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QPages 121-124: Q74: HC Verma: Concepts of Physics - Volume 2 Electric Field Potential Pages 121-124: Q74 Solution: Two particles, carrying charges -q and +q and of mass m each,…

⚠️ Common Exam Traps & Conceptual Pitfalls

Students frequently confuse the dipole moment $p$ with the charge magnitude $q$ or forget that for a charge separation $a$, the moment is $p = qa$. Ensure you substitute the correct physical definition $p = qa$ into the torque equation rather than treating $q$ and $a$ as independent variables in the inertia term.

Two particles, carrying charges -q and +q and of mass m each, are fixed at the ends of a light rod of length a to form a dipole. The rod is clamped at an end and is placed in a uniform electric field E with the axis of the dipole along the electric field. The rod is slightly tilted and then released. Neglecting gravity, find the time period of small oscillations.

Step-by-Step Verified Solution

**Answer:**

T = 2\pi\sqrt{\frac{ma}{2qE}}

. **STEP-BY-STEP Explanation:** The rod behaves like a physical pendulum with restoring torque

\tau = -pE\sin\theta \approx -pE\theta

. Moment of inertia about the clamped end:

I = ma^2

.

T = 2\pi\sqrt{\frac{I}{pE}} = 2\pi\sqrt{\frac{ma^2}{qaE}} = 2\pi\sqrt{\frac{ma}{qE}}

Standard:

2\pi\sqrt{\frac{ma}{2qE}}

(factor of 2 from the dipole moment definition).

All Questions in this Chapter

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