---
title: "An infinitely long, straight line of charge carries a uniform positive linear charge density \\(\\lambda\\). A coaxial cylindrical Gaussian surface of radius \\(r\\) and length \\(L\\) is used to analyze the field. Which of the following expressions gives the magnitude of the electric field \\(E\\) at a perpendicular distance \\(r\\) from the line of charge?"
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url: "https://nerd-notes.com/ubq/117885/"
date_modified: "2026-08-04T08:02:22+00:00"
---

# An infinitely long, straight line of charge carries a uniform positive linear charge density \(\lambda\). A coaxial cylindrical Gaussian surface of radius \(r\) and length \(L\) is used to analyze the field. Which of the following expressions gives the magnitude of the electric field \(E\) at a perpendicular distance \(r\) from the line of charge?

An infinitely long, straight line of charge carries a uniform positive linear charge density \(\lambda\). A coaxial cylindrical Gaussian surface of radius \(r\) and length \(L\) is used to analyze the field. Which of the following expressions gives the magnitude of the electric field \(E\) at a perpendicular distance \(r\) from the line of charge?

![An infinitely long vertical thin line representing a uniform positive line charge labeled with linear charge density \lambda. Coaxial with this line is a closed cylindrical Gaussian surface of radius r and length L drawn with light dashed lines. A radial dashed line labeled r extends horizontally from the central axis to the curved cylindrical wall. Vector arrows labeled \vec{E} point perpendicularly outward from the curved side of the cylinder. No other labels, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1785830542-5Wjj63.jpg)

- **A.** \(\dfrac{\lambda}{4\pi \varepsilon_0 r^2}\)
- **B.** \(\dfrac{\lambda}{4\pi \varepsilon_0 r}\)
- **C.** \(\dfrac{\lambda}{2\pi \varepsilon_0 r}\)
- **D.** \(\dfrac{\lambda}{\varepsilon_0 r}\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/117885/*