Question

A uniformly charged thin spherical shell of radius R carries uniform surface charge density of $\sigma$ per unit area. It is made of two hemispherical shells, held together by pressing them with force F (see figure). F is proportional to

• A. $\frac{1}{{ϵ}_o}{\sigma }^2{R}^2$
• B. $\frac{1}{{ϵ}_o}{\sigma }^{2}R$
• C. $\frac{1}{{ϵ}_o}\frac{{\sigma }^2}{R}$
• D. $\frac{1}{{ϵ}_o}\frac{{\sigma }^2}{R^2}$

Answer 1

The correct option is A $\frac{1}{{ϵ}_o}{\sigma }^2{R}^2$

We know that the electrostatic pressure at a point on the surface of a uniformly charged sphere is $P=\frac{{\sigma }^2}{2{ϵ}_0}$

The force on the shell is $F=$ pressure $\times$ surface area .

$F=\frac{{\sigma }^2}{2{ϵ}_0}\times 4\pi R^2$

Thus, $F\propto \frac{1}{{ϵ}_0}{\sigma }^2{R}^2$