Physics - Electrostatics Question with Solution | TestHub

Electrical force per unit area =$\frac{1}{2}{\epsilon }_0{\mathit{\text{E}}}^2=\frac{1}{2}{\epsilon }_0{\left(\frac{\sigma }{{\epsilon }_0}\right)}^2=\frac{{\sigma }^2}{2{\epsilon }_0}$

Projected area =$\pi {\mathit{\text{R}}}^2$

$\therefore$Net electrical force =$\left(\frac{{\sigma }^2}{2{\epsilon }_0}\right)\left(\pi {\mathit{\text{R}}}^2\right)$

In equilibrium, this force should be equal to the applied force.

$\therefore$$\mathit{\text{F}}=\frac{\pi {\sigma }^2{\mathit{\text{R}}}^2}{2{\epsilon }_0}$

or$\mathit{\text{F}}\propto \frac{{\sigma }^2{\mathit{\text{R}}}^2}{{\epsilon }_0}$