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Question

Physics Question on physical world

μ0\mu_0 and ε0\varepsilon_0 denote the permeability and permittivity of free space, the dimensions of μ0ε0\mu_0 \varepsilon_0 are

A

[LT−1]{[LT^{-1}]}

B

[L−2T2]{[L^{-2}T^{2}]}

C

[M−1L−3T2]{[M^{-1}L^{-3} T^{2}]}

D

[M−1L−3T2A2]{[M^{-1}L^{-3} T^{2}A^2]}

Answer

[L−2T2]{[L^{-2}T^{2}]}

Explanation

Solution

Speed of light in vacuum is given by
c=1μ0ε0c = \frac{1}{\sqrt{\mu_0 \varepsilon_0}} or μ0ε0=1c2 \mu_0 \varepsilon_0 = \frac{1}{c^2}
∴    [μ0ε0]=1[LT−1]2=[L−2T2]{ \therefore \:\:\:\: [\mu_0 \varepsilon_0 ]= \frac{1}{[LT^{-1}]^2 } = [L^{-2} T^2]}