# A long solenoid carries a sinusoidally alternating current. A small, single-turn rectangular coil is placed coaxially inside the solenoid. Explain why an alternating EMF is induced in the rectangular coil, and explain why the peak EMF induced in the coil would increase if the frequency of the alternating current in the solenoid were doubled while its peak current were kept constant.

> IB DP Physics Higher Level (2023 syllabus) — D.4 Induction (HL only) · Explain · 4 marks

## Mark scheme (4 marks)

1. The alternating current in the solenoid produces a magnetic field whose magnitude (and hence flux through the rectangular coil) changes continuously with time.
2. By Faraday's law, an EMF is induced in the coil because the rate of change of magnetic flux linkage through the coil is non-zero, producing an alternating EMF at the same frequency.
3. Doubling the frequency means the magnetic flux (and flux linkage) varies twice as rapidly with time, so the rate of change of flux linkage is doubled.
4. Because peak EMF is proportional to the rate of change of flux linkage (EMF_peak = NBAω, where ω = 2πf), doubling the frequency doubles the peak EMF.

## Key terms

- [alternating EMF](https://www.gradenine.co.uk/glossary/alternating-emf)
- [solenoid](https://www.gradenine.co.uk/glossary/solenoid)
- [coaxial](https://www.gradenine.co.uk/glossary/coaxial)

## Related

- [Revision notes for IB DP Physics Higher Level (2023 syllabus)](https://www.gradenine.co.uk/learn)
- [How to answer "Explain" questions](https://www.gradenine.co.uk/tools/command-word-cheatsheet)
- [Practice this with AI marking (free)](https://www.gradenine.co.uk/start)

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Source: [GradeNine](https://www.gradenine.co.uk/q/a-long-solenoid-carries-a-sinusoidally-3be77edf) · Published by Druglandscape Ltd.