# Explain why a positive ion travelling in a horizontal circle inside a cyclotron is accelerated each time it crosses the gap between the two dees, and explain why the radius of each successive semicircle increases even though the magnetic field strength inside the dees remains constant.

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

> A cyclotron accelerates positive ions using an alternating potential difference applied across two hollow D-shaped electrodes (dees) placed in a uniform magnetic field directed perpendicular to the plane of the dees.

## Mark scheme (4 marks)

1. The alternating potential difference creates an electric field in the gap between the dees, and this electric field exerts a force on the positive ion, doing work on it / transferring energy to it each time the ion crosses the gap.
2. The alternating potential difference reverses polarity in synchrony with the ion's semicircular motion so that the electric field always acts in the direction of the ion's motion when it enters the gap.
3. The magnetic force provides the centripetal force: qvB = mv²/r, giving r = mv/(qB); as the ion gains kinetic energy its speed v increases.
4. Because q, m, and B are all constant, each time the ion is accelerated its speed increases and therefore the radius of the next semicircle is larger, producing a spiral-like outward path.

## Key terms

- [cyclotron](https://www.gradenine.co.uk/glossary/cyclotron)
- [dee](https://www.gradenine.co.uk/glossary/dee)

## 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-positive-ion-travelling-f1d6ccdc) · Published by Druglandscape Ltd.