# Explain why a proton moving in a uniform magnetic field follows a circular path at constant speed, and explain what happens to the radius of that circular path if the proton is replaced by a deuteron (a nucleus containing one proton and one neutron) moving at the same speed.

> IB DP Physics Higher Level (2023 syllabus) — D.3 Motion in electromagnetic fields · Explain · 4 marks

## Mark scheme (4 marks)

1. The magnetic force on the proton is always perpendicular to its velocity, so the force does no work on the proton.
2. Because no work is done, the kinetic energy (and hence speed) of the proton remains constant.
3. The radius of circular motion is given by r = mv / (qB); since the deuteron has twice the mass of the proton but the same charge and the same speed, its radius is doubled.
4. Therefore the deuteron travels in a circle of radius twice that of the proton under the same magnetic field strength.

## Key terms

- [uniform magnetic field](https://www.gradenine.co.uk/glossary/uniform-magnetic-field)
- [deuteron](https://www.gradenine.co.uk/glossary/deuteron)

## Related

- [Revision notes for IB DP Physics Higher Level (2023 syllabus)](https://www.gradenine.co.uk/learn)
- [How to answer "Explain" questions](https://www.gradenine.co.uk/tools/command-word-cheatsheet)
- [Practice this with AI marking (free)](https://www.gradenine.co.uk/start)

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Source: [GradeNine](https://www.gradenine.co.uk/q/explain-why-a-proton-moving-in-565a27fd) · Published by Druglandscape Ltd.