Question

The dimensional formula of permeability of free space $\mu_0$ is

• A. $[MLT^{-2}A^{-2}]$
• B. $[M^0 L^1 T]$
• C. $[M^0 L^2 T^{-1}A^2]$
• D. none of these

Answer 1

The Correct Option is A

To determine the dimensional formula of the permeability of free space $\mu_0$, we need to understand its role in electromagnetism. The permeability of free space is a physical constant that appears in the formulation of Ampère's circuital law and the Biot-Savart law, and it is involved in defining the Magnetic field strength.

The relationship between permeability $\mu_0$, charge $q$, current $I$, and magnetic field $B$ can be derived from the equation:

$F = qvB = IlB$

Where:

• $F$ is the force.
• $B$ is the magnetic field.

Additionally, the magnetic force equation in terms of permeability is:

$B = \frac{\mu_0}{4\pi} \cdot \frac{I}{r}$

Now considering the dimensional analysis, the dimensions of $B$ in terms of fundamental quantities can be expressed as:

$[B] = [F]/[qv] = [MLT^{-2}]/[AT][L/T] = [M^1L^0T^{-2}A^{-1}]$

Thus, for $B$, the dimensional formula is $[M^1L^0T^{-2}A^{-1}]$ . The permeability $\mu_0$ thus becomes:

$[B \times L \times T \times A]=[M^1L^0T^{-2}A^{-1}] \times [L]\times [T]\times [A] = [MLT^{-2}A^{-2}]$

Therefore, the correct dimensional formula of the permeability of free space, $\mu_0$, is $[MLT^{-2}A^{-2}]$.