The dimensional formula of permeability ${\mathrm{\mu }}_0$ is 

For two parallel current carrying wires, force per unit length of a wire is given by

$\mathrm{F}=\frac{{\mathrm{\mu }}_0{\mathrm{i}}_1{\mathrm{i}}_2}{2\mathrm{\pi r}}$

$\therefore \left[{\mathrm{\mu }}_0\right]=\frac{\left[\mathrm{F}\right]\left[\mathrm{r}\right]}{\left[{\mathrm{i}}_1{\mathrm{i}}_2\right]}=\left[\frac{{\displaystyle \frac{{\mathrm{MLT}}^{-2}}{\mathrm{L}}}.\mathrm{L}}{{\mathrm{A}}^2}\right]=\left[{\mathrm{MLT}}^{-2}{\mathrm{A}}^{-2}\right]$