Question

The dimensions of ${ϵ}_0{\mu }_0$

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

Answer 1

Answer: (D)

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

We know $C=\frac{1}{\sqrt{{\mu }_0{\epsilon }_0}}$

$\Rightarrow {\mu }_0{\epsilon }_0=\frac{1}{C^2}$

$C$ is the speed of light. $C$ has dimensions $\left[M^{0}L{T}^{-1}\right]$

${\mu }_0{\epsilon }_0=\frac{1}{C^2}=\left(C^{-2}\right)$

${\mu }_0{\epsilon }_0=\left[M^0{L}^{-2}{T}^2\right]$