Question

Find the dimensional formula for ${\mu }_o$ and ${\epsilon }_o$:

Answer 1

Since, $k=\frac{1}{4\pi {ϵ}_0}$,

dimension of $\left[{ϵ}_0\right]=\left[k^{-1}\right]=[M{L}^3{T}^{-4}{A}^{-2}{]}^{-1}=[M^{-1}{L}^{-3}{T}^4{A}^2]$

Also we know that , $c=\frac{1}{\sqrt{(}{\mu }_0{ϵ}_0)}$

this gives , dimension of $\left[{\mu }_0\right]=[c^2{ϵ}_0{]}^{-1}=[ML{T}^{-2}{A}^2]$