---
title: "A thin, flexible insulating ring of radius \\(R\\) carries a net positive charge \\(+Q\\) distributed uniformly along its circumference. A point charge \\(+q\\) is held fixed at the center of the ring. An external force slowly compresses the ring symmetrically, reducing its radius to \\(\\dfrac{R}{2}\\) while keeping the point charge fixed at the center. What is the work done by the external force on the ring-charge system during this compression?"
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url: "https://nerd-notes.com/ubq/118119/"
date_modified: "2026-08-04T08:05:13+00:00"
---

# A thin, flexible insulating ring of radius \(R\) carries a net positive charge \(+Q\) distributed uniformly along its circumference. A point charge \(+q\) is held fixed at the center of the ring. An external force slowly compresses the ring symmetrically, reducing its radius to \(\dfrac{R}{2}\) while keeping the point charge fixed at the center. What is the work done by the external force on the ring-charge system during this compression?

A thin, flexible insulating ring of radius \(R\) carries a net positive charge \(+Q\) distributed uniformly along its circumference. A point charge \(+q\) is held fixed at the center of the ring. An external force slowly compresses the ring symmetrically, reducing its radius to \(\dfrac{R}{2}\) while keeping the point charge fixed at the center. What is the work done by the external force on the ring-charge system during this compression?

![A schematic diagram showing two concentric circles on a plain white background. The outer dashed circle has radius R and is labeled +Q around its perimeter. A curved arrow points inward from the outer dashed circle to an inner solid circle of radius R/2. At the exact center of both circles is a small solid dot labeled +q. A line segment from the center to the outer dashed circle is labeled R, and a shorter line segment from the center to the inner solid circle is labeled R/2. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1785830713-dV50nJ.jpg)

- **A.** \(-\dfrac{q Q}{4\pi\varepsilon_0 R}\)
- **B.** \(\dfrac{q Q}{8\pi\varepsilon_0 R}\)
- **C.** \(\dfrac{q Q}{2\pi\varepsilon_0 R}\)
- **D.** \(\dfrac{q Q}{4\pi\varepsilon_0 R}\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/118119/*