---
title: "In an experiment to determine the mass-to-charge ratio \\(m/q\\) of positive ions, ions of mass \\(m\\) and charge \\(q\\) are accelerated from rest across an adjustable potential difference \\(\\Delta V\\). The ions then enter a region containing a uniform magnetic field of known magnitude \\(B\\) directed perpendicular to their velocity, which deflects them into circular arcs of radius \\(r\\). To obtain a linear graph from the experimental data, which quantities should be plotted on the vertical and horizontal axes, and how is the mass-to-charge ratio determined from the slope \\(S\\) of the resulting best-fit line?"
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/123224/"
date_modified: "2026-09-28T11:57:58+00:00"
---

# In an experiment to determine the mass-to-charge ratio \(m/q\) of positive ions, ions of mass \(m\) and charge \(q\) are accelerated from rest across an adjustable potential difference \(\Delta V\). The ions then enter a region containing a uniform magnetic field of known magnitude \(B\) directed perpendicular to their velocity, which deflects them into circular arcs of radius \(r\). To obtain a linear graph from the experimental data, which quantities should be plotted on the vertical and horizontal axes, and how is the mass-to-charge ratio determined from the slope \(S\) of the resulting best-fit line?

In an experiment to determine the mass-to-charge ratio \(m/q\) of positive ions, ions of mass \(m\) and charge \(q\) are accelerated from rest across an adjustable potential difference \(\Delta V\). The ions then enter a region containing a uniform magnetic field of known magnitude \(B\) directed perpendicular to their velocity, which deflects them into circular arcs of radius \(r\). To obtain a linear graph from the experimental data, which quantities should be plotted on the vertical and horizontal axes, and how is the mass-to-charge ratio determined from the slope \(S\) of the resulting best-fit line?

![A schematic diagram showing two parallel vertical conducting plates on the left separated by a gap labeled with potential difference \Delta V. A positive charge starts from rest at the left plate and passes horizontally through a small opening in the right plate. To the right of the plates, a rectangular region contains a uniform grid of six small cross symbols indicating a magnetic field \vec{B} directed into the page. Inside this region, a dashed line depicts the particle path curving upward in a semicircle of radius labeled r. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1790596677-2BFUfR.jpg)

- **A.** Plot \(r^2\) on the vertical axis and \(\Delta V\) on the horizontal axis; \(\dfrac{m}{q} = \dfrac{S B^2}{2}\)
- **B.** Plot \(r^2\) on the vertical axis and \(\Delta V\) on the horizontal axis; \(\dfrac{m}{q} = S B^2\)
- **C.** Plot \(r^2\) on the vertical axis and \(\Delta V\) on the horizontal axis; \(\dfrac{m}{q} = \dfrac{B^2}{2S}\)
- **D.** Plot \(r\) on the vertical axis and \(\Delta V\) on the horizontal axis; \(\dfrac{m}{q} = \dfrac{S^2 B^2}{2}\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/123224/*