types of Permittivity – the permittivity of free space, the permittivity of a substance and Relative Permittivity. They can be discussed in tabular form –

## Derivation of the Formula of Epsilon Naught

According to Coulomb’s Law:

F = (1/4πε₀) q1q2/r2

ε₀ = (1/4πF) q1q2/r2

Dimension formula of F = M1L1T-2

Charge = q = I × T = A × T1, where A= electric current

So, ε₀ = (1/M1L1T-2)(AT1×AT1)/L2

Hence, ε₀ = M-1L-3T4A2

Therefore, the dimensional formula of Epsilon Naught turns out to be

## Importance of Epsilon Naught

Epsilon Naught is important for several reasons, including:

• It represents the dielectric permittivity of empty space or vacuum.
• Because the permittivity of space is a constant, it is frequently used in numerical calculations.
• It is used in Coulomb’s law to determine the force between two charged particles.
• Epsilon Naught is used to calculate the capacitance of an insulator.
• The value of Epsilon Naught is used to calculate the dielectric constant of a substance.

## Advantages and Limitations Of Epsilon Naught

The advantages of epsilon naught are –

• Universal Constant: Epsilon naught has a fixed value throughout the universe, making it a reliable constant for calculations.
• Foundation of Electromagnetism: It plays a crucial role in many key electromagnetism equations, allowing us to predict and understand electrical and magnetic phenomena.

The limitation of Epsilon naught is it applies only to a perfect vacuum. In real-world materials, permittivity will be different and depend on the material’s properties.

Also Read – Integration Formulas: Examples and Solutions

## Examples of Epsilon Naught in Action

• Capacitors: Understanding epsilon naught helps us grasp how capacitors work. Capacitors store electric charge by creating an electric field between plates separated by an insulator. The capacitance depends on factors like the plates’ area, their distance, and the permittivity of the insulating material (which is related to epsilon naught).
• Electromagnetic Waves: Epsilon naught, along with another constant, permeability of free space (μ₀), plays a crucial role in the equations governing electromagnetic wave propagation. These waves, encompassing radio waves, light and X-rays, rely on the properties of free space for their transmission.

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