The dimensional formula of (μ0)/(ε0) is

We know that, velocity of light $c$ is terms of ${ϵ}_{0} and {μ}_{0}$ is given by

$c = \dfrac{1}{{μ}_{0}{ε}_{0}} ⇒ c^{2} = \dfrac{1}{{μ}_{0}{ε}_{0}}$

$c^{2} = 1{μ}_{0}^{2}\dfrac{\mu0}{ε0} ⇒ c = \dfrac{1}{\mu0}\sqrt{\dfrac{\mu0}{ε0}} ⇒ \sqrt{\dfrac{\mu0}{ε0}} = c{μ}_{0}...$\left(i\right)

Dimension$of the magnetic field,B =$\dfrac{τ}{NIA} =$\left[{ML}^{2}T^{- 2}\right]\left[A\right]\left[L^{2}\right]$

$= \left[{MA}^{- 1}T^{- 2}\right]</p><p>Again,$B = {μ}_{0}nI$</p><p>$∴ {μ}_{0} = $\dfrac{B}{nl} =\left[{MA}^{- 1}T^{- 2}\right] \left[L^{- 1}\right]\left[A\right]$ = \left[{MLA}^{- 2}T^{- 2}\right]$</p><p>${μ}_{0} = \left[{MLA}^{- 2}T^{- 2}\right]$... \left(ii\right)$

and $C = \left[{LT}^{- 1}\right]$... \left(iii\right)$</p><p>From Equations. (i), (ii) and (iii), we get</p><p>$\sqrt{\dfrac{\mu0}{ϵ0}} = \left[{LT}^{- 1}\right]\left[{MLA}^{- 2}T^{- 2}\right] = \left[{ML}^{2}T^{- 3}A^{- 2}\right]