---
title: "A particle of mass \\(m\\) and positive charge \\(q\\) travels with initial speed \\(v\\) in the \\(+x\\)-direction. The particle enters a region of uniform magnetic field of magnitude \\(B\\) directed perpendicularly into the page, which spans a finite width \\(d\\) along the \\(x\\)-axis, where \\(d < \\dfrac{mv}{qB}\\). Which of the following expressions correctly gives the sine of the deflection angle, \\(\\sin\\theta\\), of the particle's velocity vector as it emerges from the right boundary of the magnetic field?"
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/123257/"
date_modified: "2026-09-28T11:58:02+00:00"
---

# A particle of mass \(m\) and positive charge \(q\) travels with initial speed \(v\) in the \(+x\)-direction. The particle enters a region of uniform magnetic field of magnitude \(B\) directed perpendicularly into the page, which spans a finite width \(d\) along the \(x\)-axis, where \(d < \dfrac{mv}{qB}\). Which of the following expressions correctly gives the sine of the deflection angle, \(\sin\theta\), of the particle's velocity vector as it emerges from the right boundary of the magnetic field?

A particle of mass \(m\) and positive charge \(q\) travels with initial speed \(v\) in the \(+x\)-direction. The particle enters a region of uniform magnetic field of magnitude \(B\) directed perpendicularly into the page, which spans a finite width \(d\) along the \(x\)-axis, where \(d < \dfrac{mv}{qB}\). Which of the following expressions correctly gives the sine of the deflection angle, \(\sin\theta\), of the particle's velocity vector as it emerges from the right boundary of the magnetic field?

![A schematic diagram in grayscale. On the left, a positive point charge labeled +q with mass m moves horizontally to the right with a horizontal vector arrow labeled v. The particle is directly in line with a vertically oriented rectangular region of width d. The magnetic field region is bounded by two vertical parallel dashed lines separated horizontally by distance d, indicated by a horizontal double-headed dimension arrow labeled d between them. Inside the rectangular region, a regular 3 by 4 array of cross symbols represents a uniform magnetic field directed into the page, labeled B at the upper right. A horizontal dashed line extends along the particle's initial path. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1790596682-LIpTVe.jpg)

- **A.** \(\dfrac{q B d}{2 m v}\)
- **B.** \(\sqrt{1 - \left(\dfrac{q B d}{m v}\right)^2}\)
- **C.** \(\dfrac{q B d}{m v}\)
- **D.** \(\dfrac{q B d}{\sqrt{(m v)^2 + (q B d)^2}}\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/123257/*