---
title: "An ion of mass \\( m = 3.3 \\times 10^{-27} \\text{ kg} \\) and charge \\( q = +1.6 \\times 10^{-19} \\text{ C} \\) is moving with a constant speed \\( v = 2.0 \\times 10^5 \\text{ m/s} \\) toward the right. It enters a region of space containing a uniform magnetic field of magnitude \\( B = 0.40 \\text{ T} \\) that is directed into the page, as shown in Figure 1. The effects of gravity are negligible."
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url: "https://nerd-notes.com/ubq/117685/"
date_modified: "2026-08-04T07:53:03+00:00"
---

# An ion of mass \( m = 3.3 \times 10^{-27} \text{ kg} \) and charge \( q = +1.6 \times 10^{-19} \text{ C} \) is moving with a constant speed \( v = 2.0 \times 10^5 \text{ m/s} \) toward the right. It enters a region of space containing a uniform magnetic field of magnitude \( B = 0.40 \text{ T} \) that is directed into the page, as shown in Figure 1. The effects of gravity are negligible.

An ion of mass \( m = 3.3 \times 10^{-27} \text{ kg} \) and charge \( q = +1.6 \times 10^{-19} \text{ C} \) is moving with a constant speed \( v = 2.0 \times 10^5 \text{ m/s} \) toward the right. It enters a region of space containing a uniform magnetic field of magnitude \( B = 0.40 \text{ T} \) that is directed into the page, as shown in Figure 1. The effects of gravity are negligible.

![A dashed rectangular region is on the right side of the image, filled with an evenly spaced grid of 'X' marks to indicate a magnetic field pointing into the page. The region is labeled 'B'. To the left of this region is a small circle with a plus sign inside it, representing a positive ion. A horizontal arrow points from the ion to the right, toward the magnetic field region, and is labeled 'v'. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1785829983-b0HPpc.jpg)

**Part a)** **Calculate** the magnitude of the magnetic force exerted on the ion the instant it enters the magnetic field. *(2 points)*

**Part b)** **Derive** an expression for the radius \( R \) of the circular path taken by the ion while it is in the magnetic field. Express your answer in terms of \( m \), \( q \), \( v \), \( B \), and fundamental constants, as appropriate. *(2 points)*

**Part c)** **Calculate** the value of the radius \( R \) for the ion described in the scenario. *(2 points)*

**Part d)** A second ion with the same mass \( m \) but a charge of \( +2q \) enters the same magnetic field with the same speed \( v \). **Indicate** whether the radius of the circular path of the second ion is greater than, less than, or equal to the radius \( R \) of the original ion. - [ ] Greater than - [ ] Less than - [ ] Equal to **Justify** your answer. *(2 points)*


*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/117685/*