# Explain why the radius of the circular path of a charged particle moving perpendicular to a uniform magnetic field increases when the particle is accelerated through a greater potential difference before entering the field.

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

> A charged particle of mass m and charge q is accelerated from rest through a potential difference V before entering a region of uniform magnetic field of flux density B, directed perpendicular to the particle's velocity.

## Mark scheme (4 marks)

1. The work done by the electric field (qV) equals the kinetic energy gained, so a greater potential difference gives the particle a greater speed on entering the field.
2. The magnetic force provides the centripetal force, giving the relationship qvB = mv²/r, which simplifies to r = mv/(qB).
3. Since r = mv/(qB) and both m, q, and B are unchanged, a greater speed v directly produces a greater radius r.
4. The magnetic force does no work on the particle (force always perpendicular to velocity), so the speed — and hence kinetic energy — remains constant throughout the circular motion, confirming the path is a circle of fixed radius.

## Key terms

- [potential difference](https://www.gradenine.co.uk/glossary/potential-difference)

## 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-the-radius-of-the-8cfb5935) · Published by Druglandscape Ltd.