---
title: "An experiment is conducted to determine the uniform linear charge density \\(\\lambda\\) of a very long, thin, positively charged wire. The electric potential \\(V\\) is measured at various radial distances \\(r\\) from the wire, with the reference potential defined such that \\(V = 0\\) at a fixed radial distance \\(r_0\\). Which of the following quantities should be plotted on the vertical and horizontal axes to produce a straight line, and what is the slope of that line in terms of \\(\\lambda\\) and fundamental constants?"
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url: "https://nerd-notes.com/ubq/124523/"
date_modified: "2026-09-28T14:08:31+00:00"
---

# An experiment is conducted to determine the uniform linear charge density \(\lambda\) of a very long, thin, positively charged wire. The electric potential \(V\) is measured at various radial distances \(r\) from the wire, with the reference potential defined such that \(V = 0\) at a fixed radial distance \(r_0\). Which of the following quantities should be plotted on the vertical and horizontal axes to produce a straight line, and what is the slope of that line in terms of \(\lambda\) and fundamental constants?

An experiment is conducted to determine the uniform linear charge density \(\lambda\) of a very long, thin, positively charged wire. The electric potential \(V\) is measured at various radial distances \(r\) from the wire, with the reference potential defined such that \(V = 0\) at a fixed radial distance \(r_0\). Which of the following quantities should be plotted on the vertical and horizontal axes to produce a straight line, and what is the slope of that line in terms of \(\lambda\) and fundamental constants?

![A vertical solid line representing a long wire is centered vertically and spans the height of the frame. Exactly four small plus signs are evenly spaced along the vertical line from top to bottom. A horizontal dashed line extends to the right from the midpoint of the vertical wire, terminating at a solid black dot labeled P. A short vertical tick mark intersects the horizontal dashed line between the wire and point P, labeled r_0 directly above the tick. A horizontal dimension line with arrowheads at both ends is positioned directly below the horizontal dashed line, extending from the vertical line to the coordinate of point P and labeled r at its center. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1790604510-GK64V8.jpg)

- **A.** Vertical axis: \(V\); Horizontal axis: \(\ln(r)\); Slope: \(-\dfrac{\lambda}{2\pi\varepsilon_0}\)
- **B.** Vertical axis: \(V\); Horizontal axis: \(\ln(r)\); Slope: \(\dfrac{\lambda}{2\pi\varepsilon_0}\)
- **C.** Vertical axis: \(V\); Horizontal axis: \(\dfrac{1}{r}\); Slope: \(-\dfrac{\lambda}{2\pi\varepsilon_0}\)
- **D.** Vertical axis: \(V\); Horizontal axis: \(\dfrac{1}{r}\); Slope: \(\dfrac{\lambda}{4\pi\varepsilon_0}\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/124523/*