---
title: "A particle of mass \\(m\\) and positive charge \\(q\\) is launched into a region containing a uniform magnetic field \\(\\vec{B}\\) directed along the \\(+z\\)-axis. The initial velocity \\(\\vec{v}_0\\) of the particle has magnitude \\(v_0\\) and makes an angle \\(\\theta\\) with the \\(+z\\)-axis, where \\(0 < \\theta < \\dfrac{\\pi}{2}\\). The resulting trajectory is a helix winding around the \\(z\\)-axis. Which of the following expressions represents the pitch \\(p\\) of the helix (the distance traveled along the \\(z\\)-axis during one complete revolution)?"
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/118497/"
date_modified: "2026-08-04T08:11:05+00:00"
---

# A particle of mass \(m\) and positive charge \(q\) is launched into a region containing a uniform magnetic field \(\vec{B}\) directed along the \(+z\)-axis. The initial velocity \(\vec{v}_0\) of the particle has magnitude \(v_0\) and makes an angle \(\theta\) with the \(+z\)-axis, where \(0 < \theta < \dfrac{\pi}{2}\). The resulting trajectory is a helix winding around the \(z\)-axis. Which of the following expressions represents the pitch \(p\) of the helix (the distance traveled along the \(z\)-axis during one complete revolution)?

A particle of mass \(m\) and positive charge \(q\) is launched into a region containing a uniform magnetic field \(\vec{B}\) directed along the \(+z\)-axis. The initial velocity \(\vec{v}_0\) of the particle has magnitude \(v_0\) and makes an angle \(\theta\) with the \(+z\)-axis, where \(0 < \theta < \dfrac{\pi}{2}\). The resulting trajectory is a helix winding around the \(z\)-axis. Which of the following expressions represents the pitch \(p\) of the helix (the distance traveled along the \(z\)-axis during one complete revolution)?

![A three-dimensional Cartesian coordinate system with three perpendicular black axis lines labeled x, y, and z. The z-axis extends vertically upward, the x-axis extends toward the lower-right, and the y-axis extends toward the upper-right. Four vertical blue parallel vector arrows point upward along the +z direction, labeled B. At the origin, a small red filled circle represents a particle labeled +q. A black arrow representing initial velocity v_0 originates at +q and points upward and to the right in the xz-plane. An arc angle labeled \theta is shown between the +z-axis and the v_0 vector arrow. A dashed spiral line begins at +q and coils upward around the z-axis in a right-handed helix. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1785831064-NfwTi9.jpg)

- **A.** \(\dfrac{2\pi m v_0 \sin\theta}{q B}\)
- **B.** \(\dfrac{2\pi m v_0}{q B \cos\theta}\)
- **C.** \(\dfrac{2\pi m v_0 \tan\theta}{q B}\)
- **D.** \(\dfrac{2\pi m v_0 \cos\theta}{q B}\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/118497/*