Question

The dimensions of $1/{\mu }_0{\epsilon }_0$. where symbols have their usual meanings, 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

The correct option is B

$\left[L^{-2}{T}^2\right]$

We know that, speed of light in vacuum, $c=\frac{1}{\sqrt{{\mu }_0{ϵ}_0}}$

$\Rightarrow {\mu }_0{ϵ}_0=\frac{1}{c^2}$

Hence, the dimension of ${\mu }_0{ϵ}_0$ is $\left[L^{-2}{T}^2\right]$.