Using mass (M), length(L), time(T) and electric current (A) as fundamental quantities, the dimensions of permittivity will be :

[MLT-1A-1] [MLT-2A-2] [M-1L-3T4A2] [M2L-2T-2A]

[M-1L-3T4A2]

By Coulomb's Law : F = \(\frac{1}{4 \pi \epsilon_o} \frac{q_1 q_2}{r^2}\) \(\epsilon_o = \frac{q_1 q_2}{4 \pi F r^2}\) \([\epsilon_o] = \frac{[(AT)(AT)]}{[MLT^{-2}L^2]}\) \([\epsilon_o] = [M^{-1}L^{-3}T^4A^2] \)