Question

What is the dimension of $\frac{1}{\mu_{0} \varepsilon_{0}} ?$
( $\mu_{0}=$ magnetic permeability $\varepsilon_{0}=$ permitivity of free space)

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

Answer 1

Answer: (A)

Velocity of electromagnetic wave in free space is given as
$c=\frac{1}{\sqrt{\mu_{0} \varepsilon_{0}}}$
$ \Rightarrow c^{2}=\frac{1}{\mu_{0} \varepsilon_{0}}$
$ \Rightarrow \frac{1}{\mu_{0} \varepsilon_{0}}=c^{2}$
$\Rightarrow $ Dimensions of $ \frac{1}{\mu_{0} \varepsilon_{0}}=\left[\frac{1}{\mu_{0} \varepsilon_{0}}\right]=\left[c^{2}\right] $
$=\left[L T^{-1}\right]^{2}=\left[L^{2} T^{-2}\right]$