---
title: "A proton of mass \\(m\\) and charge \\(+e\\) and an alpha particle of mass \\(4m\\) and charge \\(+2e\\) are each accelerated from rest through the same electric potential difference \\(\\Delta V\\). Each particle then enters a region of uniform magnetic field \\(\\vec{B}\\) directed perpendicular to its velocity, causing it to travel in a circular arc. What is the ratio of the radius of the circular path of the alpha particle to that of the proton, \\(\\dfrac{r_\\alpha}{r_p}\\)?"
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url: "https://nerd-notes.com/ubq/121221/"
date_modified: "2026-08-23T04:58:56+00:00"
---

# A proton of mass \(m\) and charge \(+e\) and an alpha particle of mass \(4m\) and charge \(+2e\) are each accelerated from rest through the same electric potential difference \(\Delta V\). Each particle then enters a region of uniform magnetic field \(\vec{B}\) directed perpendicular to its velocity, causing it to travel in a circular arc. What is the ratio of the radius of the circular path of the alpha particle to that of the proton, \(\dfrac{r_\alpha}{r_p}\)?

A proton of mass \(m\) and charge \(+e\) and an alpha particle of mass \(4m\) and charge \(+2e\) are each accelerated from rest through the same electric potential difference \(\Delta V\). Each particle then enters a region of uniform magnetic field \(\vec{B}\) directed perpendicular to its velocity, causing it to travel in a circular arc. What is the ratio of the radius of the circular path of the alpha particle to that of the proton, \(\dfrac{r_\alpha}{r_p}\)?

![A schematic diagram showing two parallel vertical plates separated by a dashed potential difference label \(\Delta V\). To the right of the plates is a rectangular region filled with a regular grid of six rows and six columns of small 'x' symbols representing a uniform magnetic field \(\vec{B}\) directed into the page. A horizontal solid line with an arrowhead enters from the left and curves upward into a circular arc inside the magnetic field region, representing a positive charge trajectory. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1787461135-2ezdvm.jpg)

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

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/121221/*