Units & Dimensions

JEE Main level, single correct, medium

147 of 149

Question 147 of 149

Dimension of 1μ0ε0\frac{1}{\mu_0 \varepsilon_0}, where symbols have their usual meaning, are

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Answer: (C) [L2 T−2]\left[\mathrm{L}^2 \mathrm{~T}^{-2}\right]

1μ0ε0=C⇒1μ0ε0=C2⇒[1μ0ε0]=[C]2\frac{1}{\sqrt{\mu_0 \varepsilon_0}}=\mathrm{C} \Rightarrow \frac{1}{\mu_0 \varepsilon_0}=\mathrm{C}^2 \Rightarrow\left[\frac{1}{\mu_0 \varepsilon_0}\right]=[\mathrm{C}]^2
[C]=LT−1[\mathrm{C}]=\mathrm{LT}^{-1} \quad or [C]2=L2 T−2\quad[\mathrm{C}]^2=\mathrm{L}^2 \mathrm{~T}^{-2}

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