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# A spherical shell of radius R has a charge Q uniformly distributed on its surface. What is the force exerted by one half over the other.

$(A)\;\frac{Q^2}{4 \pi \in _0 R^2}\\ (B)\;\frac{Q^2}{4 \pi \in _0 R^2}\times 2 \\ (C)\; \frac{Q^2}{16 \pi \in _0 R^2} \\ (D)\;\frac{Q^2}{32 \pi \in _0 R^2}$

$E= \large\frac{\sigma}{2 \in _0}$
$F= Edr=\large\frac{\sigma}{2 \in _0}$$(\sigma dA) => \large\frac{F}{dA} =\frac{\sigma^2}{\in_0}$$=P$
Force $= P \times \pi R^2$
$\qquad= \large\frac{\sigma^2}{2 \in _0} \pi R^2$
$\qquad= \large\frac{Q^2}{16 \pi^2 R^2} \frac{\pi R^2}{2 \in _0}$
=> $\large\frac{Q^2}{32 \pi \in _0 R^2}$
Hence D is the correct answer.