JEE Advance - Physics (2010 - Paper 2 Offline - No. 8)
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
$${1 \over {{\varepsilon _0}}}{\sigma ^2}{R^2}$$
$${1 \over {{\varepsilon _0}}}{\sigma ^2}R$$
$${1 \over {{\varepsilon _0}}}{{{\sigma ^2}} \over R}$$
$${1 \over {{\varepsilon _0}}}{{{\sigma ^2}} \over {{R^2}}}$$
Explanation
Electrostatic pressure is
$$\left( {{{{\sigma ^2}} \over {2{\varepsilon _0}}}} \right)$$ N/m2
The force is
$$F = {{{\sigma ^2}} \over {2{\varepsilon _0}}} \times \pi {R^2}$$
Therefore, $$F \propto {{{\sigma ^2}{R^2}} \over {{\varepsilon _0}}}$$
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