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2. Electric Potential and Capacitance
normal
A uniformly charged thin spherical shell of radius $\mathrm{R}$ carries uniform surface charge density of $\sigma$ per unit area. It is made of two hemispherical shells, held together by pressing them with force $\mathrm{F}$ (see figure). $\mathrm{F}$ is proportional to
A
$\frac{1}{\varepsilon_0} \sigma^2 R^2$
B
$\frac{1}{\varepsilon_0} \sigma^2 R$
C
$\frac{1}{\varepsilon_0} \frac{\sigma^2}{\mathrm{R}}$
D
$\frac{1}{\varepsilon_0} \frac{\sigma^2}{\mathrm{R}^2}$
(IIT-2010)
Solution
Pressure $=\frac{\sigma^2}{2 \varepsilon_0}$ and force $=\frac{\sigma^2}{2 \varepsilon_0} \times \pi \mathrm{R}^2$
Standard 12
Physics
