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title: "A thin, flat, nonconducting disk of radius \\(R\\) is centered at the origin in the \\(xy\\)-plane and carries a uniform positive surface charge density \\(\\sigma\\). Which of the following expressions represents the correct integral setup to determine the absolute electric potential \\(V\\) at a point \\(P\\) on the \\(z\\)-axis at a distance \\(z\\) from the center of the disk, assuming \\(V = 0\\) at infinity?"
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url: "https://nerd-notes.com/ubq/121072/"
date_modified: "2026-08-23T04:57:41+00:00"
---

# A thin, flat, nonconducting disk of radius \(R\) is centered at the origin in the \(xy\)-plane and carries a uniform positive surface charge density \(\sigma\). Which of the following expressions represents the correct integral setup to determine the absolute electric potential \(V\) at a point \(P\) on the \(z\)-axis at a distance \(z\) from the center of the disk, assuming \(V = 0\) at infinity?

A thin, flat, nonconducting disk of radius \(R\) is centered at the origin in the \(xy\)-plane and carries a uniform positive surface charge density \(\sigma\). Which of the following expressions represents the correct integral setup to determine the absolute electric potential \(V\) at a point \(P\) on the \(z\)-axis at a distance \(z\) from the center of the disk, assuming \(V = 0\) at infinity?

![A three-dimensional coordinate perspective showing a flat circular disk centered at the origin in the horizontal plane. The disk has a light gray fill. A straight arrow labeled R extends from the origin toward the outer edge of the circular disk at a 45-degree angle in the plane. A vertical dashed line extends upward along the z-axis from the center of the disk to a solid dot labeled P. A double-headed vertical dimension line next to the dashed axis indicates the vertical distance z from the center of the disk to point P. The symbol \sigma is placed on the surface of the disk. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1787461061-1offCP.jpg)

- **A.** \(\dfrac{\sigma}{4\pi\varepsilon_0} \int_0^R \dfrac{r}{\sqrt{r^2 + z^2}}\,dr\)
- **B.** \(\dfrac{\sigma}{2\varepsilon_0} \int_0^R \dfrac{r}{\sqrt{r^2 + z^2}}\,dr\)
- **C.** \(\dfrac{\sigma}{2\varepsilon_0} \int_0^R \dfrac{r}{r^2 + z^2}\,dr\)
- **D.** \(\dfrac{\sigma z}{2\varepsilon_0} \int_0^R \dfrac{r}{\left(r^2 + z^2\right)^{3/2}}\,dr\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/121072/*