---
title: "A thin, flat annular disk has an inner radius \\(a\\), an outer radius \\(b\\), and a uniform positive surface charge density \\(\\sigma\\). The disk lies in the \\(xy\\)-plane centered at the origin, and point \\(P\\) is located on the central \\(z\\)-axis at a distance \\(z\\) from the center of the disk. Which of the following expressions represents the correct integral setup to determine the electric potential \\(V\\) at point \\(P\\) relative to zero potential at infinity?"
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url: "https://nerd-notes.com/ubq/121056/"
date_modified: "2026-08-23T04:57:39+00:00"
---

# A thin, flat annular disk has an inner radius \(a\), an outer radius \(b\), and a uniform positive surface charge density \(\sigma\). The disk lies in the \(xy\)-plane centered at the origin, and point \(P\) is located on the central \(z\)-axis at a distance \(z\) from the center of the disk. Which of the following expressions represents the correct integral setup to determine the electric potential \(V\) at point \(P\) relative to zero potential at infinity?

A thin, flat annular disk has an inner radius \(a\), an outer radius \(b\), and a uniform positive surface charge density \(\sigma\). The disk lies in the \(xy\)-plane centered at the origin, and point \(P\) is located on the central \(z\)-axis at a distance \(z\) from the center of the disk. Which of the following expressions represents the correct integral setup to determine the electric potential \(V\) at point \(P\) relative to zero potential at infinity?

![A flat circular ring (annulus) viewed at an oblique angle, lying horizontally in perspective. The annulus has an inner circular boundary of radius labeled a and an outer circular boundary of radius labeled b. A thin concentric ring element of radius r and thickness dr is indicated within the annulus with fine dashed concentric outlines. A vertical dashed axis extends upward perpendicularly from the center of the annulus. Along this vertical axis, at a height labeled z above the center, is a single point labeled P. A straight dashed segment connects a point on the thin ring element of radius r to point P, labeled with distance \(\sqrt{r^2 + z^2}\). No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1787461059-1ILeo7.jpg)

- **A.** \(V = \dfrac{\sigma z}{2\varepsilon_0} \int_{a}^{b} \dfrac{r}{(r^2 + z^2)^{3/2}} \, dr\)
- **B.** \(V = \dfrac{\sigma}{2\varepsilon_0} \int_{a}^{b} \dfrac{r}{\sqrt{r^2 + z^2}} \, dr\)
- **C.** \(V = \dfrac{\sigma}{2\varepsilon_0} \int_{a}^{b} \dfrac{1}{\sqrt{r^2 + z^2}} \, dr\)
- **D.** \(V = \dfrac{\sigma}{2\varepsilon_0} \int_{a}^{b} \dfrac{r}{r^2 + z^2} \, dr\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/121056/*