---
title: "A thin, nonconducting ring of radius \\(R\\) carries a total positive charge \\(Q\\) distributed uniformly along its circumference. A small test particle of positive charge \\(q\\) is constrained to move along the central symmetry axis (\\(z\\)-axis) perpendicular to the plane of the ring. In terms of \\(q\\), \\(Q\\), \\(R\\), and fundamental constants, what is the maximum magnitude of the electrostatic force exerted on the test particle by the ring?"
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url: "https://nerd-notes.com/ubq/117960/"
date_modified: "2026-08-04T08:02:42+00:00"
---

# A thin, nonconducting ring of radius \(R\) carries a total positive charge \(Q\) distributed uniformly along its circumference. A small test particle of positive charge \(q\) is constrained to move along the central symmetry axis (\(z\)-axis) perpendicular to the plane of the ring. In terms of \(q\), \(Q\), \(R\), and fundamental constants, what is the maximum magnitude of the electrostatic force exerted on the test particle by the ring?

A thin, nonconducting ring of radius \(R\) carries a total positive charge \(Q\) distributed uniformly along its circumference. A small test particle of positive charge \(q\) is constrained to move along the central symmetry axis (\(z\)-axis) perpendicular to the plane of the ring. In terms of \(q\), \(Q\), \(R\), and fundamental constants, what is the maximum magnitude of the electrostatic force exerted on the test particle by the ring?

![A thin circular ring of radius R sits horizontally in perspective, drawn as a wide ellipse. The ring carries a positive surface charge label Q. A dashed vertical line representing the z-axis passes through the exact geometric center of the ring, labeled with an origin mark O at the center. At a point along the positive vertical z-axis above the center, a small solid circle represents a test particle with positive charge label q, located at a distance z from the ring's center. A thin straight dashed line extends from a point on the ring's rim to the test particle, forming a right-angled triangle with radius R and distance z. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1785830562-LxhoBn.jpg)

- **A.** \(\dfrac{q Q}{8\sqrt{2} \pi \varepsilon_0 R^2}\)
- **B.** \(\dfrac{q Q}{4\sqrt{3} \pi \varepsilon_0 R^2}\)
- **C.** \(\dfrac{q Q}{6\sqrt{3} \pi \varepsilon_0 R^2}\)
- **D.** \(\dfrac{3 q Q}{32 \pi \varepsilon_0 R^2}\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/117960/*