Three charges are placed at the vertices of an equilateral triangle as shown in the figure. For what value of charge ' $Q$ ', the electrostatic potential energy of the system is zero?

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Aicharya · Accepted Answer

Potential energy $U=\frac{1}{4 \pi \varepsilon_0} \frac{\mathrm{q}_1 \mathrm{q}_2}{\mathrm{a}}$ $\therefore \quad$ Potential energy at $A$ due to $B=\frac{q^2}{4 \pi \varepsilon_0 a}$ Potential energy at B due to $\mathrm{C}=\frac{\mathrm{Qq}}{4 \pi \varepsilon_0 \mathrm{a}}$ Potential energy at C due to $\mathrm{A}=\frac{\mathrm{Qq}}{4 \pi \varepsilon_0 \mathrm{a}}$ $\begin{aligned} & \therefore \quad \text { Total P.E }=\frac{q}{4 \pi \varepsilon_0 a}(q+Q+Q)=0 \\ & \therefore \quad 2 Q+q=0 \quad \Rightarrow Q=-\frac{q}{2}\end{aligned}$

Three charges are placed at the vertices of an equilateral triangle as shown in the figure. For what value…

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