Question

9.
A uniformly charged thin spherical
shell of radius R carries uniform
surface charge density of o per unit
area. It is made of two hemispherical
shells, held together by pressing them
with force F (see figure). F is proportional to???

Answer 1

The charge on the curved surface of the hemisphere can be,

• $\sf{q_1=2\pi R^2\sigma}$

and that on the base surface can be,

• $\sf{q_2=\pi R^2\sigma}$

The force F is balanced by the electrostatic force as follows.

$\sf{\longrightarrow F=\dfrac{kq_1q_2}{R^2}}$

$\sf{\longrightarrow F=\dfrac{1}{4\pi\epsilon_0}\cdot2\pi R^2\sigma\cdot\pi R^2\sigma\cdot\dfrac{1}{R^2}}$

$\sf{\longrightarrow F=\dfrac{1}{2\epsilon_0}\,\pi\sigma^2R^2}$

Then we get,

$\sf{\longrightarrow\underline{\underline{F\propto\dfrac{1}{\epsilon_0}\,\sigma^2R^2}}}$

Hence (1) is the answer.