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Three identical spheres , each having a charge q and radius R are kept in such a way that each touches the other two. Find magnitude of electric force on any sphere due to other two sphere,

$(A)\;\frac{1}{4 \pi \in _0} \bigg( \frac{q}{R}\bigg)^2\\ (B)\;\frac{\sqrt 3}{16 \pi \in _0} \bigg( \frac{q}{R}\bigg)^2 \\ (C)\; \frac{\sqrt 3}{4 \pi \in _0} \bigg( \frac{q}{R}\bigg)^2 \\ (D)\;\frac{\sqrt 5}{16 \pi \in _0} \bigg( \frac{q}{R}\bigg)^2 $

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For any external point charged sphere behaves as if whole charge is concentrated at its centre.
$F_{AB} =\large\frac{1}{4 \pi \in _0} \bigg(\frac{q}{2R}\bigg)^2 =\large\frac{1}{4 \pi \in _0} \frac{q^2}{4 R^2}$ along $\overrightarrow {BA}$
$F_{AC} =\large\frac{1}{4 \pi \in _0} \frac{q^2}{4R^2}$ along $\overrightarrow {CA}$
$F_{resultant}=-\sqrt {F^2+F^2 +2.FF. \cos 60^{\circ}}$
$\qquad= \sqrt 3 F$
=>$\large\frac{\sqrt 3}{16 \pi \in _0} \bigg( \frac{q^2}{4R^2}\bigg)$
Hence B is the correct answer.
answered Jan 13, 2014 by meena.p

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