Question

$\mu_0$ and $\varepsilon_0$ denote the permeability and permittivity of free space, the dimensions of $\mu_0 \varepsilon_0$ are

• A. ${[LT^{-1}]}$
• B. ${[L^{-2}T^{2}]}$
• C. ${[M^{-1}L^{-3} T^{2}]}$
• D. ${[M^{-1}L^{-3} T^{2}A^2]}$

Answer 1

The Correct Option is B

Speed of light in vacuum is given by
$c = \frac{1}{\sqrt{\mu_0 \varepsilon_0}}$ or $\mu_0 \varepsilon_0 = \frac{1}{c^2}$
${ \therefore \:\:\:\: [\mu_0 \varepsilon_0 ]= \frac{1}{[LT^{-1}]^2 } = [L^{-2} T^2]}$