Explain why a proton moving in a circular path in a uniform magnetic field does not gain kinetic energy, even though a magnetic force acts on it continuously.

IB DP Physics Higher Level (2023 syllabus) — D.2 Electric and magnetic fields · Explain · 4 marks · View as Markdown

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 φq\u00b7\u03b2\u00b7\u03c9, which is always perpendicular to the velocity vector. A force perpendicular to the velocity can only change the direction of the velocity, not its magnitude. Because the force has no component along the displacement, the work done by the magnetic field is zero. With no work performed, the kinetic energy of the proton remains constant, so it does not gain kinetic energy while moving in the circular path.

Examiner tips

  • Show the force is perpendicular to velocity; mention work requires a component along displacement; state that zero work means no change in kinetic energy; keep answer concise and use correct terminology

Common mistakes

  • Assuming the magnetic force does work because it acts continuously; confusing magnetic force with electric force; not linking zero work to constant kinetic energy.

Mark scheme (4 marks)

  1. The magnetic force on the proton is always perpendicular to its velocity.
  2. A force perpendicular to the velocity changes only the direction of the velocity, not its magnitude.
  3. No work is done by the magnetic force because work requires a force component along the displacement.
  4. Since no work is done on the proton, its kinetic energy remains constant and cannot increase.

Key terms in this question

magnetic force · circular path · kinetic energy

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