---
title: "A thin, nonconducting ring of radius \\(R\\) lies in the \\(xy\\)-plane with its center at the origin. A total positive charge \\(Q\\) is distributed non-uniformly along the perimeter of the ring. Which of the following correctly states the electric potential \\(V\\) at the center of the ring relative to infinity, along with the correct physical justification?"
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url: "https://nerd-notes.com/ubq/118054/"
date_modified: "2026-08-04T08:04:55+00:00"
---

# A thin, nonconducting ring of radius \(R\) lies in the \(xy\)-plane with its center at the origin. A total positive charge \(Q\) is distributed non-uniformly along the perimeter of the ring. Which of the following correctly states the electric potential \(V\) at the center of the ring relative to infinity, along with the correct physical justification?

A thin, nonconducting ring of radius \(R\) lies in the \(xy\)-plane with its center at the origin. A total positive charge \(Q\) is distributed non-uniformly along the perimeter of the ring. Which of the following correctly states the electric potential \(V\) at the center of the ring relative to infinity, along with the correct physical justification?

![A circular ring of radius R centered at the origin in the xy-plane. The ring is shaded unevenly to represent a non-uniform charge distribution. A dashed radial line extends from the origin O to a point on the perimeter of the ring, labeled R. A tiny segment of the ring is highlighted and labeled dq. No other vectors, lines, or labels appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-ring-diagram-1785830694-0PTjTP.jpg)

- **A.** \(V = 0\), because the electric potential vectors from opposing charge elements along the ring sum to zero.
- **B.** \(V = \dfrac{1}{4\pi\varepsilon_0}\dfrac{Q}{R^2}\), because the electric potential of a continuous charge distribution depends on distance in the same way as the electric field magnitude.
- **C.** \(V = \dfrac{1}{4\pi\varepsilon_0}\dfrac{Q}{R}\), because electric potential is a scalar quantity and every charge element on the ring is located at the distance \(R\) from the center.
- **D.** \(V = \dfrac{1}{4\pi\varepsilon_0}\dfrac{Q}{R}\), because a non-uniform charge distribution always creates a net zero electric field at the center of the ring.

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/118054/*