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If \({\mu }_{0}\) and \({\epsilon }_{0}\) are the permeability and permittivity of free space, respectively, then the di…

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If \({\mu }_{0}\) and \({\epsilon }_{0}\) are the permeability and permittivity of free space, respectively, then the dimension of \(\left(\frac{1}{{\mu }_{0}{\epsilon }_{0}}\right)\) is :

[JEE Main 2025, 2 Apr (Shift 2)]

a

\({\mathrm{T}}^{2}/{\mathrm{L}}^{2}\)

b

\(\mathrm{L}/{\mathrm{T}}^{2}\)

c

\({\mathrm{L}}^{2}{\mathrm{T}}^{-2}\)

d

\({\mathrm{T}}^{2}/\mathrm{L}\)

✓ Correct answer: c)

\({\mathrm{L}}^{2}{\mathrm{T}}^{-2}\)

Explanation

\(C=\frac{1}{\sqrt{\mu_0 \varepsilon_0}} \Rightarrow \frac{1}{\mu_0 \varepsilon_0}=C^2=L^2 T^{-2}\)

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