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.
Written & reviewed by James Millett — Biology (Imperial College London), PGCE Science (University of Cambridge).
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.
Model answer (4 marks)
The alternating potential difference across the gap produces an electric field that exerts a force on the positive ion, doing work on it each time it crosses the gap.
The 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.
The magnetic force provides the centripetal force: qvB = mv²/r, giving r = mv/(qB). As the ion gains kinetic energy its speed v increases.
Because q, m and B are 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.
The 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.
The magnetic force provides the centripetal force: qvB = mv²/r, giving r = mv/(qB). As the ion gains kinetic energy its speed v increases.
Because q, m and B are 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.
Examiner tips
- Use the word ‘explain’ to show cause–effect: electric field does work, magnetic field supplies centripetal force.
- Show the key equation r = mv/(qB) and note that v increases with energy.
- Mention the synchronisation of the alternating field with the ion’s motion.
- Keep the answer concise – 4 marks, so one sentence per point is enough.
Common mistakes
- Saying the ion is accelerated by the magnetic field – it is the electric field that changes its kinetic energy.
- Forgetting that the electric field must be in the direction of motion – the polarity must reverse each half‑cycle.
- Using the wrong equation for radius (e.g. r = mv²/(qB) – the correct form is r = mv/(qB)).
Mark scheme (4 marks)
- 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.
- 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.
- The magnetic force provides the centripetal force: qvB = mv²/r, giving r = mv/(qB); as the ion gains kinetic energy its speed v increases.
- 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 in this question
Related
- All IB DP Physics Higher Level (2023 syllabus) revision notes →
- How to answer a "Explain" question →
- Decode the mark scheme abbreviations →
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