---
title: "An infinitely long, straight wire carries a uniform positive line charge density \\(\\lambda\\). A small particle with mass \\(m\\) and negative charge \\(-q\\) (where \\(q > 0\\)) is initially located at a distance \\(r_0\\) from the wire. The particle is projected radially away from the wire with an initial speed \\(v_0\\). What is the minimum initial speed \\(v_0\\) required for the particle to reach a distance of \\(5r_0\\) from the wire?"
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url: "https://nerd-notes.com/ubq/118130/"
date_modified: "2026-08-04T08:05:21+00:00"
---

# An infinitely long, straight wire carries a uniform positive line charge density \(\lambda\). A small particle with mass \(m\) and negative charge \(-q\) (where \(q > 0\)) is initially located at a distance \(r_0\) from the wire. The particle is projected radially away from the wire with an initial speed \(v_0\). What is the minimum initial speed \(v_0\) required for the particle to reach a distance of \(5r_0\) from the wire?

An infinitely long, straight wire carries a uniform positive line charge density \(\lambda\). A small particle with mass \(m\) and negative charge \(-q\) (where \(q > 0\)) is initially located at a distance \(r_0\) from the wire. The particle is projected radially away from the wire with an initial speed \(v_0\). What is the minimum initial speed \(v_0\) required for the particle to reach a distance of \(5r_0\) from the wire?

![A long vertical line carrying a positive charge density labeled \lambda. To the right of the wire, a small sphere labeled -q with mass m is positioned at a radial distance r_0 from the wire. A horizontal arrow labeled v_0 points to the right away from the wire toward a vertical dashed line at radial distance 5r_0. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1785830721-I8ltux.jpg)

- **A.** \(\sqrt{\dfrac{q\lambda \ln 5}{\pi \varepsilon_0 m}}\)
- **B.** \(\sqrt{\dfrac{4q\lambda}{5\pi \varepsilon_0 m}}\)
- **C.** \(\sqrt{\dfrac{q\lambda \ln 5}{2\pi \varepsilon_0 m}}\)
- **D.** \(\sqrt{\dfrac{4q\lambda}{\pi \varepsilon_0 m}}\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/118130/*