Q 11-01-022JEE MainEAMCET 2011 (Engineering)Medium
The dimensional formula of $\dfrac{1}{2}\mu_0 H^2$ ($\mu_0$ is the permeability of free space and $H$ is the magnetic field intensity) is
Answer: (C) $[ML^{-1}T^{-2}]$
$\tfrac12\mu_0H^2$ is the energy stored per unit volume in a magnetic field (since $B = \mu_0 H$, it equals $\dfrac{B^2}{2\mu_0}$).
$$\left[\tfrac12\mu_0H^2\right] = \frac{[\text{Energy}]}{[\text{Volume}]} = \frac{[ML^2T^{-2}]}{[L^3]} = [ML^{-1}T^{-2}]$$
Tip: energy density always has the same dimensions as pressure.
Solution by Sreeraj P, M.Sc Physics