Apply Faraday's and Lenz's laws
Relate induced e.m.f. to the rate of change of flux linkage and use Lenz's law to determine its opposing direction.
A Level; Cambridge International Physics 9702, 2025–2027 syllabus, Topic 20. These original explanations and calculations are study aids; full timed assessment and human subject-teacher review remain outstanding.
Before you begin
- Use current, charge, force, velocity, vectors, area and SI units; distinguish conventional current from electron flow.
Work on paper. Try each question before revealing help, and explain why your method works.
Quick readiness check
What does Faraday's law relate induced e.m.f. to?
What you will learn
- Use Faraday's law for induced e.m.f. magnitude
- Apply Lenz's law to determine induced direction
- Explain how the induced effect opposes its cause
Faraday's law links e.m.f. to changing flux linkage
Faraday's law states that the magnitude of induced e.m.f. is proportional to the rate of change of magnetic flux linkage. For a coil of N turns, |ε| = |Δ(NΦ)/Δt| over an interval, or |ε| = N|dΦ/dt| for a uniform rate.
A larger change in flux or a shorter time produces a larger e.m.f. If the linkage stays constant, the rate of change is zero and there is no induced e.m.f.
Lenz's law gives the opposing direction
Lenz's law states that the induced current is in a direction such that its magnetic effect opposes the change in flux that produced it. It opposes the change, not necessarily the original field itself: if flux is increasing, the induced field acts against that increase; if flux is decreasing, it acts to support the original flux.
The minus sign in ε = −Δ(NΦ)/Δt represents this opposition. Use the sequence: identify the original flux direction, decide whether it is increasing or decreasing, choose the induced field that opposes that change, then use the coil orientation to infer current direction.
Pause and explain
If flux linkage doubles in the same time interval, what happens to average induced e.m.f. magnitude?
Worked example
A 100-turn coil's flux per turn changes from 0.80 mWb to 0.20 mWb in 0.050 s. Find the average induced e.m.f. magnitude.
Show the worked solution
- Find the change in flux linkage: NΔΦ.
- Convert mWb to Wb and divide by time.
- Use magnitude; infer direction separately with Lenz's law.
Answer |ε| = 100 × 0.60 × 10⁻³/0.050 = 1.2 V.
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A 200-turn coil's flux per turn changes by 3.0 × 10⁻⁴ Wb in 0.020 s. Calculate average induced e.m.f. magnitude.
Give me a hint
Use |ε| = N|ΔΦ|/Δt and include the turn count before dividing by the time.
Compare my reasoning
- Δ(NΦ) = 200 × 3.0 × 10⁻⁴ = 0.060 Wb-turn.
- |ε| = 0.060/0.020.
- State volts.
|ε| = 3.0 V.
Look for these in your work
- Turns included
- Linkage change calculated
- Time division and unit correct
An upward magnetic flux through a coil is increasing. In which direction must the induced magnetic field act?
Give me a hint
Apply Lenz's law to oppose the increase in upward flux.
Compare my reasoning
- The original flux points upward and is increasing.
- The induced effect opposes that increase.
- The induced magnetic field points downward.
Downward, opposing the increase in upward flux.
Look for these in your work
- Original direction identified
- Increasing trend identified
- Opposing field stated
A coil's flux linkage changes by the same amount in 0.10 s and in 0.025 s. Compare the induced e.m.f. magnitudes.
Give me a hint
For a fixed linkage change, e.m.f. magnitude is inversely proportional to time.
Compare my reasoning
- The second interval is one quarter of the first.
- The same linkage change occurs four times as quickly.
- The induced e.m.f. magnitude is four times as large in 0.025 s.
The shorter-interval change induces four times the e.m.f. magnitude.
Look for these in your work
- Time ratio found
- Rate comparison made
- E.m.f. ratio stated
Common mistakes
- Applying Faraday's law to flux but omitting the number of turns
- Using a final flux instead of change in flux
- Saying Lenz's law opposes the magnetic field in all cases
- Ignoring the time interval when comparing induced e.m.f.
What can you explain now?
What does Faraday's law relate induced e.m.f. to?
Compare with the explanation
Rate of change of flux linkage
A more rapid linkage change gives a larger e.m.f.
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Make it stick
How do Faraday's law and Lenz's law together determine induced e.m.f. magnitude and direction?
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