---
title: "A particle with mass \\(m\\), speed \\(v\\), and positive charge \\(q\\) enters a uniform magnetic field \\(B\\) directed perpendicular to its velocity, causing it to travel in a circular path of radius \\(r_1\\). A second particle with the same mass \\(m\\) and speed \\(v\\), but with charge \\(2q\\), enters the same magnetic field perpendicular to its velocity and travels in a circular path of radius \\(r_2\\). What is the ratio \\(\\dfrac{r_2}{r_1}\\)?"
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url: "https://nerd-notes.com/ubq/116289/"
date_modified: "2026-08-03T12:23:20+00:00"
---

# A particle with mass \(m\), speed \(v\), and positive charge \(q\) enters a uniform magnetic field \(B\) directed perpendicular to its velocity, causing it to travel in a circular path of radius \(r_1\). A second particle with the same mass \(m\) and speed \(v\), but with charge \(2q\), enters the same magnetic field perpendicular to its velocity and travels in a circular path of radius \(r_2\). What is the ratio \(\dfrac{r_2}{r_1}\)?

A particle with mass \(m\), speed \(v\), and positive charge \(q\) enters a uniform magnetic field \(B\) directed perpendicular to its velocity, causing it to travel in a circular path of radius \(r_1\). A second particle with the same mass \(m\) and speed \(v\), but with charge \(2q\), enters the same magnetic field perpendicular to its velocity and travels in a circular path of radius \(r_2\). What is the ratio \(\dfrac{r_2}{r_1}\)?

![A schematic diagram showing a uniform magnetic field represented by a grid of small x symbols directed into the page. On the left side, a particle with charge +q and mass m moves to the right with velocity vector v perpendicular to the field lines. A curved dashed circular arc bends upward, representing the trajectory of radius r_1. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1785759800-4Ct52z.jpg)

- **A.** \(\dfrac{1}{2}\)
- **B.** \(1\)
- **C.** \(2\)
- **D.** \(4\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/116289/*