The dimensions of \( \frac{1}{\mu_0\varepsilon_0} \), where the symbols have their usual meanings, are
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → \( [\mathrm{L^{2}T^{-2}}] \)
The speed of electromagnetic waves in vacuum depends on the free-space constants, \( c=1/\sqrt{\mu_0\varepsilon_0} \). So \( 1/\mu_0\varepsilon_0 \) is the square of a speed:
\( \begin{aligned} \left[\frac{1}{\mu_0\varepsilon_0}\right] &= [c^{2}] \\ &= [\mathrm{LT^{-1}}]^{2} \\ &= [\mathrm{L^{2}T^{-2}}] \end{aligned} \)
NCERT (2026-27):
Summary – “5. The speed c of electromagnetic wave in vacuum is related to μ0 and ε0 (the free space permeability and permittivity constants) as follows:
\( c=1/\sqrt{\mu_0\varepsilon_0} \)
The value of c equals the speed of light obtained from optical measurements.”