Question

The dimension of ${\mu }_0{ϵ}_0$, where symbols have their usual meanings, is -

• 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 $\left[L^{-2}{T}^2\right]$

The speed of an electromagnetic wave is given by,

$c=\frac{1}{\sqrt{{\mu }_0{ϵ}_0}}$

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

$\Rightarrow \left[{\mu }_0{ϵ}_0\right]=\frac{1}{\left[c^2\right]}$

$\Rightarrow \left[{\mu }_0{ϵ}_0\right]=\frac{1}{{\left[L{T}^{-1}\right]}^2}$

$\Rightarrow \left[{\mu }_0{ϵ}_0\right]={\left[L{T}^{-1}\right]}^{-2}=\left[L^{-2}{T}^2\right]$

Hence, option $\left(B\right)$ is the correct answer.