Electromagnetic induction: flux, laws and transformers
Key idea: Define the linked quantity before taking its rate of change, use Lenz's law as an energy-consistent direction rule, and keep simple applications and ideal-transformer ratios within their stated assumptions.
Before you start: Electromagnetic Forces objective chainCurrent Electricity objective chain
By the end, you can
- Define and calculate magnetic flux and flux linkage with correct orientation.
- Infer induction behaviour from experiments and apply Faraday's and Lenz's laws.
- Explain simple motional-e.m.f. and eddy-current applications using energy conservation.
- Explain simple iron-core transformer operation and apply ideal voltage/current ratios.
Starting-point self-check
1. Check your starting point
Attempt all four groups without notes and mark the first area, linkage, rate, polarity, application or ideal-model decision you cannot justify. Use the recorded topic diagnostic above when you want scoring and a personalised repair plan.
Induction experiments, Faraday's law and Lenz's law 18(d)–(e)
Question 1
A 200-turn coil's flux per turn falls from 5.0 μWb to 1.0 μWb in 8.0 ms. Find average induced e.m.f. magnitude and state its polarity principle.
Check the model response
|E| = |Δ(NΦ)/Δt| = 200(4.0 × 10⁻⁶)/(8.0 × 10⁻³) = 0.100 V. Lenz's law fixes the polarity so the induced effect opposes the flux change.
repair
2. Repair the common breaks
Use only the correction matching an error, then retry the corresponding diagnostic.
Induction experiments, Faraday's law and Lenz's law 18(d)–(e)
Check this idea
Misconception: A nonzero flux always induces an e.m.f.
Repair: An e.m.f. requires changing flux linkage; constant nonzero linkage gives zero induced e.m.f.
Check this idea
Misconception: Lenz's law opposes the magnetic field or all motion.
Repair: The induced effect opposes the change in flux linkage that produces it.
worked example
3. Follow four worked models
Follow how each solution fixes area orientation, linkage sign, energy pathway or ideal-transformer assumptions before calculating.
Induction experiments, Faraday's law and Lenz's law 18(d)–(e)
Model 1
Flux linkage rises linearly from −0.030 to +0.050 Wb turn in 0.020 s. Find the signed induced e.m.f.
Check the model response
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.
guided practice
4. Guided practice
Use each hint only to select the correct perpendicular area, linkage rate, motional geometry or turns ratio.
Induction experiments, Faraday's law and Lenz's law 18(d)–(e)
Question 1
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 the model response
E = −d(NΦ)/dt = 0 because linkage is not changing.
independent practice
5. Independent practice
Solve without repair notes and state sign conventions, field geometry, circuit closure and ideal-transformer assumptions.
Induction experiments, Faraday's law and Lenz's law 18(d)–(e)
Question 1
Describe an experiment with a coil, magnet and galvanometer and infer all three syllabus conclusions.
Check the model response
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.
Practice exit check
6. Practice assessment
Use this as extra closed-book practice, then complete the separate recorded assessment in your plan.
Induction experiments, Faraday's law and Lenz's law 18(d)–(e)
Question 1
Flux linkage changes uniformly from 0.12 to −0.06 Wb turn in 30 ms. Find signed e.m.f. and interpret its sign.
Check the model response
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.
Re-test practice
7. Delayed re-test practice
Return after at least three days and solve these fresh contexts without reopening earlier responses. The recorded plan enforces the delay and uses a separate re-test family for selected-response skill-group evidence.
Induction experiments, Faraday's law and Lenz's law 18(d)–(e)
Question 1
Linkage changes by 0.015 Wb turn in 5.0 ms. Find average e.m.f. magnitude.
Check the model response
|E| = 0.015/0.0050 = 3.0 V.