Physics - Unit & Dimension Question with Solution | TestHub

We know that the force per unit length of a wire carrying current due to another parallel wire carrying current is given by $$\begin{array}{c}\frac{dF}{dl}=\frac{{\mu }_0{i}_1{i}_2}{2\pi d}\Rightarrow {\mu }_0=\frac{2\pi d}{i_1{i}_2}\frac{dF}{dl}\\ \therefore \left[{\mu }_0\right]=\frac{[\mathrm{L}]}{\left[{\mathrm{A}}^2\right]}\cdot \frac{\left[{\mathrm{MLT}}^{-2}\right]}{[\mathrm{L}]}\\ \text{ or }\left[{\mu }_0\right]=\left[{\mathrm{MLT}}^{-2}\right]\left[{\mathrm{A}}^{-2}\right]=\left[{\mathrm{MLT}}^{-2}{\mathrm{A}}^{-2}\right].\end{array}$$