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title: "An experiment is conducted to determine the charge-to-mass ratio \\(q/m\\) of an unknown ion. Ions of mass \\(m\\) and positive charge \\(q\\) are accelerated from rest through a variable electric potential difference \\(\\Delta V\\) and then enter a region of uniform magnetic field of magnitude \\(B\\) directed perpendicular to their velocity. The ions follow a semicircular trajectory of radius \\(r\\), which is measured for several values of \\(\\Delta V\\) while \\(B\\) remains constant. Which of the following indicates the quantities that should be plotted on the vertical and horizontal axes to produce a linear graph, along with the correct expression for \\(q/m\\) in terms of the slope \\(M\\) of the best-fit line and \\(B\\)?"
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url: "https://nerd-notes.com/ubq/121266/"
date_modified: "2026-08-23T04:59:05+00:00"
---

# An experiment is conducted to determine the charge-to-mass ratio \(q/m\) of an unknown ion. Ions of mass \(m\) and positive charge \(q\) are accelerated from rest through a variable electric potential difference \(\Delta V\) and then enter a region of uniform magnetic field of magnitude \(B\) directed perpendicular to their velocity. The ions follow a semicircular trajectory of radius \(r\), which is measured for several values of \(\Delta V\) while \(B\) remains constant. Which of the following indicates the quantities that should be plotted on the vertical and horizontal axes to produce a linear graph, along with the correct expression for \(q/m\) in terms of the slope \(M\) of the best-fit line and \(B\)?

An experiment is conducted to determine the charge-to-mass ratio \(q/m\) of an unknown ion. Ions of mass \(m\) and positive charge \(q\) are accelerated from rest through a variable electric potential difference \(\Delta V\) and then enter a region of uniform magnetic field of magnitude \(B\) directed perpendicular to their velocity. The ions follow a semicircular trajectory of radius \(r\), which is measured for several values of \(\Delta V\) while \(B\) remains constant. Which of the following indicates the quantities that should be plotted on the vertical and horizontal axes to produce a linear graph, along with the correct expression for \(q/m\) in terms of the slope \(M\) of the best-fit line and \(B\)?

![A rectangular chamber showing two parallel vertical plates labeled + and - on the left, with an ion trajectory starting at the positive plate, passing through an aperture in the negative plate, and entering a region on the right. The region on the right contains nine small x symbols in a three-by-three grid, representing a magnetic field directed into the page labeled \vec{B}. A semicircular dashed line curves upward and back to the left, with a radial arrow labeled r extending from the center of curvature to the path. A potential difference label \Delta V is shown across the accelerating plates. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1787461145-WlZp9o.jpg)

- **A.** Vertical axis: \(\Delta V\) Horizontal axis: \(r^2\) Charge-to-mass ratio: \(\dfrac{q}{m} = \dfrac{2M}{B^2}\)
- **B.** Vertical axis: \(r^2\) Horizontal axis: \(\Delta V\) Charge-to-mass ratio: \(\dfrac{q}{m} = \dfrac{2M}{B^2}\)
- **C.** Vertical axis: \(\Delta V\) Horizontal axis: \(r^2\) Charge-to-mass ratio: \(\dfrac{q}{m} = \dfrac{M}{2B^2}\)
- **D.** Vertical axis: \(\Delta V\) Horizontal axis: \(r\) Charge-to-mass ratio: \(\dfrac{q}{m} = \dfrac{2M}{B^2}\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/121266/*