Question

What is the dimension of $\frac{1}{{\mu }_0{\epsilon }_0}?$
( ${\mu }_0=$ magnetic permeability ${\epsilon }_0=$ permitivity of free space)

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

Answer 1

Answer: (A)

Velocity of electromagnetic wave in free space is given as
$c=\frac{1}{\sqrt{{\mu }_0{\epsilon }_0}}$
$\Rightarrow c^2=\frac{1}{{\mu }_0{\epsilon }_0}$
$\Rightarrow \frac{1}{{\mu }_0{\epsilon }_0}=c^2$
$\Rightarrow$ Dimensions of $\frac{1}{{\mu }_0{\epsilon }_0}=\left[\frac{1}{{\mu }_0{\epsilon }_0}\right]=\left[c^2\right]$
$={\left[L{T}^{-1}\right]}^2=\left[L^2{T}^{-2}\right]$