Three identical charged balls,each of charge | vedclass

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(D) Let the charge on each ball be $q = 2 \, C$ and the distance between any two balls be $r = 1 \, m$.The electrostatic force $F$ between any two cha

Vedclass · Accepted Answer

$\sqrt{3}: 1$

Vedclass · Answer

(D) Let the charge on each ball be $q = 2 \, C$ and the distance between any two balls be $r = 1 \, m$.The electrostatic force $F$ between any two charged balls is given by Coulomb's law:$F = \frac{k q^2}{r^2} = \frac{k (2)^2}{(1)^2} = 4k$Consider one of the charged balls. It experiences two electrostatic forces from the other two balls. Since the balls form an equilateral triangle,the angle between these two forces is $60^{\circ}$.The net electrostatic force $F_{	ext{net}}$ on one ball due to the other two is the vector sum of these two forces:$F_{	ext{net}} = \sqrt{F^2 + F^2 + 2 F^2 \cos 60^{\circ}} = \sqrt{2F^2 + 2F^2 (0.5)} = \sqrt{3F^2} = F \sqrt{3}$Therefore,the ratio of the net electrostatic force to the force between any two charged balls is:$\frac{F_{	ext{net}}}{F} = \frac{F \sqrt{3}}{F} = \sqrt{3} = \frac{\sqrt{3}}{1}$Thus,the correct option is $D$.

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