---
title: "A thin, nonconducting rod of length \\(L\\) lies along the \\(x\\)-axis with its ends at \\(x = 0\\) and \\(x = L\\). The rod carries a total positive charge \\(Q\\) uniformly distributed along its length. A small particle with mass \\(m\\) and positive charge \\(q\\) is released from rest at position \\(x = 2L\\). As the particle is repelled along the positive \\(x\\)-axis, what is its speed when it reaches position \\(x = 3L\\)?"
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url: "https://nerd-notes.com/ubq/118170/"
date_modified: "2026-08-04T08:05:40+00:00"
---

# A thin, nonconducting rod of length \(L\) lies along the \(x\)-axis with its ends at \(x = 0\) and \(x = L\). The rod carries a total positive charge \(Q\) uniformly distributed along its length. A small particle with mass \(m\) and positive charge \(q\) is released from rest at position \(x = 2L\). As the particle is repelled along the positive \(x\)-axis, what is its speed when it reaches position \(x = 3L\)?

A thin, nonconducting rod of length \(L\) lies along the \(x\)-axis with its ends at \(x = 0\) and \(x = L\). The rod carries a total positive charge \(Q\) uniformly distributed along its length. A small particle with mass \(m\) and positive charge \(q\) is released from rest at position \(x = 2L\). As the particle is repelled along the positive \(x\)-axis, what is its speed when it reaches position \(x = 3L\)?

![A horizontal x-axis with a right-pointing arrow labeled x. A thin shaded rectangle representing a rod lies along the axis, with its left end at x = 0 and its right end at x = L. The rod is marked with a plus sign inside to indicate positive charge Q. A small filled circle representing a particle of mass m and charge q is positioned on the x-axis at x = 2L, to the right of the rod. A small rightward arrow originates from the particle, pointing toward a dashed tick mark on the x-axis labeled x = 3L. Vertical dashed lines extend downward from the axis at x = 0, x = L, x = 2L, and x = 3L to mark their respective positions. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1785830740-6cg0vn.jpg)

- **A.** \(\sqrt{ \dfrac{q Q}{12\pi\varepsilon_0 m L} }\)
- **B.** \(\sqrt{ \dfrac{q Q}{4\pi\varepsilon_0 m L} \ln\left( \dfrac{4}{3} \right) }\)
- **C.** \(\sqrt{ \dfrac{q Q}{2\pi\varepsilon_0 m L} \ln\left( \dfrac{3}{2} \right) }\)
- **D.** \(\sqrt{ \dfrac{q Q}{2\pi\varepsilon_0 m L} \ln\left( \dfrac{4}{3} \right) }\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/118170/*