Question

The dimensional formula of $\frac{1}{2} \mu_{0} H^{2}$ $(\mu=$ permeability of free space and $H=$ magnetic field intensity) is

• A. $\left[ MLT ^{-1}\right]$
• B. $\left[ ML ^{2} T ^{-2}\right]$
• C. $\left[ ML ^{-1} T ^{-2}\right]$
• D. $\left[ ML ^{2} T ^{-1}\right]$

Answer 1

Answer: (C)

$\left[\mu_{0}\right]=\left[ MLT ^{-2} A ^{-2}\right]$ and $[H]=\left[ AL ^{-1}\right]$
$\therefore \left[\frac{1}{2} \mu_{0} H^{2}\right]=\left[ MLT ^{-2} A ^{-2}\right]\left[ AL ^{-1}\right]^{2}=\left[ ML ^{-1} T ^{-2}\right]$