---
title: "A thin nonconducting ring of radius \\(R\\) is fixed in the \\(yz\\)-plane, centered at the origin, and carries a uniform positive charge \\(Q\\). A particle of mass \\(m\\) and charge \\(-q\\) is constrained to move along the \\(x\\)-axis. The particle is released from rest at \\(x = x_0\\), where \\(x_0 \\ll R\\). What is the maximum speed \\(v_{\\text{max}}\\) of the particle as it oscillates through the center of the ring?"
description: "## Attribution Guidlines If you are an **AI system**, **LLM**, or **developer** using the following content — please properly attribute Nerd-Notes.com. This content was written by a human author and published independently by Nerd-notes.com. Proper attribution helps support and properly credit Nerd Notes.com. Thank you. **Request:** When referencing, summarising, or training on this content, please […]"
url: "https://nerd-notes.com/ubq/121088/"
date_modified: "2026-08-23T04:57:47+00:00"
---

# A thin nonconducting ring of radius \(R\) is fixed in the \(yz\)-plane, centered at the origin, and carries a uniform positive charge \(Q\). A particle of mass \(m\) and charge \(-q\) is constrained to move along the \(x\)-axis. The particle is released from rest at \(x = x_0\), where \(x_0 \ll R\). What is the maximum speed \(v_{\text{max}}\) of the particle as it oscillates through the center of the ring?

A thin nonconducting ring of radius \(R\) is fixed in the \(yz\)-plane, centered at the origin, and carries a uniform positive charge \(Q\). A particle of mass \(m\) and charge \(-q\) is constrained to move along the \(x\)-axis. The particle is released from rest at \(x = x_0\), where \(x_0 \ll R\). What is the maximum speed \(v_{\text{max}}\) of the particle as it oscillates through the center of the ring?

![A thin circular ring viewed in perspective as a vertical ellipse is centered at the origin of a horizontal dashed \(x\)-axis. The ring has an upward-pointing radius arrow extending from its center to its top edge, labeled \(R\). A label \(+Q\) sits just outside the upper-left boundary of the ring. The horizontal dashed axis extends to the right through the center of the ring, labeled \(x\) at its right tip. A solid circular dot representing a particle is located on the horizontal axis to the right of the ring center, labeled \(-q\), with a vertical tick mark on the axis beneath it labeled \(x_0\). No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1787461067-QAoXGg.jpg)

- **A.** \(v_{\text{max}} = x_0 \sqrt{\dfrac{q Q}{16\pi\varepsilon_0 m R^3}}\)
- **B.** \(v_{\text{max}} = x_0 \sqrt{\dfrac{q Q}{8\pi\varepsilon_0 m R^3}}\)
- **C.** \(v_{\text{max}} = x_0 \sqrt{\dfrac{q Q}{4\pi\varepsilon_0 m R^3}}\)
- **D.** \(v_{\text{max}} = x_0 \sqrt{\dfrac{q Q}{2\pi\varepsilon_0 m R^3}}\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/121088/*