The value of relative permittivity of air is

A. \[8.854\times {{10}^{-12}}{{C}^{2}}{{N}^{-1}}{{m}^{-2}}\]

B. \[9\times {{10}^{9}}{{C}^{2}}{{N}^{-1}}{{m}^{-2}}\]

C. 1

D. $8.854\times {{10}^{12}}$

The value of relative permittivity of air is best represented by option C, which is 1. To understand why this is the case, let's delve into the concept of permittivity and its significance in the context of electric fields and materials.

Understanding Permittivity

Permittivity is a measure of how much electric field is 'permitted' to pass through a material. It essentially quantifies the ability of a material to store electrical energy in an electric field. There are two types of permittivity: absolute permittivity and relative permittivity.

Absolute vs. Relative Permittivity

Absolute permittivity, denoted by the symbol ε, is the measure of permittivity in a vacuum, which is approximately \(8.854 \times 10^{-12} \, \text{C}^2/\text{N m}^2\). Relative permittivity, on the other hand, is a dimensionless quantity that compares the permittivity of a material to that of a vacuum. It is given by the formula:

Relative Permittivity (εr) = ε / ε0

Where ε0 is the absolute permittivity of free space (vacuum). For air, which is very close to a vacuum in terms of its electrical properties, the relative permittivity is approximately 1.

Why is Air's Relative Permittivity Close to 1?

Air is composed of a mixture of gases, primarily nitrogen and oxygen, which have very low polarizability. This means that when an electric field is applied, the molecules in air do not significantly distort or align themselves in response to the field. As a result, air does not store electric energy effectively, leading to a relative permittivity that is nearly equal to that of a vacuum.

Comparative Values

• Vacuum: εr = 1
• Air: εr ≈ 1
• Water: εr ≈ 80
• Glass: εr ≈ 4-10

This comparison illustrates how different materials respond to electric fields, with air being one of the least polarizable substances.

Clarifying the Options

Now, let’s analyze the options provided:

• A: \(8.854 \times 10^{-12} \, \text{C}^2/\text{N m}^2\) - This is the absolute permittivity of free space.
• B: \(9 \times 10^{9} \, \text{C}^2/\text{N m}^2\) - This value is not relevant to the concept of permittivity in this context.
• C: 1 - Correct, as this represents the relative permittivity of air.
• D: \(8.854 \times 10^{12}\) - This value is incorrect and does not relate to permittivity.

In summary, the relative permittivity of air is approximately 1, making option C the correct choice. This understanding is crucial in fields such as electromagnetism and electrical engineering, where the behavior of electric fields in different materials is fundamental to the design and analysis of various systems.