Question

Find the dimensional formula of ε₀.

Answer 1

By Coulomb's Law,  \[F = \frac{1}{4\pi \epsilon_0}\frac{q_1 q_2}{r^2}\]

\[\Rightarrow  \epsilon_0  = \frac{1}{4\pi F}\frac{q_1 q_2}{r^2}\]

Using [F] = [MLT⁻²]
[r] = [M⁰L¹T⁰]
[q] = [M⁰L⁰T¹A¹], we get
[ε₀] = [M⁻¹L⁻³T⁴A²]