Verified Solution • 2025–26 Session moderate

QPages 121-124: Q39: HC Verma: Concepts of Physics - Volume 2 Electric Field Potential Pages 121-124: Q39 Solution: A positive charge Q is distributed uniformly over a circular…

⚠️ Common Exam Traps & Conceptual Pitfalls

Students often drop the negative sign of the test charge q, treating $kQq$ as positive and concluding the force is repulsive; this hides the fact that for $x\ll R$ the force is $F\approx-\frac{|kQq|}{R^3}x$, a true restoring force leading to SHM. Always keep the sign of $q$ (or use the magnitude and insert a minus sign for the restoring direction) when linearising the expression.

A positive charge Q is distributed uniformly over a circular ring of radius R. A particle of mass m, and a negative charge q, is placed on its axis at a distance x from the centre. Find the force on the particle. Assuming

x \ll R

, find the time period of oscillation of the particle if it is released from there.

Step-by-Step Verified Solution

**Answer:**

F = \frac{kQq x}{(R^2 + x^2)^{3/2}}

,

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

. **Step-BY-STEP Explanation:** For a ring of charge Q and a charge -q on the axis, the force is directed toward the centre. For

x \ll R

,

F \approx \frac{kQq}{R^3}x

, giving SHM with

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

.

All Questions in this Chapter

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