Explain why an electron moving in a circle within a uniform magnetic field does not gain kinetic energy, even though a magnetic force acts on it continuously.

IB DP Physics Standard 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).

An electron travels in a circular path when it enters a region of uniform magnetic field directed perpendicular to its velocity.

Model answer (4 marks)

1. The magnetic force is always perpendicular to the velocity of the electron.
2. A force perpendicular to velocity changes only the direction of motion, not the speed.
3. No work is done on the electron because work requires a force component parallel to the displacement.
4. Since no work is done on the electron, its kinetic energy remains constant.

Examiner tips

  • Use the term ‘magnetic force is perpendicular to velocity’ first to show understanding of Lorentz force. Show that work = F·d and that F⊥v gives zero dot product, earning the work point.

Common mistakes

  • Confusing magnetic force with electric force and claiming it does work. Assuming the electron gains energy because it is moving in a circle, ignoring the perpendicular nature of the force.

Mark scheme (4 marks)

  1. The magnetic force is always perpendicular to the velocity of the electron.
  2. A force perpendicular to velocity changes only the direction of motion, not the speed.
  3. No work is done on the electron because work requires a force component parallel to the displacement.
  4. Since no work is done on the electron, its kinetic energy remains constant.

Key terms in this question

magnetic force · kinetic energy

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