---
title: "Electrons in a cathode-ray device are accelerated from rest through an initial potential difference \\(V_0\\) before entering a region containing a uniform magnetic field of magnitude \\(B\\) directed perpendicular to the electrons’ velocity. Inside the magnetic field, the electrons travel along a circular arc of radius \\(R_0\\). If the accelerating potential difference is increased to \\(4V_0\\) while the magnetic field magnitude remains unchanged, what is the new radius of curvature of the electron beam’s path inside 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/118539/"
date_modified: "2026-08-04T08:11:15+00:00"
---

# Electrons in a cathode-ray device are accelerated from rest through an initial potential difference \(V_0\) before entering a region containing a uniform magnetic field of magnitude \(B\) directed perpendicular to the electrons’ velocity. Inside the magnetic field, the electrons travel along a circular arc of radius \(R_0\). If the accelerating potential difference is increased to \(4V_0\) while the magnetic field magnitude remains unchanged, what is the new radius of curvature of the electron beam’s path inside the magnetic field?

Electrons in a cathode-ray device are accelerated from rest through an initial potential difference \(V_0\) before entering a region containing a uniform magnetic field of magnitude \(B\) directed perpendicular to the electrons' velocity. Inside the magnetic field, the electrons travel along a circular arc of radius \(R_0\). If the accelerating potential difference is increased to \(4V_0\) while the magnetic field magnitude remains unchanged, what is the new radius of curvature of the electron beam's path inside the magnetic field?

![A horizontal cathode-ray tube setup. On the left, two parallel vertical plate electrodes represent the accelerating region labeled with potential difference V_0, with an electron trajectory starting from rest at the left plate and moving horizontally to the right. To the right of the plates, a rectangular shaded region represents a uniform magnetic field directed into the page, indicated by four evenly spaced cross symbols (x). Inside this magnetic field region, the electron trajectory curves upward in a circular arc of radius R_0. A coordinate arrow or arc shows the radius R_0 centered on the circle of curvature. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1785831074-GiEQAr.jpg)

- **A.** \(\dfrac{1}{2} R_0\)
- **B.** \(2 R_0\)
- **C.** \(4 R_0\)
- **D.** \(16 R_0\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/118539/*