MHT CET · Physics · Electrostatics
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?
- A \(-q\)
- B \(\frac{\mathrm{q}}{2}\)
- C \(-2 q\)
- D \(-\frac{\mathrm{q}}{2}\)
Answer & Solution
Correct Answer
(D) \(-\frac{\mathrm{q}}{2}\)
Step-by-step Solution
Detailed explanation
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 \(\mathrm{A}=\frac{\mathrm{Qq}}{4 \pi \varepsilon_0 \mathrm{a}}\)
\(\begin{aligned} & \therefore \quad \text { Total P.E }=\frac{q}{4 \pi \varepsilon_0 a}(q+Q+Q)=0 \\ & \therefore \quad 2 Q+q=0 \quad \Rightarrow Q=-\frac{q}{2}\end{aligned}\)
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