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Question: \(\mu_{0}\) and \(\varepsilon_{0}\) denote the permeability and permittivity of free space, the dime...

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

(a) LT−1LT^{- 1}

A

(b) L−2T2L^{- 2}T^{2}

A

(c) M−1L−3Q2T2M^{- 1}L^{- 3}Q^{2}T^{2}

A

(d) M−1L−3I2T2M^{- 1}L^{- 3}I^{2}T^{2}

Explanation

Solution

(b)

Sol. C=1μ0ε0C = \frac{1}{\sqrt{\mu_{0}\varepsilon_{0}}}⇒μ0ε0=(1C2)\mu_{0}\varepsilon_{0} = \left( \frac{1}{C^{2}} \right) (where C = velocity of light)

∴ [μ0ε0]=L−2T2\lbrack\mu_{0}\varepsilon_{0}\rbrack = L^{- 2}T^{2}