The dimensional formula of $\frac{1}{2} \mu_0 H^2$ ( $\mu=$ permeability of free space and $H=$ magnetic…

The dimensional formula of $\frac{1}{2} \mu_0 H^2$ ( $\mu=$ permeability of free space and $H=$ magnetic field intensity) is
  1. $\left[\mathrm{MLT}^{-1}\right]$
  2. $\left[\mathrm{ML}^2 \mathrm{~T}^{-2}\right]$
  3. $\left[\mathrm{ML}^{-1} \mathrm{~T}^{-2}\right]$
  4. $\left[\mathrm{ML}^2 \mathrm{~T}^{-1}\right]$

Solution

$\begin{aligned} & {\left[\mu_0\right]=\left[\mathrm{MLT}^{-2} \mathrm{~A}^{-2}\right] \text { and }[H]=\left[\mathrm{AL}^{-1}\right]} \\ & \therefore \\ & {\left[\frac{1}{2} \mu_0 H^2\right]=\left[\mathrm{MLT}^{-2} \mathrm{~A}^{-2}\right]\left[\mathrm{AL}^{-1}\right]^2=\left[\mathrm{ML}^{-1} \mathrm{~T}^{-2}\right]}\end{aligned}$

Asked in: AP EAMCET 2011

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