Verified Solution • 2025–26 Session moderate

QPages 121-124: Q32.3: HC Verma: Concepts of Physics - Volume 2 Electric Field Potential Pages 121-124: Q32.3 Solution: Two particles A and B, each carrying a charge Q, are held fixed …

⚠️ Common Exam Traps & Conceptual Pitfalls

Students often assume the motion is SHM without verifying the sign of the product $Qq$; for the restoring force to be directed toward the equilibrium point, the interaction must be attractive, requiring $Q$ and $q$ to have opposite signs.

Two particles A and B, each carrying a charge Q, are held fixed with a separation d between them. A particle C of mass m and charge q is kept at the middle point of the line AB. Under what conditions will the particle C execute simple harmonic motion if it is released after such a small displacement? Find the time period of the oscillations if these conditions are satisfied.

Step-by-Step Verified Solution

**Answer:**

T = 2\pi\sqrt{\frac{md^3}{16kQq}}

. **Step-BY-STEP Explanation:** Since

F = -kx

with

k = \frac{16kQq}{d^3}

, the motion is SHM. The time period is:

T = 2\pi\sqrt{\frac{m}{k}} = 2\pi\sqrt{\frac{md^3}{16kQq}}

All Questions in this Chapter

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