Explain why a straight conducting rod moving at constant velocity through a uniform magnetic field develops an electromotive force (emf) across its ends, and why this emf remains constant as long as the velocity and field are unchanged.
Written & reviewed by James Millett — Biology (Imperial College London), PGCE Science (University of Cambridge).
A straight conducting rod of length L is oriented horizontally and moved horizontally at constant velocity v through a uniform magnetic field directed vertically downward. The rod's motion is perpendicular to both its length and the field direction.
Model answer (4 marks)
The free electrons in the rod are carried with the rod and therefore move through the magnetic field. They experience a magnetic force
F_B=qvB (directed along the rod). This force pushes electrons toward one end, causing charge to accumulate and a potential difference to develop. When the electric force qE produced by the separated charges balances the magnetic force, no further charge separation occurs. At this equilibrium the induced emf is
ε=BLv. Since v, B and L are constant, the balance condition and thus the emf remain constant.
F_B=qvB (directed along the rod). This force pushes electrons toward one end, causing charge to accumulate and a potential difference to develop. When the electric force qE produced by the separated charges balances the magnetic force, no further charge separation occurs. At this equilibrium the induced emf is
ε=BLv. Since v, B and L are constant, the balance condition and thus the emf remain constant.
Examiner tips
- State the magnetic force on moving charges, the resulting charge separation, the equilibrium condition, and give ε=BLv.
- Use correct symbols (B, L, v) and UK spelling.
- Show the reasoning in a logical sequence.
- Mention that the emf is constant because v, B and L are unchanged.
Common mistakes
- Confusing the direction of the magnetic force or the induced emf.
- Forgetting to mention the equilibrium electric force.
- Using the wrong formula (e.g. ε=BL instead of ε=BLv).
Mark scheme (4 marks)
- The free (conduction) electrons in the rod experience a magnetic force because they are moving with the rod through the magnetic field.
- This magnetic force causes electrons to accumulate at one end of the rod, creating a separation of charge (a potential difference) across the rod's ends.
- An equilibrium is reached when the electric force due to the accumulated charge exactly opposes the magnetic force on further charge carriers, at which point the emf equals BLv.
- Because v, B, and L are all constant, the equilibrium condition and hence the emf (= BLv) remain unchanged over time.
Key terms in this question
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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