---
title: "A thin circular ring of radius \\(R\\) carries a total positive charge \\(Q\\) distributed uniformly along its circumference. Point \\(P\\) lies on the central axis perpendicular to the plane of the ring at a distance \\(z\\) from the center of the ring. At what distance \\(z\\) is the magnitude of the electric field at point \\(P\\) a maximum?"
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url: "https://nerd-notes.com/ubq/117916/"
date_modified: "2026-08-04T08:02:34+00:00"
---

# A thin circular ring of radius \(R\) carries a total positive charge \(Q\) distributed uniformly along its circumference. Point \(P\) lies on the central axis perpendicular to the plane of the ring at a distance \(z\) from the center of the ring. At what distance \(z\) is the magnitude of the electric field at point \(P\) a maximum?

A thin circular ring of radius \(R\) carries a total positive charge \(Q\) distributed uniformly along its circumference. Point \(P\) lies on the central axis perpendicular to the plane of the ring at a distance \(z\) from the center of the ring. At what distance \(z\) is the magnitude of the electric field at point \(P\) a maximum?

![A thin circular ring of radius \(R\) lies horizontally in perspective. The central perpendicular axis extends vertically through the center of the ring. A point \(P\) is marked on the vertical axis at a distance \(z\) above the ring center. Dashed lines connect opposite points on the ring perimeter to point \(P\). A charge label \(+Q\) is placed next to the ring. No other labels, lines, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1785830554-QfoBI7.jpg)

- **A.** \(z = 0\)
- **B.** \(z = \dfrac{R}{4}\)
- **C.** \(z = \dfrac{R}{2}\)
- **D.** \(z = \dfrac{R}{\sqrt{2}}\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/117916/*