Induction experiments, Faraday's law and Lenz's law
Key idea: H2 Physics lessons on magnetic flux, induction laws, applications and ideal transformers.
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Big question: How does a changing magnetic environment produce an e.m.f.?
Faraday's law says induced e.m.f. equals the rate of change of flux linkage. Lenz's law gives its direction: the induced effect opposes the change that produces it, conserving energy. Demonstrate this by moving a magnet through a coil or changing current in a nearby coil and observing a centre-zero meter.
Read Faraday's law as a rate
Faraday's law gives induced e.m.f. ε = −d(NΦ)/dt. Its magnitude depends on how quickly flux linkage changes, not simply on how large the flux is. On an NΦ–t graph, induced e.m.f. is the negative gradient.
A constant flux gives zero induced e.m.f.; a steadily changing flux gives constant e.m.f. Sharp changes in an idealised graph imply large brief values but real systems change over finite time.
Check your understanding: Flux linkage is large but constant. What is induced e.m.f.?
Zero, because its rate of change is zero.
Use Lenz's law as energy conservation
The minus sign encodes Lenz's law: induced current produces effects opposing the change in flux linkage that caused it. It opposes the change, not necessarily the original field.
Decide first whether external flux into a chosen surface is increasing or decreasing. Then choose the induced field that resists that change and use the grip rule for current. If induced effects assisted the change, energy could grow without external work.
Check your understanding: A north pole approaches a coil. Which pole does the near face become?
North, so it repels the approaching north pole and opposes the increase in flux.
Key ideas to keep
- A steady flux produces no induced e.m.f., even if the flux is large.
- The induced field opposes the change in flux, not necessarily the original field.
- Faster change gives a larger e.m.f.
See the reasoning
Worked example
Use a signed flux-linkage gradient
Question: Flux linkage rises linearly from −0.030 to +0.050 Wb turn in 0.020 s. Find the signed induced e.m.f.
Step 1: Calculate the signed change
Why: Crossing from negative to positive linkage requires subtracting the initial negative value.
Working: Δ(NΦ) = 0.050 − (−0.030) = +0.080 Wb turn.
Step 2: Divide by time
Why: Faraday's law uses a rate of change.
Working: Δ(NΦ)/Δt = 0.080/0.020 = +4.0 V.
Step 3: Apply Lenz's sign
Why: Induced polarity opposes the chosen positive linkage change.
Working: ε = −4.0 V relative to the defined circuit direction.
Answer: E = −Δ(NΦ)/Δt = −[0.050 − (−0.030)]/0.020 = −4.0 V. The minus sign encodes Lenz's law relative to the chosen positive linkage direction.
Check: The magnitude is 4.0 V; the sign has meaning only after a positive circuit direction is defined.
Use a hint if needed
Practise with support
Try this
A constant flux linkage persists for 0.50 s. State induced e.m.f.
Hint: Flux can be nonzero while its rate of change is zero.
Check your answer
E = −d(NΦ)/dt = 0 because linkage is not changing.
Now work without the hint
Practise independently
Your turn
Describe an experiment with a coil, magnet and galvanometer and infer all three syllabus conclusions.
Check your answer
Relative motion that changes coil flux produces a galvanometer deflection; stationary magnet and coil give none. Reversing motion reverses deflection, showing the induced e.m.f. opposes the change. Faster change, stronger field, more turns or greater linked area increases magnitude because |E| is the rate of change of linkage.
Avoid these traps
Common mistakes
Common mistake
A nonzero flux always induces an e.m.f.
What is wrong with this reasoning?
Show better thinking
An e.m.f. requires changing flux linkage; constant nonzero linkage gives zero induced e.m.f.
Common mistake
Lenz's law opposes the magnetic field or all motion.
What is wrong with this reasoning?
Show better thinking
The induced effect opposes the change in flux linkage that produces it.
Write for the examiner
Exam guidance
State the original flux change, the opposing induced field and then the current direction.
Exam-style practice [6 marks]
Flux linkage changes uniformly from 0.12 to −0.06 Wb turn in 30 ms. Find signed e.m.f. and interpret its sign.
Plan before you answer
- Retain both linkage signs.
- Convert milliseconds.
- Interpret the Faraday minus sign.
Mark your answer and compare the model
Marking points
Tick each point only if your answer states it clearly.
Model answer
E = −[−0.06 − 0.12]/0.030 = +6.0 V. Positive means the induced polarity is in the chosen positive circuit direction, opposing the specified negative linkage change.
Come back in three days
Check what stayed with you
Recall question
Linkage changes by 0.015 Wb turn in 5.0 ms. Find average e.m.f. magnitude.
Check the answer
|E| = 0.015/0.0050 = 3.0 V.
Syllabus and review details
This lesson covers the listed H2 Physics 9478 outcomes. Flux uses area perpendicular to B; flux linkage is NΦ for N linked turns. Faraday's law uses the rate of change of linkage and Lenz's law fixes polarity from the change being opposed. The simple Blv motional-e.m.f. form requires mutually perpendicular conductor length, velocity and uniform field. Ideal transformer ratios assume common linked flux, alternating operation and no winding or core losses. More advanced induction applications are not required here.
- GCE A-Level H2 PhysicsTopic 18(d) / Topic 18(e) · 2027Checked against the syllabus · partial topic coverageOfficial 9478 syllabus
Course and syllabus information
- Course
- GCE A-Level H2 Physics
- Edition
- GCE A-Level H2 Physics 2027