Question

Dimensions of $\frac{1}{{\mu }_0{ϵ}_0}$, 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)

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

We know that the speed of light is represented by:

$c=\frac{1}{\sqrt{{\mu }_0{ϵ}_0}}$

So, we can write:

$\frac{1}{{\mu }_0{ϵ}_0}=c^2$

The dimension of speed of light is represented as $\left[L{T}^{-1}\right]$

So, for $\frac{1}{{\mu }_0{ϵ}_0}=\left[L^2{T}^{-2}\right]$.