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# $\mu$ and $\in _0$ denote the permeability and permitting of free space, the dimensions of $\mu_0\in _0$ are

$(a)\;LT^{-1} \quad (b)\;L^{-2}T^{2} \quad (c)\;M^{-1}L^{-3}Q^2T^2 \quad (d)\;M^{-1}L^{-3}I^2T^2$

Can you answer this question?

We Know $\large\frac{1}{\sqrt {\mu_0 \in_0}}=c$
Where $c$ is velocity of light.
Therefore $\mu_0 \in _0=\large\frac{1}{c^2}$
$\mu_0 \in_0=\large\frac{1}{[LT^{-1}]^2}$
$\qquad=[L^{-2}T^{2}]$
The dimensions of $\mu_0 \in_0$ are $L^{-2}T^{2}$
Hence b is the correct answer.

answered Jun 17, 2013 by
edited Jan 9, 2014 by meena.p