Explanation

From Coulomb’s law $\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ F = \frac{1}{4\pi\varepsilon_{0}}\frac{q_{1}q_{2}}{r^{2}}$ $\Rightarrow \left\lbrack \frac{1}{4\pi\varepsilon_{0}} \right\rbrack = \frac{\lbrack F\ \times r^{2}\rbrack}{\lbrack q\rbrack^{2}}$ $\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ = \frac{\lbrack newton\rbrack\lbrack metre\rbrack^{2}}{\lbrack coulomb\rbrack^{2}}$ $\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ = {Nm}^{2}C^{- 2}$