---
title: "Two identical particles, each with mass \\(m\\) and positive charge \\(q\\), are injected into a uniform magnetic field \\(\\vec{B}\\). Particle 1 enters with speed \\(v_1\\) at an angle of \\(30^\\circ\\) relative to the direction of \\(\\vec{B}\\), and Particle 2 enters with speed \\(v_2\\) at an angle of \\(60^\\circ\\) relative to \\(\\vec{B}\\). Both particles follow helical paths that have the same radius \\(R\\). What is the ratio of the pitch of Particle 2’s path to the pitch of Particle 1’s path, \\(\\dfrac{p_2}{p_1}\\)?"
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url: "https://nerd-notes.com/ubq/121211/"
date_modified: "2026-08-23T04:58:52+00:00"
---

# Two identical particles, each with mass \(m\) and positive charge \(q\), are injected into a uniform magnetic field \(\vec{B}\). Particle 1 enters with speed \(v_1\) at an angle of \(30^\circ\) relative to the direction of \(\vec{B}\), and Particle 2 enters with speed \(v_2\) at an angle of \(60^\circ\) relative to \(\vec{B}\). Both particles follow helical paths that have the same radius \(R\). What is the ratio of the pitch of Particle 2’s path to the pitch of Particle 1’s path, \(\dfrac{p_2}{p_1}\)?

Two identical particles, each with mass \(m\) and positive charge \(q\), are injected into a uniform magnetic field \(\vec{B}\). Particle 1 enters with speed \(v_1\) at an angle of \(30^\circ\) relative to the direction of \(\vec{B}\), and Particle 2 enters with speed \(v_2\) at an angle of \(60^\circ\) relative to \(\vec{B}\). Both particles follow helical paths that have the same radius \(R\). What is the ratio of the pitch of Particle 2's path to the pitch of Particle 1's path, \(\dfrac{p_2}{p_1}\)?

![A line diagram showing a single helical trajectory winding horizontally around a central axis. On the left side, three horizontal dashed arrows pointing to the right represent a uniform magnetic field labeled \(\vec{B}\). A positively charged particle marked with a plus sign sits at the start of the helix, with a velocity vector arrow \(\vec{v}\) angled upward and to the right at an acute angle \(\theta\) relative to the field lines. A vertical double-headed arrow spanning from the central axis to the outer edge of the helix is labeled \(R\). A horizontal double-headed arrow spanning one complete loop of the helix is labeled \(p\). No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1787461132-fna2xS.jpg)

- **A.** \(\dfrac{1}{3}\)
- **B.** \(\dfrac{1}{\sqrt{3}}\)
- **C.** \(1\)
- **D.** \(3\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/121211/*