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.
Written & reviewed by James Millett — Biology (Imperial College London), PGCE Science (University of Cambridge).
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.
Model answer (4 marks)
The magnetic force on the proton is always perpendicular to its velocity, so it can only change the direction of motion, not the speed; therefore it cannot increase the proton’s kinetic energy.
The alternating electric field in the gap between the two dees exerts a force along the direction of the proton’s motion. When the proton crosses the gap the field is in the same direction as its velocity, so the field does work on the proton and increases its kinetic energy each time it passes.
Inside each dee the proton follows a circular path because the magnetic force provides the required centripetal force:
qvB = mv²/r → r = mv/(qB).
After each gap crossing the proton’s speed v has increased, and with the same magnetic field B and charge q the radius r therefore increases according to r = mv/(qB).
The alternating electric field in the gap between the two dees exerts a force along the direction of the proton’s motion. When the proton crosses the gap the field is in the same direction as its velocity, so the field does work on the proton and increases its kinetic energy each time it passes.
Inside each dee the proton follows a circular path because the magnetic force provides the required centripetal force:
qvB = mv²/r → r = mv/(qB).
After each gap crossing the proton’s speed v has increased, and with the same magnetic field B and charge q the radius r therefore increases according to r = mv/(qB).
Examiner tips
- Mention that the magnetic force is perpendicular to velocity and does no work; state that the electric field does work when the proton crosses the gap; give the centripetal force equation and the radius formula; link increased speed to increased radius.
Common mistakes
- Saying the magnetic field increases the speed; confusing the role of the electric field; forgetting to include the equation r = mv/(qB) or the fact that the magnetic force is perpendicular to velocity.
Mark scheme (4 marks)
- 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.
- 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.
- Inside each dee the proton moves in a circle because the magnetic force provides the centripetal force (mv²/r = qvB).
- 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
- All IB DP Physics Standard Level (2023 syllabus) revision notes →
- How to answer a "Explain" question →
- Decode the mark scheme abbreviations →
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