Explain how Lenz's law is consistent with the principle of conservation of energy, using the example of a conducting ring falling vertically through a region of uniform horizontal magnetic field.
Written & reviewed by James Millett — Biology (Imperial College London), PGCE Science (University of Cambridge).
A conducting ring falls vertically downward and enters a region of uniform horizontal magnetic field directed perpendicular to the plane of the ring. An induced current flows in the ring as it enters the field region.
Model answer (4 marks)
1. As the ring enters the field the magnetic flux through it increases, producing an EMF and a current.
2. Lenz’s law states the induced current creates a magnetic field that opposes the increase in flux, i.e. it opposes the ring’s downward motion.
3. The resulting upward magnetic force on the ring retards its fall, so gravity must do work against this force; the work supplied by gravity becomes the energy of the induced current.
4. If the current were to aid the motion, the ring would accelerate without any external energy input, violating conservation of energy; thus Lenz’s law preserves energy conservation by requiring an external energy source for every induced current.
2. Lenz’s law states the induced current creates a magnetic field that opposes the increase in flux, i.e. it opposes the ring’s downward motion.
3. The resulting upward magnetic force on the ring retards its fall, so gravity must do work against this force; the work supplied by gravity becomes the energy of the induced current.
4. If the current were to aid the motion, the ring would accelerate without any external energy input, violating conservation of energy; thus Lenz’s law preserves energy conservation by requiring an external energy source for every induced current.
Examiner tips
- Use the word ‘opposes’ to show Lenz’s law; link flux change to EMF; explain work done by gravity; mention energy conservation explicitly.
Common mistakes
- Saying the current *creates* a magnetic field that *adds* to the external field; confusing direction of induced force; ignoring the work done by gravity as the energy source.
Mark scheme (4 marks)
- As the ring enters the field, the magnetic flux through the ring increases, inducing an EMF and hence a current in the ring.
- By Lenz's law, the direction of the induced current is such that its magnetic effect opposes the change causing it — here, opposing the increase in flux / opposing the downward motion of the ring.
- The opposing (upward) force on the current-carrying ring means that work must be done by gravity against this retarding force to maintain the ring's motion, providing the energy input to the system.
- If Lenz's law were reversed (current aided the motion), the ring would accelerate without any energy input, violating conservation of energy; thus Lenz's law ensures energy is conserved by requiring an external energy source for every induced current.
Key terms in this question
Lenz's law · conservation of energy
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