Physics - EMI/AC Question with Solution | TestHub

Electrical force per unit area $=\frac{1}{2}{\epsilon }_0{E}^2$ $$=\frac{1}{2}{\epsilon }_0{\left(\frac{\sigma }{{\epsilon }_0}\right)}^2=\frac{{\sigma }^2}{2{\epsilon }_0}$$ Projected area $=\pi R^2$ $\therefore$ net electrical force $=\left(\frac{{\sigma }^2}{2{\epsilon }_0}\right)\left(\pi R^2\right)$ In equilibrium, this force should be equal to the applied force. $\therefore F=\frac{\pi {\sigma }^2{R}^2}{2{\epsilon }_0}$ or $F\propto \frac{{\sigma }^2{R}^2}{{\epsilon }_0}$ $\therefore$ The correct option is (a).