H2 Physics Electromagnetic Induction Notes | 9478

Q: What does A-Level Physics: 18) Electromagnetic Induction Guide cover?
A: Magnetic flux, Faraday's law, Lenz's minus sign and the transformer equation - this post unpacks Section V Topic 18 of the 2026 H2 Physics syllabus.

TL;DR
Induction is the bridge between electricity and magnetism that powers bike dynamos, phone chargers and the entire national grid.
For Paper 2 and Paper 4, memorise $\phi = BA$, drill the chain rule for $\mathscr{E} = -\dfrac{\mathrm{d}(N\phi)}{\mathrm{d}t}$, and practise sketching transformer energy flow diagrams under timed conditions.

Concrete example: how to use this page

If a coil moves into a magnetic field, ask what changes: field strength, area, angle, or time. Then use Faraday's law for size and Lenz's law for direction.

Keep the induction toolkit tied to the rest of the electromagnetism arc via the H2 Physics notes hub; it bundles this chapter with electromagnetism, AC circuits, and Modern Physics extensions.

Lenz's law and sensitive-balance route

Searches for "sensitive balance" can mean two different H2 Physics tasks. SEAB 9478 Topic 17 names the current-balance method for measuring magnetic flux density; Topic 18 names Faraday's and Lenz's laws for induction. Use the route below before choosing a rule.

Induction decision map

Use this map before writing equations. Induction questions usually go wrong when students calculate a magnitude first and only later realise they tracked the wrong changing quantity.

Why students find this topic hard

Electromagnetic induction is hard because the question often hides the important step before the equation. You must identify the changing flux, decide the induced direction, and only then calculate the magnitude. The equations are short; the hard part is knowing which direction to point things.

Failure mode 1: Direction of induced current

Students know Faraday's Law but cannot consistently determine the direction of induced EMF or current in non-trivial geometries - rotating coils, partial loops, or a bar moving on rails. The root cause is applying Lenz's Law as a memorised rule rather than understanding the underlying energy argument: the induced current must oppose the change because any other direction would create energy from nothing.

Failure mode 2: Rotating coil scenarios

The sinusoidal EMF from a rotating coil requires understanding which component of the area vector is changing as the coil rotates. Students frequently confuse the angle between B and the area normal, particularly when a question uses a non-standard starting orientation or asks about the instant when EMF is maximum versus zero.

Failure mode 3: Lenz's Law energy argument

Students can state Lenz's Law but cannot deploy the energy conservation reasoning to verify their answer. The check is straightforward: if removing the opposing effect would allow the induced current to reinforce the flux change indefinitely, energy would be created from nothing - so any answer that does not oppose the change is wrong by construction.

Direction check: After determining the direction of induced current, ask yourself: does this current act to reduce the flux change that caused it? If yes, your direction is correct. If your answer would instead amplify the change, you have the direction reversed. A current that reinforces its own cause would produce perpetual motion - that is the tell.

Moving-conductor direction checkpoint

For a rod or loop moving through a magnetic field, decide the direction in two passes: first name the flux change, then check that the magnetic force opposes the motion that caused the induction.

Worked check: a vertical rod slides to the right on horizontal rails in a magnetic field into the page. The loop area increases, so into-page flux increases. The induced current must produce an out-of-page field, so the loop current is anticlockwise. In the moving rod, the current is upward; with $B$ into the page, the magnetic force on the rod is leftward, opposing the rightward motion.

Misconception check: Lenz's law does not say the induced current always makes a field opposite to the original field. It makes a field that opposes the change in flux.

1 Magnetic flux $(\phi)$ and flux linkage

1.1 Definition

Magnetic flux is the product of magnetic flux density $(B)$ and the area $(A)$ perpendicular to that field:

$$\phi = BA$$

1.2 Flux linkage

For a coil with $N$ identical turns, the magnetic flux linkage is $$N\phi = NBA.$$

IP Exam Cue: The unit for flux is the weber $(\pu{Wb} = \pu{T.m2})$. Always show the superscript “2” - examiners dock marks for $\pu{m2}$ written as $\pu{m}$

2 Faraday's and Lenz's laws

2.1 Faraday's law

A changing magnetic flux linkage induces an e.m.f.: $$\mathscr{E} = -\frac{\mathrm{d}(N\phi)}{\mathrm{d}t}.$$ The magnitude is proportional to the rate of change of $N\phi$.

2.2 Lenz's law

The negative sign shows that the induced e.m.f. acts to oppose the change producing it - a direct consequence of energy conservation.

2.3 Required practical

Push a bar magnet into a coil connected to a galvanometer: the needle deflects; pull it out and the needle swings the opposite way. The faster you move, or the stronger the magnet, the larger the deflection.

2.4 Current-balance connection

When a sensitive-balance setup appears in an induction question, use two layers:

1. Induction layer: identify the change in magnetic flux and use Lenz's law to decide the induced current direction.
2. Force layer: once the induced current direction is known, use the Topic 17 motor-effect rule to decide the force on the conductor or magnet assembly.

That two-layer sequence prevents the common error of using Fleming's left-hand rule before deciding which way the induced current flows.

2.5 What affects $\mathscr{E}$?

Flux-change setup checkpoint

Before substituting into Faraday's law, separate the flux value from the reason it changes.

Misconception check: induction depends on the rate of change of flux linkage. A high flux value by itself is not enough; the graph must have a slope.

Timing hack: In WA calculations, write the chain rule in one line to earn a method mark even if algebra slips.

3 Power transformers

3.1 Principle of operation

Two coils share a laminated soft-iron core, enabling almost all magnetic flux from the primary to link the secondary via mutual induction.

3.2 Ideal transformer equation

Assuming perfect coupling and zero losses: $$\frac{V_s}{V_p} = \frac{N_s}{N_p}.$$

Transformer ratio checkpoint

Before using transformer equations, decide whether you are comparing voltage, current, or power. The turns ratio sets the voltage ratio; ideal power balance then fixes the current ratio.

Worked check: an ideal transformer steps $\pu{240 V}$ down to $\pu{12 V}$. The voltage ratio is $20:1$, so a $\pu{2.0 A}$ secondary current corresponds to $P_s = 12 \times 2.0 = \pu{24 W}$

Misconception check: step-up and step-down describe voltage, not power. In the ideal model, raising voltage lowers current for the same power.

3.3 Efficiency and real-world tweaks

Thin insulated laminations in the core slash eddy-current losses and cut heating. High-grade silicon steel further reduces hysteresis loss.

3.4 IP-level application checks

• Step-up transformer: boosts voltage, lowers current, cuts $I^{2} R$ transmission loss.
• Step-down transformer: renders mains $\pu{230 V}$ safe for the USB-C charger on your desk.

4 Everyday induction heroes

• Bicycle dynamo: converts wheel rotation into light.
• Credit-card stripe reader: reads data via changing magnetic flux.
• Wireless phone charging: coils in the pad and phone form a tightly-coupled transformer at $\sim \pu{100 kHz}$.

Parents' insight: These real objects make abstract equations tangible, boosting engagement during tuition sessions.

5 Three tuition take-aways

1. Master the minus sign. Most lost marks come from forgetting Lenz's direction.
2. Sketch before solving. Draw flux linkage vs time graphs to see slopes.
3. Practise with data-logger traces. Paper 4 often gives non-linear graphs of $\phi$ or $N\phi$ - be ready to estimate gradients.

Need structured practice on Electromagnetic Induction? Our A-Level Physics tuition Singapore programme covers this topic with weekly problem sets and Paper 4 practical drills.

Comprehensive revision pack

9478 Section V, Topic 18 Syllabus outcomes

Candidates should be able to:

• (a) define magnetic flux as the product of magnetic flux density and the cross-sectional area perpendicular to the direction of the magnetic flux density.
• (b) show an understanding of and use the concept of magnetic flux linkage.
• (c) recall and use $\Phi = BA$ and $N\Phi = NBA$ to solve problems, where $N$ is the number of turns.
• (d) infer from appropriate experiments on electromagnetic induction: (i) that a changing magnetic flux can induce an e.m.f., (ii) that the direction of the induced e.m.f. opposes the change producing it, and (iii) the factors affecting the magnitude of the induced e.m.f.
• (e) recall and solve problems using Faraday's law of electromagnetic induction and Lenz's law.

Concept map (in words)

Flux linkage changes drive induced e.m.f. Use $\phi = BA$ to compute flux, then multiply by turns $N$. Faraday's law links the rate of change to induced voltage via $\mathscr{E} = -\frac{\mathrm{d}(N\phi)}{\mathrm{d}t}$

Key relations

Derivations & reasoning to master

1. Bar cutting flux: derive $\mathscr{E} = B L v$ from changing linkage or Lorentz-force arguments.
2. Rotating coil waveform: compute $\phi = B A \cos\theta$, differentiate to recover the sinusoidal e.m.f.
3. Lenz's minus sign: articulate energy conservation argument to justify opposition.
4. Transformer losses: relate eddy currents, hysteresis, copper losses to design features (laminations, soft iron, thick windings).

Worked example 1 - induced e.m.f. in rotating coil

A 200-turn coil of area $\pu{0.015 m2}$ rotates at $\pu{25 Hz}$ in a $\pu{0.35 T}$ uniform field. Find the maximum induced e.m.f. and write its time dependence.

Solution: $\mathscr{E}_0 = N B A \omega$ with $\omega = 2\pi f$. Therefore $\mathscr{E}(t) = \mathscr{E}_0 \sin(2\pi f t)$

$$\omega = 2\pi(25)=157\,\pu{rad.s-1},\qquad \mathscr{E}_0 = (200)(0.35)(0.015)(157) \approx \pu{1.65e2 V}.$$

So $\mathscr{E}(t) \approx (1.65\times 10^2)\sin(2\pi\times 25t)\,\pu{V}$.

Worked example 2 - transformer efficiency

A transformer steps $\pu{240 V}$ down to $\pu{12 V}$ for a $\pu{2.0 A}$ load. The primary current is $\pu{0.12 A}$. Determine the efficiency and estimate the power loss (assume input minus output is mainly copper loss).

Method: Calculate $P_\text{out} = V_s I_s$ and $P_\text{in} = V_p I_p$

Calculation: compute $P_\text{out}$ and $P_\text{in}$, then $\eta$ and the loss from the power difference.

$$P_\text{out} = 12\times 2.0 = \pu{24 W},\qquad P_\text{in} = 240\times 0.12 = \pu{28.8 W}.$$

$$\eta = \dfrac{24}{28.8}\times 100\% = 83\%\;\text{(3 s.f.)},\qquad P_\text{loss} \approx 28.8-24 = \pu{4.8 W}.$$

Practical & data tasks

• Use datalogger to record induced e.m.f. vs time when dropping a magnet through a coil; integrate area to estimate flux change.
• Build a simple generator with hand crank and LED; relate speed to brightness (frequency).
• Perform transformer experiment measuring $\dfrac{V_s}{V_p}$ vs $\dfrac{N_s}{N_p}$

Common misconceptions & exam traps

• Forgetting the cosine factor in $\phi = BA \cos\theta$ when the area is tilted.
• Dropping the negative sign in $\mathscr{E} = -\dfrac{\mathrm{d}(N\phi)}{\mathrm{d}t}$

Quick self-check quiz

1. Define magnetic flux. - Product of magnetic flux density and perpendicular area $\phi = BA$.
2. What does Lenz's law state? - Induced e.m.f. acts to oppose the change causing it.
3. How can you increase induced e.m.f. in a generator? - Increase $N$, $A$, $B$ or rotation speed so $\lvert \mathscr{E} \rvert$

Revision workflow

1. Re-derive $\mathscr{E} = B L v$ and the rotating-coil waveform $\mathscr{E}(t) = N B A \omega \sin(\omega t)$ weekly to keep intuition sharp.
2. Practise interpreting flux linkage graphs and calculating gradients quickly.
3. Summarise transformer loss mechanisms ($I^{2} R$

Practice Quiz

Test yourself on the key concepts from this guide.

6 Further reading

• SEAB H2 Physics 9478 syllabus (2026)
• Khan Academy - Magnetic flux & Faraday's law
• Wikipedia - Flux linkage
• Electronics-Tutorials - Electromagnetic induction

Last updated 14 Jul 2025. Next review when SEAB issues the 2027 draft syllabus.