# Dimensional Formula of the Permittivity of Vacuum

Consider ε0 to represent the dimensional formula of permittivity of vacuum.

From Coulomb’s law, we know

$$F=frac{1}{4pi epsilon _{0}}frac{q_{1}q_{2}}{R^{2}}$$

ε0 = $$frac{q_{1}q_{2}}{4pi FR^{2}}$$

Substituting the values, we get

ε0 = $$frac{C^{2}}{N-m}$$

ε0 = $$frac{[AT]^{2}}{[MLT^{-2}][L^{2}]}$$

ε0 = [M-1L-3T4A2]

Therefore, the dimensional formula of permittivity of vacuum is [M-1L-3T4A2].