---
title: "A thin, flat disk of radius \\(R\\) lies in the \\(xy\\)-plane centered at the origin and carries a uniform surface charge density \\(\\sigma\\). Which of the following expressions represents the correct integral setup to calculate the magnitude of the electric field \\(E\\) along the \\(z\\)-axis at a distance \\(z > 0\\) from the center of the disk?"
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url: "https://nerd-notes.com/ubq/117933/"
date_modified: "2026-08-04T08:02:37+00:00"
---

# A thin, flat disk of radius \(R\) lies in the \(xy\)-plane centered at the origin and carries a uniform surface charge density \(\sigma\). Which of the following expressions represents the correct integral setup to calculate the magnitude of the electric field \(E\) along the \(z\)-axis at a distance \(z > 0\) from the center of the disk?

A thin, flat disk of radius \(R\) lies in the \(xy\)-plane centered at the origin and carries a uniform surface charge density \(\sigma\). Which of the following expressions represents the correct integral setup to calculate the magnitude of the electric field \(E\) along the \(z\)-axis at a distance \(z > 0\) from the center of the disk?

![A perspective view of a circular disk lying horizontally in the xy-plane, centered at the origin of a three-dimensional coordinate system. A vertical axis labeled z extends upward from the center of the disk. The circular disk has a radius labeled R, indicated by a straight line segment extending from the center of the disk to its outer rim. A point on the vertical z-axis above the center of the disk is labeled at a height z. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1785830557-csiYYU.jpg)

- **A.** \(\dfrac{\sigma z}{2\varepsilon_0} \int_0^R \dfrac{dr}{(r^2 + z^2)^{3/2}}\)
- **B.** \(\dfrac{\sigma}{2\varepsilon_0} \int_0^R \dfrac{r \, dr}{r^2 + z^2}\)
- **C.** \(\dfrac{\sigma z}{2\varepsilon_0} \int_0^R \dfrac{r \, dr}{(r^2 + z^2)^{3/2}}\)
- **D.** \(\dfrac{\sigma z}{2\varepsilon_0} \int_0^R \dfrac{r^2 \, dr}{(r^2 + z^2)^{3/2}}\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/117933/*