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.
Magnetic flux and flux linkage 18(a)–(c)
Question 1
A 40-turn coil of area 3.0 × 10⁻³ m² is perpendicular to a uniform 0.20 T field. Find flux per turn and flux linkage.
Check the model response
The area normal is parallel to B, so Φ = BA = 6.0 × 10⁻⁴ Wb and NΦ = NBA = 2.4 × 10⁻² Wb turn.
repair
2. Repair the common breaks
Use only the correction matching an error, then retry the corresponding diagnostic.
Magnetic flux and flux linkage 18(a)–(c)
Check this idea
Misconception: Flux is BA regardless of orientation.
Repair: Use the area perpendicular to B, or equivalently BA cos θ where θ is between B and the area normal.
Check this idea
Misconception: Flux and flux linkage are identical for every coil.
Repair: Flux is per surface/turn; linkage is NΦ for N turns linking the same flux.
worked example
3. Follow four worked models
Follow how each solution fixes area orientation, linkage sign, energy pathway or ideal-transformer assumptions before calculating.
Magnetic flux and flux linkage 18(a)–(c)
Model 1
A loop of area A has its normal at angle θ to B. Connect the general orientation model to the syllabus form Φ = BA.
Check the model response
General flux is Φ = BA cos θ, where θ is between B and the area normal. The syllabus wording uses cross-sectional area perpendicular to B, so its effective perpendicular area is A⊥ = A cos θ and Φ = BA⊥. When the loop plane is perpendicular to B, θ = 0 and Φ = BA.
guided practice
4. Guided practice
Use each hint only to select the correct perpendicular area, linkage rate, motional geometry or turns ratio.
Magnetic flux and flux linkage 18(a)–(c)
Question 1
Area doubles and B halves while orientation and N stay fixed. State the linkage factor.
Hint: Track N, B and perpendicular area separately.
Check the model response
NΦ = NBA is unchanged because the factors 2 and 1/2 cancel.
independent practice
5. Independent practice
Solve without repair notes and state sign conventions, field geometry, circuit closure and ideal-transformer assumptions.
Magnetic flux and flux linkage 18(a)–(c)
Question 1
Define magnetic flux and flux linkage with units, orientation and the meanings of N and area.
Check the model response
Magnetic flux through a surface is flux density times cross-sectional area perpendicular to B: Φ = BA⊥, unit weber. Flux linkage NΦ is the sum of flux linked by N turns, unit Wb turn. N is total linked turns; area is per turn.
Practice exit check
6. Practice assessment
Use this as extra closed-book practice, then complete the separate recorded assessment in your plan.
Magnetic flux and flux linkage 18(a)–(c)
Question 1
A 120-turn coil of area 5.0 cm² has its plane perpendicular to 0.80 T. Find Φ and NΦ.
Check the model response
A = 5.0 × 10⁻⁴ m². Φ = BA = 4.0 × 10⁻⁴ Wb and NΦ = 4.8 × 10⁻² Wb turn.
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.
Magnetic flux and flux linkage 18(a)–(c)
Question 1
A loop plane turns from perpendicular to parallel with B. State the flux change.
Check the model response
Its area normal turns from parallel to perpendicular to B, so flux falls from BA to zero.