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
Select the correct option:
A
$\frac{1}{\varepsilon_0} \sigma^2 \mathrm{R}^2$
B
$\frac{1}{\varepsilon_0} \sigma^2 \mathrm{R}$
C
$\frac{1}{\varepsilon_0} \frac{\sigma^2}{R}$
D
$\frac{1}{\varepsilon_0} \frac{\sigma^2}{R^2}$
✓ Correct! Well done.
✗ Incorrect. Try again or view the solution.
Solution
Pressure $=\frac{\sigma^2}{2 \varepsilon_0}$ and force $=\frac{\sigma^2}{2 \varepsilon_0} \times \pi \mathrm{R}^2$
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