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Three charges each Q are placed at three vertices of an equilateral triangle. A fourth charge q is placed at the centre of the triangle. The ratio $|\frac{q}{Q}|$ so as to keep the system in equilibrium is

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$1 : \sqrt{3}$

1:3

$2 : \sqrt{3}$

$\sqrt{3} : 1$

answer is B.

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Detailed Solution

For ‘Q’ to be in equilibrium

$2 F \cos (30) = F^{1}$

$2. \frac{1}{4 π ϵ_{0}} \frac{Q^{2}}{l^{2}} \cdot \frac{\sqrt{3}}{2} = \frac{1}{4 π ϵ_{0}} \frac{Q \cdot q}{{(\frac{l}{\sqrt{3}})}^{2}}$

$\Rightarrow \frac{q}{Q} = \frac{1}{\sqrt{3}}$

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