Question

Dimentional formula of permeability of free space ${\mu }_0$ is given by

• A. $\left[M^{0}L{T}^{-2}{A}^{-2}\right]$
• B. $\left[M{L}^2{T}^{-1}{A}^{-2}\right]$
• C. $\left[ML{T}^{-2}{A}^{-2}\right]$
• D. $\left[M^{0}L{T}^{-1}{A}^{-1}\right]$

Answer 1

The correct option is C $\left[ML{T}^{-2}{A}^{-2}\right]$

$c^2=\frac{1}{{\mu }_0{\epsilon }_0}\Rightarrow {\mu }_0=\frac{1}{C^2{\epsilon }_0}$ $c=L{T}^{-1}\&{\epsilon }_0=\frac{q_1{q}_2}{F{r}^2}=\frac{A^2{T}^2}{L^{2}ML{T}^{-2}}$
$\therefore {\mu }_0=\frac{L^{2}ML{T}^{-2}}{L^2{T}^{-2}\times A^2{T}^2}=ML{T}^{-2}{A}^{-2}$