COMEDK · Physics · 17. Electrostatics

Three charges, \(\mathrm{Q},-\mathrm{q}\) and 2 q are placed at the vertices of a right-angled isosceles triangle. What is the value of \(q\) for the net electrostatic energy of the configuration to be zero?

A \(Q\left[\dfrac{1}{2 \sqrt{2}}-1\right]\)
B \(Q\left[1+\dfrac{1}{2 \sqrt{2}}\right]\)
C \(Q\left[1-\dfrac{1}{2 \sqrt{2}}\right]\)
D \(Q\left[\dfrac{2 \sqrt{2}+1}{2}\right]\)

Verified Solution

Answer & Solution

Correct Answer

(C) \(Q\left[1-\dfrac{1}{2 \sqrt{2}}\right]\)

Step-by-step Solution

Detailed explanation

The electrostatic potential energy \(U\) of a system of point charges is given by the sum of the potential energies of all pairs of charges: \(U = \sum \dfrac{k q_i q_j}{r_{ij}}\). The charges are \(Q\), \(2q\), and \(-q\). The distances between the pairs are \(r\), \(r\), and…

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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