# Explain why a proton moving in a circle inside a cyclotron must be accelerated each time it crosses the gap between the two dees, and explain why the radius of the proton's circular path increases with each half-revolution.

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

> A cyclotron is a device that accelerates charged particles using a combination of a uniform magnetic field and an alternating electric field. The particles spiral outwards as they gain energy.

## Mark scheme (4 marks)

1. The magnetic force on the proton acts perpendicular to its velocity, so it does no work on the proton and cannot increase its kinetic energy / speed.
2. The alternating electric field in the gap between the dees exerts a force along the direction of motion, doing work on the proton and increasing its kinetic energy / speed each time it crosses.
3. Inside each dee the proton moves in a circle because the magnetic force provides the centripetal force (mv²/r = qvB).
4. As the proton's speed increases after each gap crossing, the radius of circular motion increases because r = mv/qB, so a greater speed gives a larger radius for the same magnetic field and charge.

## Related

- [Revision notes for IB DP Physics Standard Level (2023 syllabus)](https://www.gradenine.co.uk/learn)
- [How to answer "Explain" questions](https://www.gradenine.co.uk/tools/command-word-cheatsheet)
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