Question

The dimensions of $\frac{B^2}{2{\mu }_0}$, where $B$ is magentic field and ${\mu }_0$ is the magnetic permiability of vaccum, is

• A. $ML{T}^{-2}$
• B. $M{L}^2{T}^{-1}$
• C. $M{L}^2{T}^{-2}$
• D. $M{L}^{-1}{T}^{-2}$

Answer 1

The correct option is D $M{L}^{-1}{T}^{-2}$

The quantity of $\frac{B^2}{2{\mu }_0}$ is the energy density of magnetic field.

$\Rightarrow \left[\frac{B^2}{2{\mu }_0}\right]=\frac{\text{Energy}}{\text{Volume}}$

$\Rightarrow \left[\frac{B^2}{2{\mu }_0}\right]\frac{\text{Force × displacement}}{{\text{(length)}}^3}$

$\Rightarrow \left[\frac{B^2}{2{\mu }_0}\right]=\left[\frac{\left[ML{T}^{-2}\right]\left[L\right]}{L^3}\right]$

$\Rightarrow \left[\frac{B^2}{2{\mu }_0}\right]=M{L}^{-1}{T}^{-2}$

Hence, option $\left(D\right)$ is correct.