Question

The dimensions of
${\left({\mu }_0{\epsilon }_0\right)}^{-1/2}$ are:

• A. $\left[L^{-1}T\right]$
• B. $\left[L{T}^{-1}\right]$
• C. $\left[L^{1/2}{T}^{1/2}\right]$
• D. $\left[L^{1/2}{T}^{-1/2}\right]$

Answer 1

The correct option is B $\left[L{T}^{-1}\right]$

We know that the speed of an electromagnetic wave is given by :

$c=\frac{1}{\sqrt{{\mu }_0{\epsilon }_0}}$

Therefore, $({\mu }_0{\epsilon }_0{)}^{-1/2}$ has the dimension the same as that of the speed.

$\therefore dimensionL{T}^{-1}$