---
title: "A long, solid cylindrical conductor of radius \\(R\\) carries a uniform current \\(I\\) distributed evenly over its cross section. A particle of mass \\(m\\) and positive charge \\(q\\) moves parallel to the central axis of the cylinder with constant speed \\(v_0\\). The particle is evaluated at two locations: point 1 at a radial distance \\(r_1 = \\dfrac{R}{2}\\) inside the conductor, and point 2 at a radial distance \\(r_2 = 2R\\) outside the conductor. What is the ratio of the magnitude of the spatial rate of change of the particle’s acceleration with respect to radial position at point 1 to that at point 2, \\(\\dfrac{|da/dr|_{r_1}}{|da/dr|_{r_2}}\\)?"
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/118622/"
date_modified: "2026-08-04T08:12:09+00:00"
---

# A long, solid cylindrical conductor of radius \(R\) carries a uniform current \(I\) distributed evenly over its cross section. A particle of mass \(m\) and positive charge \(q\) moves parallel to the central axis of the cylinder with constant speed \(v_0\). The particle is evaluated at two locations: point 1 at a radial distance \(r_1 = \dfrac{R}{2}\) inside the conductor, and point 2 at a radial distance \(r_2 = 2R\) outside the conductor. What is the ratio of the magnitude of the spatial rate of change of the particle’s acceleration with respect to radial position at point 1 to that at point 2, \(\dfrac{|da/dr|_{r_1}}{|da/dr|_{r_2}}\)?

A long, solid cylindrical conductor of radius \(R\) carries a uniform current \(I\) distributed evenly over its cross section. A particle of mass \(m\) and positive charge \(q\) moves parallel to the central axis of the cylinder with constant speed \(v_0\). The particle is evaluated at two locations: point 1 at a radial distance \(r_1 = \dfrac{R}{2}\) inside the conductor, and point 2 at a radial distance \(r_2 = 2R\) outside the conductor. What is the ratio of the magnitude of the spatial rate of change of the particle's acceleration with respect to radial position at point 1 to that at point 2, \(\dfrac{|da/dr|_{r_1}}{|da/dr|_{r_2}}\)?

![A cross-sectional view of a solid circular cylinder of radius R centered at the origin. The interior of the circle is shaded light gray to represent a conductor. A dashed central axis perpendicular to the plane passes through the origin. Point 1 is marked with a black dot on the horizontal axis at a distance r_1 = R/2 to the right of the center. Point 2 is marked with a black dot on the horizontal axis at a distance r_2 = 2R to the right of the center, outside the shaded circle. A radial arrow labeled r extends from the origin along the positive horizontal axis. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1785831129-CTBaE0.jpg)

- **A.** \(1\)
- **B.** \(2\)
- **C.** \(4\)
- **D.** \(8\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/118622/*