Physics - Electrostatics Question with Solution | TestHub

Key Idea : Search for the relations of electric potential and electric field at a particular point. At any point, electric potential due to charge $Q$ is $$V=\frac{1}{4\pi {\epsilon }_0}\cdot \frac{Q}{r}$$ where $r$ is the distance of observation point from the charge. At the same point, electric field is $$E=\frac{1}{4\pi {\epsilon }_0}\cdot \frac{Q}{r^2}$$ Combining Eqs. (i) and (ii), we have $$\begin{array}{rl}E& =\frac{4\pi {\epsilon }_0{V}^2}{Q}=\frac{4\pi {\epsilon }_0\times {\left(Q\times 10^{11}\right)}^2}{Q}\\ & =4\pi {\epsilon }_0\mathrm{Q}\times 10^{22}\mathrm{V}/\mathrm{m}\end{array}$$