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].

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