Explain why a proton moving in a uniform magnetic field follows a circular path at constant speed, and explain what happens to the radius of that circular path if the proton is replaced by a deuteron (a nucleus containing one proton and one neutron) moving at the same speed.
Written & reviewed by James Millett — Biology (Imperial College London), PGCE Science (University of Cambridge).
Model answer (4 marks)
The magnetic force on a charged particle is
F = qvB
and is always perpendicular to the velocity. Because the force is perpendicular, it does no work and the kinetic energy, and therefore the speed, of the proton remains constant. With constant speed the particle undergoes uniform circular motion, the radius being
r = mv/(qB). A deuteron has the same charge as a proton but twice the mass. Replacing the proton with a deuteron at the same speed gives r' = (2m)v/(qB) = 2r. Thus the deuteron follows a circle of twice the radius.
F = qvB
and is always perpendicular to the velocity. Because the force is perpendicular, it does no work and the kinetic energy, and therefore the speed, of the proton remains constant. With constant speed the particle undergoes uniform circular motion, the radius being
r = mv/(qB). A deuteron has the same charge as a proton but twice the mass. Replacing the proton with a deuteron at the same speed gives r' = (2m)v/(qB) = 2r. Thus the deuteron follows a circle of twice the radius.
Examiner tips
- Show the force is perpendicular to velocity to justify no work; link to constant speed; write the radius formula and substitute the doubled mass; keep the answer concise and use correct symbols (q, B, m, v).
Common mistakes
- Forgetting that the magnetic force is perpendicular and therefore does no work; incorrectly assuming the speed changes; using the wrong radius formula (e.g. r = mv/qB instead of r = mv/(qB)).
Mark scheme (4 marks)
- The magnetic force on the proton is always perpendicular to its velocity, so the force does no work on the proton.
- Because no work is done, the kinetic energy (and hence speed) of the proton remains constant.
- The radius of circular motion is given by r = mv / (qB); since the deuteron has twice the mass of the proton but the same charge and the same speed, its radius is doubled.
- Therefore the deuteron travels in a circle of radius twice that of the proton under the same magnetic field strength.
Key terms in this question
uniform magnetic field · deuteron
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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