Two charges $+q$ each are kept ' $2 a$ ' distance apart. A third charge $-2 q$ is placed midway between them. The potential energy of the system is -

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Correct answer: c) $\frac{-7 q^2}{8 \pi \varepsilon_0 a }$. ${U}_{T}=\frac{1}{4\pi {\epsilon }_{0}}\left[-\frac{2{q}^{2}}{a}-\frac{2{q}^{2}}{a}+\frac{{q}^{2}}{2a}\right]\ =\frac{1}{4\pi {\epsilon }_{0}a}\left[-4+\frac{1}{2}\right]\ {U}_{T}=\frac{-7{q}^{2}}{8\pi {\epsilon }_{0}a}\$

Two charges \(+q\) each are kept ' \(2 a\) ' distance apart. A third charge \(-2 q\) is placed midway between them. The …

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