---
title: "Charged Particles Moving in a Magnetic Field"
description: "A charge crossing a magnetic field feels a force BQv that stays at right angles to its velocity, so the path curves into a circle. Setting BQv equal to mv squared over r gives the radius."
canonical: https://lightmysky.com/learn/science/charged-particles-moving-in-a-magnetic-field-mt_evuhZ6cSfI
source: https://lightmysky.com/learn/science/charged-particles-moving-in-a-magnetic-field-mt_evuhZ6cSfI.md
retrieved: 2026-09-12
---

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# Charged Particles Moving in a Magnetic Field

A charge crossing a magnetic field feels a force BQv that stays at right angles to its velocity, so the path curves into a circle. Setting BQv equal to mv squared over r gives the radius.

Subject: Science · Area: Forces & Motion · Ages 17 to 18
Page: https://lightmysky.com/learn/science/charged-particles-moving-in-a-magnetic-field-mt_evuhZ6cSfI

## Ready when they can

- Gives the direction of the force on a positive and on a negative charge in the same field
- Derives r = mv over BQ and uses it to compare particles of different mass or charge
- Explains why a magnetic field changes a particle's direction but never its speed

## Lesson: Steering charges with magnets

Mass spectrometers steer charged particles by bending their paths in a magnetic field. A charge crossing the field feels F equals B Q v, sideways to both its motion and the field. Positive charges bend one way and negative charges bend the opposite way in the same field. Motion parallel to the field feels nothing at all.

Crossing a uniform field at right angles, the charge travels in a circle. A fixed sideways push is exactly what circular motion needs. Setting B Q v equal to m v squared over r gives r equals m v over B Q. Fast or heavy swings wide, while highly charged curls tight.

The push stays across the motion, so it turns the particle without doing work. Speed never changes and kinetic energy is untouched. The field steers but never pays: direction changes, pace stays.

**Recap.** Bend charges sideways by sign, size the circle by momentum over charge, and keep the speed untouched.

## Practice

8 questions on this page, each with its working shown.

## Needs first

- [Circular Motion: Angular Speed and Centripetal Force](https://lightmysky.com/learn/science/circular-motion-angular-speed-and-centripetal-force-mt_PW1G6nYStq)
- [Magnetic Flux Density and the Force on a Current-Carrying Wire](https://lightmysky.com/learn/science/magnetic-flux-density-and-the-force-on-a-current-carrying-wire-mt_zuqc4gjBVh)

## Opens up

- [Electron Spin and the Stern-Gerlach Experiment](https://lightmysky.com/learn/science/electron-spin-and-the-stern-gerlach-experiment-mt_HVFLoNe6wk)
- [Mass Spectrometry: Ionisation Methods and Mass Analysers](https://lightmysky.com/learn/science/mass-spectrometry-ionisation-methods-and-mass-analysers-mt_JTTb7FM1L4)
- [The Biot-Savart Law and the Field of a Current Element](https://lightmysky.com/learn/science/the-biot-savart-law-and-the-field-of-a-current-element-mt_RRsHUaXrFq)
- [Magnetic Flux, Flux Linkage and Faraday's Law](https://lightmysky.com/learn/science/magnetic-flux-flux-linkage-and-faradays-law-mt_ZoN5JePCpt)