Question

Dimensions of $\frac{1}{{\mu }_0{\epsilon }_0}$, where symbols have their usual meaning, are

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

Answer 1

Answer: (C)

Velocity is given by
$v=\frac{1}{\sqrt{{\mu }_0{\epsilon }_0}}$
$\therefore v^2=\frac{1}{{\mu }_0{\epsilon }_0}={\left[L{T}^{-1}\right]}^2$
$\therefore \frac{1}{{\mu }_0{\epsilon }_0}=\left[L^2{T}^{-2}\right]$