Question

What is the relative permeability of air?
A. 1
B. 2
C. 3
D. 4

Answer 1

In electrostatics, the relative permeability of the material is the ratio of the permeability of any medium to the permeability of air or vacuum.

Formula used:
$Relative{\text{ }}permeability\left( {\mu r} \right) = absolute{\text{ }}permeability\left( \mu \right)/absolute{\text{ }}permeability{\text{ }}of{\text{ }}air\left( {\mu o} \right)$

Complete step by step answer:
A measure of the opposition offered by any material against the formation of an electric field is called permittivity whereas permeability is the measure of the ability of the material to allow the formation of magnetic lines of force or magnetic flux within.
The SI unit of permeability is $H{\text{ }}{m^{ - 1}}$.
Mathematically, relative permeability is ratio of number of lines of magnetic induction per unit area in a material to number of lines per unit area in a vacuum
Also relative permeability of the material is defined as the ratio of the permeability of any medium to the permeability of air or vacuum.
$Relative{\text{ }}permeability\left( {\mu r} \right) = {\text{ }}permeability{\text{ }}of{\text{ }}medium\left( \mu \right)/absolute{\text{ }}permeability{\text{ }}of{\text{ }}air\left( {\mu o} \right)$The permeability of air medium is :
Relative permeability is a dimensionless quantity, It is the ratio of two quantities with the equivalent units. Hence, relative permeability has no unit.
Now, $relative{\text{ }}permeability{\text{ }}of{\text{ }}air\left( {\mu r} \right) = 1.257 \times {10^{ - 6}}H{\text{ }}{m^{ - 1}} = 1.257 \times {10^{ - 6}}H{\text{ }}{m^{ - 1}} = 1$
∴ $\mu r{\text{ }} = 1$
∴ Relative permeability of air is always 1.
So, option A is the correct answer.

Note: As we know, relative permeability of the material is the ratio of the permeability of any medium to the permeability of air or vacuum. Relative permeability is a ratio of two quantities with the same units, so relative permeability has no unit.
There can be some material which has relative permeability less than 1, these materials are diamagnetic in nature. Cobalt iron is the material with the highest relative permeability of 18000.