Physics - Unit & Dimension Question with Solution | TestHub

Force of attraction between two charges is given by $$\begin{array}{rl}F& =\frac{1}{4\pi {\epsilon }_0}\frac{q_1{q}_2}{r^2}\\ \Rightarrow {\epsilon }_0& =\frac{1}{4\pi }\frac{1}{F}\frac{q_1{q}_2}{r^2}=\frac{{\mathrm{A}}^2{\mathrm{T}}^2}{{\mathrm{MLT}}^{-2}{\mathrm{L}}^2}\\ & =\left[{\mathrm{M}}^{-1}{\mathrm{L}}^{-3}{\mathrm{T}}^4{\mathrm{A}}^2\right].\end{array}$$ (where $4\pi$ is dimensionless) $=\left[{\mathrm{M}}^{-1}{\mathrm{L}}^{-3}{\mathrm{T}}^4{\mathrm{A}}^2\right]$