---
title: "An infinite, nonconducting, flat sheet carries a uniform positive surface charge density \\(\\sigma\\). Points \\(A\\) and \\(B\\) are located on the same side of the sheet at perpendicular distances \\(x_1\\) and \\(x_2\\) from the sheet, respectively, where \\(x_2 > x_1\\). What is the magnitude of the electric potential difference \\(\\Delta V = |V_B – V_A|\\) between points \\(A\\) and \\(B\\)?"
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url: "https://nerd-notes.com/ubq/118076/"
date_modified: "2026-08-04T08:04:59+00:00"
---

# An infinite, nonconducting, flat sheet carries a uniform positive surface charge density \(\sigma\). Points \(A\) and \(B\) are located on the same side of the sheet at perpendicular distances \(x_1\) and \(x_2\) from the sheet, respectively, where \(x_2 > x_1\). What is the magnitude of the electric potential difference \(\Delta V = |V_B – V_A|\) between points \(A\) and \(B\)?

An infinite, nonconducting, flat sheet carries a uniform positive surface charge density \(\sigma\). Points \(A\) and \(B\) are located on the same side of the sheet at perpendicular distances \(x_1\) and \(x_2\) from the sheet, respectively, where \(x_2 > x_1\). What is the magnitude of the electric potential difference \(\Delta V = |V_B - V_A|\) between points \(A\) and \(B\)?

![A vertical shaded planar surface representing an infinite sheet of positive charge labeled +\sigma. A horizontal dashed axis perpendicular to the sheet extends to the right. Point A is located on the dashed line at distance x_1 from the sheet. Point B is located further to the right on the same dashed line at distance x_2 from the sheet. Dimension arrows beneath the dashed line indicate the distance x_1 from the sheet to point A and the distance x_2 from the sheet to point B. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1785830699-S5QFvV.jpg)

- **A.** \(\dfrac{\sigma}{2\varepsilon_0}(x_2 - x_1)\)
- **B.** \(\dfrac{\sigma}{\varepsilon_0}(x_2 - x_1)\)
- **C.** \(\dfrac{\sigma}{2\varepsilon_0}\ln\left(\dfrac{x_2}{x_1}\right)\)
- **D.** \(\dfrac{\sigma}{2\varepsilon_0}\left(\dfrac{1}{x_1} - \dfrac{1}{x_2}\right)\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/118076/*