---
title: "A particle with mass \\(m\\) and positive charge \\(q\\) travels with constant speed \\(v\\) in the \\(+x\\)-direction. At time \\(t = 0\\), the particle enters a region of uniform magnetic field of magnitude \\(B\\) directed perpendicular to its velocity, bounded by the line \\(x = 0\\). The particle follows a semicircular trajectory inside the field before exiting back across the boundary at \\(x = 0\\). Which of the following correctly pairs the radius \\(r\\) of the particle’s path with the total time \\(\\Delta t\\) the particle spends inside the magnetic field region?"
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url: "https://nerd-notes.com/ubq/118491/"
date_modified: "2026-08-04T08:11:03+00:00"
---

# A particle with mass \(m\) and positive charge \(q\) travels with constant speed \(v\) in the \(+x\)-direction. At time \(t = 0\), the particle enters a region of uniform magnetic field of magnitude \(B\) directed perpendicular to its velocity, bounded by the line \(x = 0\). The particle follows a semicircular trajectory inside the field before exiting back across the boundary at \(x = 0\). Which of the following correctly pairs the radius \(r\) of the particle’s path with the total time \(\Delta t\) the particle spends inside the magnetic field region?

A particle with mass \(m\) and positive charge \(q\) travels with constant speed \(v\) in the \(+x\)-direction. At time \(t = 0\), the particle enters a region of uniform magnetic field of magnitude \(B\) directed perpendicular to its velocity, bounded by the line \(x = 0\). The particle follows a semicircular trajectory inside the field before exiting back across the boundary at \(x = 0\). Which of the following correctly pairs the radius \(r\) of the particle's path with the total time \(\Delta t\) the particle spends inside the magnetic field region?

![A vertical line representing the boundary x = 0 separates two regions. The region to the left of x = 0 is labeled 'B = 0'. The region to the right of x = 0 contains a uniform grid of small 'x' symbols labeled B into the page. A small black circle representing a particle labeled +q, m is located to the left of x = 0, moving rightward with a horizontal arrow labeled v perpendicular to the x = 0 boundary. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1785831063-wNSbbp.jpg)

- **A.** Radius: \(r = \dfrac{mv}{2qB}\) | Time: \(\Delta t = \dfrac{2\pi m}{qB}\)
- **B.** Radius: \(r = \dfrac{mv}{qB}\) | Time: \(\Delta t = \dfrac{2\pi m}{qB}\)
- **C.** Radius: \(r = \dfrac{2mv}{qB}\) | Time: \(\Delta t = \dfrac{\pi m}{qB}\)
- **D.** Radius: \(r = \dfrac{mv}{qB}\) | Time: \(\Delta t = \dfrac{\pi m}{qB}\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/118491/*