also \(\mathrm{E}=\mathrm{F} \cdot \mathrm{s}=\frac{\mathrm{k} q \cdot \mathrm{q}}{\mathrm{r}^{2}} \cdot \mathrm{r}\)

Therefore dimensionally

\(\mathrm{mc}^{2}=\frac{1}{4 \pi \epsilon_{0}} \frac{\mathrm{q}^{2}}{\mathrm{r}}\)

\(\Rightarrow r=\frac{e^{2}}{4 \pi \epsilon_{0} m c^{2}}\)