A beam of electrons enters a region where a uniform magnetic field acts perpendicular to their velocity. Explain why the electrons follow a circular path and why their speed remains constant throughout this motion.
Written & reviewed by James Millett — Biology (Imperial College London), PGCE Science (University of Cambridge).
Electrons in a cathode-ray tube are directed into a region of uniform magnetic field oriented perpendicular to the initial velocity of the electrons.
Model answer (4 marks)
The magnetic force on a moving electron is given by φ=qvB and is always perpendicular to the velocity. A force that is always perpendicular to the velocity acts as a centripetal force, continuously changing the direction of motion without changing the magnitude of velocity, so the electrons follow a circular path. Because the magnetic force is perpendicular to the velocity it does no work on the electron. Since no work is done, the kinetic energy remains constant, and therefore the speed of the electrons remains constant throughout the motion.
Examiner tips
- Use the formula φ=qvB to show the force is perpendicular; link this to centripetal force; state that work = F·d = 0; conclude speed constant.
- Keep the answer concise and use the exact terminology: magnetic force, centripetal force, work, kinetic energy.
Common mistakes
- Claiming the magnetic force changes the speed; forgetting that work is zero; not explicitly stating the force is perpendicular to velocity.
Mark scheme (4 marks)
- The magnetic force on a moving electron is always perpendicular to its velocity.
- A force that is always perpendicular to the velocity acts as a centripetal force, continuously changing the direction of motion without changing the magnitude of velocity, causing circular motion.
- Since the magnetic force is always perpendicular to the velocity, it does no work on the electron.
- Because no work is done, the kinetic energy of the electron remains constant, and therefore its speed remains constant.
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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