Verified Solution • 2025–26 Session moderate

QPages 121-124: Q27: HC Verma: Concepts of Physics - Volume 2 Electric Field Potential Pages 121-124: Q27 Solution: Two particles A and B with charges q and 2q, respectively, are…

⚠️ Common Exam Traps & Conceptual Pitfalls

Because the two given charges are not equal, the point where the third charge must be placed is not the midpoint. Students often set the third charge at the midpoint and then solve for its magnitude, which gives an incorrect position and charge. The correct approach is to write separate force‑balance equations for A and B, include the direction of each Coulomb force, and solve simultaneously for the distance of C from the midpoint and its charge. Ignoring the asymmetry leads to a wrong answer.

Two particles A and B with charges q and 2q, respectively, are placed on a smooth table with a separation d. A third particle C is to be clamped on the table in such a way that the particles A and B remain at rest on the table under electrical forces. What should be the charge on C and where should it be clamped?

Step-by-Step Verified Solution

**Answer:** Charge on C = −2q33-\frac{2q}{3\sqrt{3}}, placed at distance d3\frac{d}{\sqrt{3}} from the midpoint towards the 2q2q charge. **Step-BY-STEP Explanation:** For A and B to remain at rest, the net force on each must be zero. This requires C to be placed such that the forces balance. By symmetry and solving the equations, the charge on C is −2q/33-2q/3\sqrt{3} at a specific position .

All Questions in this Chapter

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