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

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Aicharya · Accepted Answer

For external points, a charged sphere behaves as if the whole of its charge were concentrated at its center.

Force on $A$ due to $B$,
$F_{A B}=\frac{1}{4 \pi \varepsilon_{0}} \frac{q^{2}}{(2 R)^{2}}=\frac{1}{4 \pi \varepsilon_{0}} \frac{q^{2}}{4 R^{2}}$ along BA
And force on $A$ due to $C$
$F_{A C}=\frac{1}{4 \pi \varepsilon_{0}(2 R)^{2}}=\frac{1}{4 \pi \varepsilon_{0}} \frac{q^{2}}{4 R^{2}} \text { along } \mathrm{CA}$
Now as angle between $B A$ and $C A$ is $60^{\circ}$ and
$|F_{AB}|=|F_{AC}|=F$ $\therefore \quad F_{A}=\sqrt{F^{2}+F^{2}+2 F \cdot F \cdot \cos 60}=\sqrt{3} F$
$F_{A}=\frac{1}{4 \pi \varepsilon_{0}} \frac{\sqrt{3}}{4}\left(\frac{q}{R}\right)^{2}$

Three identical spheres, each having a change \(q\) and radius \(R\), are kept in such a way that each…

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