Three charges $Q, + q$ and $+ q$ are placed at the vertices of a right-angled isosceles triangle between as shown. The net electrostatic energy of the configuration is zero if $Q$ is equal to

\frac{- 2 q}{1 + \sqrt{2}}

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\frac{2 q}{2 + \sqrt{2}}

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- 2 q

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+ q

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Solution

The correct option is A $\frac{- 2 q}{1 + \sqrt{2}}$
$\begin{matrix} P o t e n t i a l E n e r g y o f s y s t e m o f t w o c h e - U = \frac{k Q_{1} Q_{2}}{r} (S . I) U = \frac{Q_{1} Q_{2}}{r} (C . G . S) w h e r e i n K = \frac{1}{4 π E_{0}} P o t e n t i a l e n e r g y o f t h e c o n f i g u r a t i o n i s U = k . \frac{Q q}{a} + k \frac{q^{2}}{a} + k \frac{q Q}{a \sqrt{2}} = 0 \Rightarrow Q = \frac{- \sqrt{2} q}{\sqrt{2} + 1} \end{matrix}$

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