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QPages 121-124: Q52: HC Verma: Concepts of Physics - Volume 2 Electric Field Potential Pages 121-124: Q52 Solution: A block of mass containing a net positive charge q is placed on …

⚠️ Common Exam Traps & Conceptual Pitfalls

Students often assume that any periodic motion is simple harmonic and apply the SHM period formula. In this problem the force is constant ($F=qE$), so the acceleration is constant and not proportional to displacement. The motion is periodic but not SHM; use kinematics ($d= frac12at^2$) to find the time to reach the wall and then double it for the full period.

A block of mass containing a net positive charge q is placed on a smooth horizontal table which terminates in a vertical wall as shown in the figure. The distance of the block from the wall is d. A horizontal electric field E towards the right is switched on. Assuming elastic collisions if any), find the time period of the resulting oscillatory motion. Is it a simple harmonic motion?

Step-by-Step Verified Solution

**Answer:** T=22mdqET = 2\sqrt{\frac{2md}{qE}}. It is not simple harmonic motion. **Step-BY-STEP Explanation:** The block accelerates under the electric field, hits the wall, and rebounds elastically. The motion is periodic but not SHM because the force is constant (not proportional to displacement). Time to reach wall: d=12at2⇒t=2d/ad = \frac{1}{2}at^2 \Rightarrow t = \sqrt{2d/a} where a=qE/ma = qE/m. Total period: T=2t=22mdqET = 2t = 2\sqrt{\frac{2md}{qE}} .

All Questions in this Chapter

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