Faraday's and Lenz's laws Cambridge International AS & A Level Physics revision
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In plain words
Push a magnet into a coil and a voltage appears, but only while the magnet is moving. The faster the change, the bigger the voltage. And the current it drives always pushes back against whatever you are doing: nature doesn't give energy away for nothing.
5 things to know
- Faraday's law: the induced e.m.f. is proportional to the rate of change of magnetic flux linkage. Its size is Δ(NΦ) ÷ Δt.
- Lenz's law: the induced e.m.f. is in the direction that opposes the change producing it. Putting the two together: ε = −Δ(NΦ) ÷ Δt.
- Lenz's law is the conservation of energy at work. If the induced current helped the change, energy would appear from nowhere.
- Moving a magnet into or out of a coil: the e.m.f. is bigger if the magnet moves faster, if the magnet is stronger, or if the coil has more turns.
- An e.m.f. is also induced in a coil when the current changes in another coil linked with it.
Worked example
The flux through each turn of a 200-turn coil falls from 3.0 × 10⁻⁴ Wb to zero in 0.020 s. Find the e.m.f. induced.
- Change in flux linkage = 200 × 3.0 × 10⁻⁴ = 0.060 Wb.
- E.m.f. = change in flux linkage ÷ time = 0.060 ÷ 0.020.
- = 3.0 V.
Tips and tricks
- No change, no e.m.f. A magnet sitting still inside a coil induces nothing, however strong it is.
- Using Lenz's law: when a north pole comes towards a coil, the near end of the coil becomes a north pole, to repel it.
It lands in your notebook with its questions as flashcards.
Faraday's and Lenz's laws: 5 questions and answers
These are the quiz’s questions. Do the quiz first, then come back here for the ones that got you.
What is the size of an induced e.m.f. proportional to?
A steady flux, however large, induces nothing.
Lenz's law is a consequence of which principle?
The induced current must oppose the change, or energy would appear from nowhere.
A magnet is held still inside a coil. What e.m.f. is induced?
The flux linkage isn't changing.
A magnet is pushed into a coil twice as fast as before. What happens to the induced e.m.f.?
The flux linkage changes in half the time.
The north pole of a magnet is pushed towards one end of a coil. What does that end of the coil become?
It repels the approaching magnet, opposing the change.
Quiz
5 questions
Tap an answer and you’ll see straight away whether it’s right, and why.
Worksheet
4 questions, 10 marks. Write your answers on paper, then check them.
Faraday's and Lenz's laws
Cambridge International AS & A Level Physics 9702 · 10 marks · papermunch.org
Name ______________________________ Date ______________
State Faraday's law and Lenz's law.[2]
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Faraday's law: the induced e.m.f. is proportional to the rate of change of magnetic flux linkage. Lenz's law: the induced e.m.f. acts in the direction that opposes the change producing it.
The flux linkage of a coil changes by 0.040 Wb in 0.10 s. Find the e.m.f. induced.[2]
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0.40 V.
A straight wire 0.20 m long moves at 5.0 m/s at right angles to a magnetic field of flux density 0.10 T. Find the e.m.f. induced across it.[3]
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0.10 V. Each second it sweeps out an area of 0.20 × 5.0 = 1.0 m², so it cuts a flux of 0.10 Wb each second.
A magnet takes much longer to fall through a copper tube than through a plastic one. Explain why.[3]
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The falling magnet changes the flux through the copper, inducing e.m.f.s and currents in it. By Lenz's law these currents oppose the change, so their magnetic field exerts an upward force on the magnet and slows its fall. Plastic does not conduct, so no currents flow.
Answers: Faraday's and Lenz's laws
- 1. Faraday's law: the induced e.m.f. is proportional to the rate of change of magnetic flux linkage. Lenz's law: the induced e.m.f. acts in the direction that opposes the change producing it.
- 2. 0.40 V.
- 3. 0.10 V. Each second it sweeps out an area of 0.20 × 5.0 = 1.0 m², so it cuts a flux of 0.10 Wb each second.
- 4. The falling magnet changes the flux through the copper, inducing e.m.f.s and currents in it. By Lenz's law these currents oppose the change, so their magnetic field exerts an upward force on the magnet and slows its fall. Plastic does not conduct, so no currents flow.