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If three charges ‘q’ each are placed at the vertices of an equilateral triangle. What is the net potential energy, if the side of equilateral triangle is $l c m$ ?

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$\frac{1}{4 π ε_{0}} \frac{q^{2}}{l}$

$\frac{1}{4 π ε_{0}} \frac{2 q^{2}}{l}$

$\frac{1}{4 π ε_{0}} \frac{3 q^{2}}{l}$

$\frac{1}{4 π ε_{0}} \frac{4 q^{2}}{l}$

answer is C.

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Detailed Solution

$U = \frac{1}{2} \sum_{\begin{array}{l} i, j = 1 \\ i \neq j \end{array}}^{n} \frac{1}{4 π ε_{0}} \frac{q_{i} q_{j}}{r_{i j}}$

$U = 3 \frac{1}{4 π ε_{0}} \frac{q^{2}}{l}$

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