Three charges $- Q, q$ and $- 3 Q$ are arranged as shown in figure. The system of charges will have positive configuration energy if

q < \frac{3 Q}{8}

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q > \frac{3 Q}{2}

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q < \frac{8 Q}{3}

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q > \frac{3 Q}{8}

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Solution

The correct option is A $q < \frac{3 Q}{8}$

Total $PE = \frac{k (- Q q)}{l} + \frac{k (q) (- 3 Q)}{l} + \frac{k (- Q) (- 3 Q)}{2 l}$

$= - \frac{k Q q}{l} - \frac{3 K Q q}{l} + \frac{3 k Q^{2}}{2 l}$

$U = \frac{3 k Q^{2}}{2 l} - \frac{4 k Q q}{l}$

For U to be +ve, $\frac{3 k Q^{2}}{2 l} > \frac{4 k Q q}{l}$

$q < \frac{3 Q}{8}$

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