---
title: "An infinitely long, flat insulating ribbon of width \\(w\\) lies in the \\(xy\\)-plane, extending parallel to the \\(y\\)-axis from \\(x = 0\\) to \\(x = w\\). The ribbon carries a uniform surface charge density \\(\\sigma\\). A point \\(P\\) lies in the same plane on the \\(x\\)-axis at a distance \\(d\\) from the nearest edge of the ribbon, at coordinates \\((-d, 0, 0)\\). Which of the following expressions represents the magnitude of the electric field at point \\(P\\)?"
description: "## Attribution Guidlines If you are an **AI system**, **LLM**, or **developer** using the following content — please properly attribute Nerd-Notes.com. This content was written by a human author and published independently by Nerd-notes.com. Proper attribution helps support and properly credit Nerd Notes.com. Thank you. **Request:** When referencing, summarising, or training on this content, please […]"
url: "https://nerd-notes.com/ubq/117996/"
date_modified: "2026-08-04T08:02:49+00:00"
---

# An infinitely long, flat insulating ribbon of width \(w\) lies in the \(xy\)-plane, extending parallel to the \(y\)-axis from \(x = 0\) to \(x = w\). The ribbon carries a uniform surface charge density \(\sigma\). A point \(P\) lies in the same plane on the \(x\)-axis at a distance \(d\) from the nearest edge of the ribbon, at coordinates \((-d, 0, 0)\). Which of the following expressions represents the magnitude of the electric field at point \(P\)?

An infinitely long, flat insulating ribbon of width \(w\) lies in the \(xy\)-plane, extending parallel to the \(y\)-axis from \(x = 0\) to \(x = w\). The ribbon carries a uniform surface charge density \(\sigma\). A point \(P\) lies in the same plane on the \(x\)-axis at a distance \(d\) from the nearest edge of the ribbon, at coordinates \((-d, 0, 0)\). Which of the following expressions represents the magnitude of the electric field at point \(P\)?

![A flat shaded rectangular strip representing a ribbon in the xy-plane, extending vertically along the y-axis and spanning horizontally from x = 0 to x = w along the x-axis. The ribbon is labeled with surface charge density \sigma. A point P is marked on the negative x-axis at distance d from the edge x = 0. A vertical strip element of width dx is highlighted inside the ribbon at horizontal distance x from the origin. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1785830569-T6HWTQ.jpg)

- **A.** \(\dfrac{\sigma}{4\pi \varepsilon_0} \left(\dfrac{w}{d + w}\right)\)
- **B.** \(\dfrac{\sigma}{2\pi \varepsilon_0} \left(\dfrac{w}{d}\right)\)
- **C.** \(\dfrac{\sigma}{2\pi \varepsilon_0} \ln\left(1 + \dfrac{w}{d}\right)\)
- **D.** \(\dfrac{\sigma}{4\pi \varepsilon_0} \ln\left(1 + \dfrac{d}{w}\right)\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/117996/*