Question

Dimensions of $\frac{1}{\mu_{0}\varepsilon_{0}}$, 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. $\left[LT^{-1}\right]$

Answer 1

Answer: (C)

Velocity is given by
$v=\frac{1}{\sqrt{\mu_{0}\varepsilon_{0}}}$
$\therefore v^{2}=\frac{1}{\mu_{0}\varepsilon_{0}}=\left[LT^{-1}\right]^{2}$
$\therefore \frac{1}{\mu_{0}\varepsilon_{0}}=\left[L^2T^{-2}\right]$