Question 28 of 311

Three identical charged balls each of charge $2C$ are suspended from a common point $P$ by silk threads of $2m$ each (as shown in figure). They form an equilateral triangle of side $1m$.
The ratio of net force on a charged ball to the force between any two charged balls will be

A$\sqrt{3}:1$B$\sqrt{3}:2$C$1:1$D$1:4$

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Answer: (A) $\sqrt{3}:1$

We have force between any two charge${F}_{1}={F}_{2}=\dfrac{{q}^{2}}{4\pi {\epsilon }_{0}{l}^{2}}=F$
Resultant electrostatics force ${F}_{R}=\sqrt{{F}_{1}^{2}+{F}_{2}^{2}+2{F}_{1}{F}_{2}\cos 60^{\circ}}$
$=\sqrt{{F}^{2}+{F}^{2}+\left(2{F}^{2}\times \dfrac{1}{2}\right)}=\sqrt{3{F}^{2}}$
So, the ratio of net force on a charged ball to the force between any charged balls is
$\Rightarrow \dfrac{{F}_{R}}{F}=\sqrt{3}$