The dimensions $[ML{T}^{-2}{A}^{-2}]$ belong to the:

From Ampere's law, the magnetic field $B=\frac{{\mu }_{0}I}{2\pi r}⟹{\mu }_0\propto \frac{Br}{I}$.Force on a current carrying wire is $F=BIl⟹B=\frac{F}{Il}$.Dimensions of $B$:
$$[B]=\frac{[ML{T}^{-2}]}{[A][L]}=[M{T}^{-2}{A}^{-1}]$$
Dimensions of ${\mu }_0$:
$$[{\mu }_0]=\frac{[B][L]}{[A]}=\frac{[M{T}^{-2}{A}^{-1}][L]}{[A]}=[ML{T}^{-2}{A}^{-2}]$$
This corresponds to Magnetic Permeability (${\mu }_0$).