---
title: "A thin, flat, nonconducting annular disk lies in the \\(xy\\)-plane centered at the origin. The disk has an outer radius \\(R\\), a central circular hole of radius \\(\\dfrac{R}{2}\\), and carries a uniform surface charge density \\(\\sigma\\). A point \\(P\\) is located on the positive \\(z\\)-axis at a distance \\(z\\) from the origin. Which of the following expressions gives the magnitude of the electric field at point \\(P\\)?"
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url: "https://nerd-notes.com/ubq/117951/"
date_modified: "2026-08-04T08:02:40+00:00"
---

# A thin, flat, nonconducting annular disk lies in the \(xy\)-plane centered at the origin. The disk has an outer radius \(R\), a central circular hole of radius \(\dfrac{R}{2}\), and carries a uniform surface charge density \(\sigma\). A point \(P\) is located on the positive \(z\)-axis at a distance \(z\) from the origin. Which of the following expressions gives the magnitude of the electric field at point \(P\)?

A thin, flat, nonconducting annular disk lies in the \(xy\)-plane centered at the origin. The disk has an outer radius \(R\), a central circular hole of radius \(\dfrac{R}{2}\), and carries a uniform surface charge density \(\sigma\). A point \(P\) is located on the positive \(z\)-axis at a distance \(z\) from the origin. Which of the following expressions gives the magnitude of the electric field at point \(P\)?

![A 3D perspective diagram showing a flat annular disk lying horizontally in the xy-plane, centered at the origin. The outer radius of the disk is labeled R, and the inner hole radius is labeled \dfrac{R}{2}. A vertical z-axis extends upward from the center of the disk through the origin. A point P is marked on the z-axis at a height z above the xy-plane. A dashed line connects the origin to point P along the z-axis. Shading indicates the thin ring-shaped region of the disk between r = \dfrac{R}{2} and r = R. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1785830560-afmF2B.jpg)

- **A.** \(\dfrac{\sigma z}{2\varepsilon_0} \left( \dfrac{1}{\sqrt{R^2 + z^2}} - \dfrac{1}{\sqrt{\dfrac{1}{4}R^2 + z^2}} \right)\)
- **B.** \(\dfrac{\sigma z}{2\varepsilon_0} \left( \dfrac{1}{z} - \dfrac{1}{\sqrt{R^2 + z^2}} \right)\)
- **C.** \(\dfrac{\sigma z}{2\varepsilon_0} \left( \dfrac{1}{z} - \dfrac{1}{\sqrt{\dfrac{3}{4}R^2 + z^2}} \right)\)
- **D.** \(\dfrac{\sigma z}{2\varepsilon_0} \left( \dfrac{1}{\sqrt{\dfrac{1}{4}R^2 + z^2}} - \dfrac{1}{\sqrt{R^2 + z^2}} \right)\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/117951/*