First slide

Electrostatic force

Question

Three charges (each Q) are placed at the three corners of an equilateral triangle. A fourth charge q is placed at the center of the triangle. The ratio ' q/Q' so as to make the system in equilibrium is

Moderate

A

1:3
B

$1 : \sqrt{3}$
C

$\sqrt{3} : 1$
D

$2 : \sqrt{3}$

Solution

Net force on q will be zero for any values of q and Q. Net force on each Q should also be zero. For this, q should be negative of Q.
$\begin{array}{l} F_{2} = 2 F_{1} \cos 30^{\circ} \\ or \frac{k q Q}{(a / \sqrt{3})^{2}} = 2 \frac{k Q^{2}}{a^{2}} \frac{\sqrt{3}}{2} or \frac{q}{Q} = \frac{1}{\sqrt{3}} \end{array}$

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