From Coulomb’s law, the force of attraction/repulsion between two point charges $q$, $q$ separated by distance $r$ is
$F = \frac{1}{4\,\pi\,\varepsilon_{0}} \frac{q^{2}}{r^{2}}$
$\Rightarrow \varepsilon _{0} = \frac{1}{4\,\pi } \cdot \frac{q^{2}}{Fr^{2}}$
where $ε_{0}$ is electric permittivity.
Dimensions of $\varepsilon_{0} =\frac{\left[AT\right]^{2}}{\left[MLT^{-2}\right]\left[L^{2}\right]}$
$\varepsilon_{0} = \left[A^{2}\,M^{-1}\,L^{-3}\,T^{4}\right]$