If $\mu_0$ and $\varepsilon_0$ are the permeability and permittivity of free space, respectively, then the…

If $\mu_0$ and $\varepsilon_0$ are the permeability and permittivity of free space, respectively, then the dimension of $\left(\frac{1}{\mu_0 \varepsilon_0}\right)$ is :
  1. $\mathrm{L} / \mathrm{T}^2$
  2. $L^2 / T^2$
  3. $T^2 / L$
  4. $\mathrm{T}^2 / \mathrm{L}^2$

Solution

$\mathrm{C}=\frac{1}{\sqrt{\mu_0 \varepsilon_0}} \Rightarrow \frac{1}{\mu_0 \varepsilon_0}=\mathrm{C}^2=\mathrm{L}^2 \mathrm{~T}^{-2}$

Asked in: JEE Main 2025 (02 Apr Shift 2)

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