Is Lenz's law on the HSC data sheet?

Not as words, but it is there: the minus sign in Faraday's law, ε = −NΔΦ/Δt, is Lenz's law. It says the induced emf acts to oppose the change in flux. The flux equation Φ = BA cos θ and both transformer equations are also on the 2019 data sheet.

What is the difference between Faraday's law and Lenz's law?

Faraday's law gives the size of the induced emf: it depends on the rate of change of flux and the number of turns. Lenz's law gives its direction: the induced current's field opposes the change in flux.

Why is Lenz's law an example of conservation of energy?

If the induced current helped the change, a magnet moving towards a coil would be pulled in faster and faster, creating kinetic and electrical energy from nothing. Because the induced current opposes the change, work must be done to keep the motion going, and that work is the electrical energy produced.

Do transformers work with DC?

No. A transformer needs a changing flux in its core, and a steady direct current makes a steady flux, so no emf is induced in the secondary (apart from a brief pulse when the current is switched on or off).

Why is electricity transmitted at high voltage?

For the same power, a higher voltage means a smaller current, and the heat lost in the lines is I^2R. Ten times the voltage gives one tenth of the current and one hundredth of the loss.

The north pole of a bar magnet is pulled away from one end of a coil connected in a closed circuit. What pole forms at that end of the coil?

A south pole, which attracts the magnet

No pole, because the flux is decreasing

A north pole, which attracts the magnet

Why does a strong magnet fall more slowly through a vertical copper tube than through a plastic tube of the same size?

The changing flux induces eddy currents in the copper, and their field opposes the magnet's motion.

Copper is a magnetic material, so it attracts the magnet.

The copper tube traps more air, so there is more air resistance.

The magnet makes the copper permanently magnetic, and it repels the magnet.

Why is a transformer core made of thin, insulated sheets instead of a solid block of iron?

To reduce eddy currents in the core, and so reduce heating

To stop all eddy currents in the core

To increase the resistance of the copper windings

To let the transformer work on DC

HSC Physics · Module 6 · Electromagnetism · 16 min read

Electromagnetic induction

Change the magnetic field through a coil and a voltage appears in it. That is electromagnetic induction, and it is how generators, transformers, induction cooktops and magnetic brakes work. It has been on every HSC Physics paper from 2019 to 2025, and the question asked most often is some version of 'explain using Lenz's law'.

This guide covers magnetic flux, Faraday's law, Lenz's law as conservation of energy (with the chain of reasoning markers look for), eddy currents and braking, ideal and real transformers, and why power lines run at high voltage. Then the mistakes that cost marks, a quick quiz and a full worked example.

What you need to know

Use Φ = B_∥A = BA cos θ to describe how the magnetic flux through an area can be changed.
Analyse examples of Faraday's law, ε = −NΔΦ/Δt, and Lenz's law, in words and with numbers, tracing the energy transfers and transformations: for example a magnet moving relative to a straight conductor, a metal plate or a solenoid, and an emf induced in one solenoid by a nearby one that moves or has a changing current.
Analyse ideal transformers with V_p/V_s = N_p/N_s and V_pI_p = V_sI_s.
Evaluate where the ideal transformer model breaks down (incomplete flux linkage, eddy currents, resistive heating) and how real transformers are made more efficient.
Analyse where transformers step voltage up or down, including high-voltage power transmission.
Connect Lenz's law to conservation of energy, and apply energy conservation to a DC motor and to magnetic braking.

The equations (from the 2019 HSC data sheet unless marked):

Φ = B_∥A = BA cos θMagnetic flux in webers (Wb). θ is the angle between the field and the normal to the area.

ε = −N ΔΦ/ΔtAverage induced emf in a coil of N turns. The minus sign is Lenz's law: the emf opposes the change.

V_p/V_s = N_p/N_sIdeal transformer: the voltage ratio equals the turns ratio.

V_pI_p = V_sI_sIdeal transformer: power in equals power out, so stepping voltage up steps current down.

P_loss = I²R not on the data sheetHeating in a transmission line of resistance R carrying current I. It comes from P = VI and V = IR, which are on the sheet.

Dot points: PH-M6-08, PH-M6-09, PH-M6-10, PH-M6-11, PH-M6-12, PH-M6-15 (2017 Physics syllabus, HSC 2026 and 2027), in our own words.

Mini lesson

Magnetic flux: how much field passes through an area

Magnetic flux Φ measures how much magnetic field passes through an area. For a uniform field B through a flat area A, Φ = BA cos θ, where θ is the angle between the field and the normal to the area. The unit is the weber (1 Wb = 1 T m²).

The flux is greatest when the area faces the field square-on (θ = 0) and zero when the field runs along the surface (θ = 90°). So there are three ways to change it: change the field strength B, change the area A inside the field, or change the angle θ (for example by rotating a coil). If a coil is turned right over, the flux through it reverses sign: from +BA to −BA.

Φ = BA cos θ. Measure θ from the field to the normal (orange), not to the surface. Tilt the area until it lies along the field and the flux through it is zero.

Faraday's law: the rate of change of flux

An emf is induced in a conductor whenever the flux through it changes. Steady flux, however large, induces nothing. Faraday's law gives the size: ε = −N ΔΦ/Δt for a coil of N turns. The faster the change, the bigger the emf, so always say 'the rate of change of flux'.

An emf does not need a complete circuit. An open coil or a cut ring still has an emf across it when the flux changes; it just has no current. Close the circuit and a current flows, I = ε ÷ R.

Ways to induce a bigger emf: a stronger magnet, faster motion, more turns, or a bigger coil area. Each one makes ΔΦ/Δt or N larger.

Lenz's law and conservation of energy

Lenz's law: the induced current flows in the direction that makes its own magnetic field oppose the change in flux that produced it. It opposes the change, not the field itself: if the flux is falling, the induced field tries to top it back up.

Why it must be this way: energy conservation. Suppose the induced current helped the change instead. Push a magnet towards a coil and the coil would pull it in faster, which would induce a bigger current, which would pull harder. Kinetic energy and electrical energy would both grow from nothing. That never happens, because energy is conserved. So the induced current must oppose the change, which means work has to be done to keep the magnet moving, and that work is exactly the electrical energy that appears in the coil (and then becomes heat in its resistance).

To find a direction, use four steps:

1. Which way does the original flux through the coil point?
2. Is it increasing or decreasing?
3. The induced field points the opposite way if it is increasing, the same way if it is decreasing.
4. Use the right-hand grip rule on that induced field to get the direction of the current.

The magnet's N pole approaches, so the flux to the right through the coil increases. The induced current makes the near end a north pole, which repels the magnet: the change is opposed, so you must do work to push it in.

How to write the 'explain' answer. Markers want the full chain, in order, with each link named: (1) the relative motion changes the magnetic flux through the conductor; (2) by Faraday's law the rate of change of flux induces an emf; (3) the conductor forms a closed path, so a current flows; (4) by Lenz's law that current's magnetic field opposes the change in flux; (5) so there is a force (or torque) opposing the motion, and an equal and opposite force on the magnet or coil that caused it (Newton's third law); (6) energy: the work done against this force becomes electrical energy, then heat in the conductor's resistance.

Eddy currents and magnetic braking

In a solid piece of metal there is no wire to follow, so changing flux induces swirling loops of current called eddy currents. By Lenz's law they oppose the change, which means they oppose the relative motion between the metal and the magnet.

Drop a strong magnet down a copper tube and it falls slowly. The flux through each ring of the tube changes as the magnet passes, eddy currents are induced, and their fields oppose the magnet's motion. The faster it falls, the faster the flux changes and the bigger the opposing force, until that force equals its weight and it falls at a constant terminal speed. The tube feels an equal and opposite force downward. Once it is at terminal speed, the magnet's gravitational potential energy becomes electrical energy and then heat in the copper, not extra kinetic energy.

The same idea brakes trains, roller coasters and exercise bikes with no contact and no wear. The braking force depends on speed, so it is strong at high speed and fades to nothing as the motion stops. Cutting slots in the metal breaks up the eddy-current loops and weakens the braking. Note that copper and aluminium are not magnetic: the force comes from the induced currents, not from the magnet attracting the metal.

Ideal transformers

A transformer is two coils wound on a shared iron core. An alternating current in the primary coil makes a changing flux in the core, and that changing flux passes through the secondary coil and induces an emf in it. A steady DC makes a steady flux, so a transformer does not work on DC (except for a brief pulse when it is switched on or off).

For an ideal transformer the voltage ratio equals the turns ratio, V_p/V_s = N_p/N_s. More turns on the secondary steps the voltage up; fewer steps it down. No energy is lost, so V_pI_p = V_sI_s: stepping the voltage up steps the current down by the same factor.

The primary current depends on what is connected to the secondary. Add more load (more appliances in parallel), the secondary current rises, and so the primary current rises to supply the extra power.

The changing flux Φ in the core links the two coils. With fewer secondary turns, as here, it is a step-down transformer: V_s = V_p × N_s/N_p.

Real transformers and high-voltage transmission

Real transformers lose some energy, mostly as heat. Each design feature targets one loss:

Incomplete flux linkage: some flux from the primary misses the secondary. A soft-iron core, with the coils wound on the same core (often one over the other), improves the flux linkage.
Eddy currents in the core: the core is a conductor in a changing field, so eddy currents heat it. Thin, insulated laminations cut the paths, which reduces (does not stop) the eddy currents and their heating.
Resistive heating in the coils: current through the windings heats them (I²R). Thick, low-resistance copper wire reduces it.
Hysteresis (not named in the syllabus, but strong 2025 HSC answers mentioned it): energy is used re-magnetising the core every cycle. A soft-iron core, easy to magnetise and demagnetise, keeps this small.

Power stations send energy over long lines, and the lines lose power as heat, P_loss = I²R. For the same power P = VI, a higher voltage means a lower current, and the loss falls with the square of the current. Example: sending 1.0 MW through lines of total resistance 5.0 Ω at 11 kV needs 91 A and loses about 41 kW (4.1%); at 132 kV it needs 7.6 A and loses about 0.29 kW (0.029%). So step-up transformers raise the voltage at the power station and step-down transformers lower it again near homes, where high voltage would be dangerous.

Use the line current in I²R. Putting the transmission voltage into V²/R gives a nonsense answer, because that voltage is not across the line's resistance.

Common mistakes

Saying an emf is induced because there is a magnetic flux through the coil.An emf is induced only when the flux changes, and its size depends on the rate of change of flux, ΔΦ/Δt.
Writing 'the induced current opposes the magnet' or 'opposes the field'.It opposes the change in flux. Then say what that means here: the force on the magnet opposes its motion relative to the coil.
Taking ΔΦ = BA when a coil is turned right over in a field.The flux goes from +BA to −BA, so ΔΦ = −2BA. Work out Φ_final − Φ_initial with signs every time.
Explaining magnetic braking as the magnet attracting or repelling the copper or aluminium.Those metals are not magnetic. The changing flux induces eddy currents, and the eddy currents' field opposes the motion (Lenz's law).
Saying laminations stop eddy currents, or that a transformer works on DC.Laminations reduce eddy currents and the heat they produce. A transformer needs a changing flux, so the primary must carry AC.
Finding line losses with V²/R using the transmission voltage.Find the line current from P = VI, then P_loss = I²R with the line's resistance.

Worked example

A small flat search coil of 150 turns, 5.0 cm × 4.0 cm, sits inside a long solenoid with its plane at right angles to the solenoid's axis. The solenoid's current makes a uniform 0.12 T field along its axis. The search coil is connected to a meter, and the total resistance of the search coil's circuit is 3.2 Ω. The solenoid's current is then reversed at a steady rate, so that in 0.15 s the field changes from 0.12 T in one direction to 0.12 T in the opposite direction.

(a) Calculate the average emf induced in the search coil. (3 marks)

(b) Calculate the average current in the search coil's circuit. (1 mark)

(c) Use Lenz's law to explain the direction of the magnetic field produced by the induced current while the solenoid's field reverses. (2 marks)

(6 marks)

I'll think out loud, the way you should in the exam, using KNOW-UD: Knowns, Not known, Organise, Work it out, Units, Direction.

Prediction first. The flux through the coil is BA = 0.12 × 0.0020 ≈ 2.4 × 10⁻⁴ Wb. If the field just dropped to zero, the emf would be about 150 × 2.4 × 10⁻⁴ ÷ 0.15 ≈ 0.24 V. But the field reverses, so the flux goes from +BA to −BA and the change is twice that: I predict about 0.5 V, and about 0.5 ÷ 3.2 ≈ 0.15 A.

K · Knowns

I sketch the search coil edge-on inside the solenoid, with the field before and after. The coil doesn't move; the field through it changes. I take the solenoid's original field direction as positive, so the field goes from +0.12 T to −0.12 T. I convert the coil size to square metres first.

N = 150, Δt = 0.15 s, R = 3.2 Ω
A = 0.050 m × 0.040 m = 2.0 × 10⁻³ m²
B_initial = +0.12 T, B_final = −0.12 T (coil plane at right angles to B, so θ = 0 and Φ = BA)

Knowns on the sketch: B = 0.12 T, reversed in 0.15 s, N = 150, 5.0 cm × 4.0 cm, R = 3.2 Ω. Taking the original field direction as positive, the flux goes from +BA to −BA.

N · Not known

Two numbers and an explanation. The emf comes from the change in flux, so I need Φ before and after.

(a) ε = ? V (on the way: ΔΦ = ? Wb)
(b) I = ? A
(c) the direction of the induced current's field

O · Organise

I write each equation in symbols. The key line is ΔΦ = Φ_final − Φ_initial, keeping the signs.

Φ = BA (plane at right angles to B)
ΔΦ = Φ_final − Φ_initial
ε = −N ΔΦ/Δt
I = ε ÷ R

W · Work it out

Flux before and after, then the change with its sign, then Faraday's law. For (c) I follow the flux through the whole reversal, not just the end points.

Φ_initial = (+0.12) × 2.0 × 10⁻³ = +2.4 × 10⁻⁴ Wb
Φ_final = (−0.12) × 2.0 × 10⁻³ = −2.4 × 10⁻⁴ Wb
ΔΦ = (−2.4 × 10⁻⁴) − (+2.4 × 10⁻⁴) = −4.8 × 10⁻⁴ Wb
ε = −150 × (−4.8 × 10⁻⁴) ÷ 0.15 = +0.48 V
I = 0.48 ÷ 3.2 = 0.15 A
(c) Take the solenoid's original field as pointing right. As its current reverses, the flux to the right through the search coil falls to zero, then builds up to the left. This changing flux induces a current in the search coil (Faraday). By Lenz's law the induced current's magnetic field opposes the change in flux, so inside the coil it points to the right, the original direction, the whole time: first it opposes the fall of the rightward flux, then the growth of the leftward flux. The energy that heats the search coil's circuit comes from the solenoid's power supply.

U · Units

Webers per second is volts, and volts per ohm is amps. The data are to two significant figures.

(a) ε = 0.48 V
(b) I = 0.15 A

D · Direction

The emf came out positive because ΔΦ was negative: that's the minus sign in Faraday's law at work. With the original field direction taken as positive, a positive emf drives a current whose field points in that positive direction, which matches the Lenz's law answer to (c).

The induced current's field points along the solenoid's original field direction throughout the reversal, opposing the change in flux.

(a) The average emf is 0.48 V. (b) The average current is 0.15 A. (c) The induced current's field points along the solenoid's original field direction throughout, opposing the change in flux: first the fall of the original flux, then the build-up of the reversed flux.

Check against the prediction. I predicted about 0.5 V and 0.15 A, twice the 0.24 V a simple drop to zero would give. The answers are 0.48 V and 0.15 A, so the doubled flux change was the key step.

HSC advice

What markers keep saying

Find the change in flux as final minus initial flux, notice when it comes out negative, and carry every minus sign through Faraday's law and the working that follows.NESA marking feedback, 2021, summarised
Link the induced emf, and so the force on a ring or coil, to the rate of change of flux through it, not just to 'the flux' or 'a change in flux'.NESA marking feedback, 2023, summarised
Run the induction chain in order and keep Faraday and Lenz separate: Faraday gives the emf, Lenz gives the direction of the induced current's field (opposing the change in flux, not 'opposing the magnet').NESA marking feedback, 2022, summarised
When a question asks about energy, name every transformation (for example kinetic energy to electrical energy in the eddy currents, then heat), rather than only describing forces or electron movement.NESA marking feedback, 2024, summarised
Include the Newton's third law force on the other object (the tube, the coil or the balance), and when there are two observations to explain, explain both.NESA marking feedback, 2025, summarised
For transformer efficiency, link each design feature to the loss it reduces. Laminations reduce eddy currents (they don't eliminate them), and use the term flux linkage.NESA marking feedback, 2022, summarised
A bigger load on the secondary increases the secondary current, and by V_pI_p = V_sI_s the primary current increases too. Say why: energy is conserved.NESA marking feedback, 2023, summarised

Summaries in our own words. Read NESA's own feedback with the exam packs: 2021 · 2022 · 2023 · 2024 · 2025.

How often it is examined

Electromagnetic induction questions were worth 69 marks across the seven HSC Physics exams from 2019 to 2025 (about 9.9 marks a paper), and appeared in 7 of 7 papers.

Marks per paper (Module 6, Electromagnetic Induction). Source: CortexHSC's own tagging of the NESA HSC Physics exams 2019–2025, each question counted under its main topic, so treat the numbers as close, not exact.

FAQ

Is Lenz's law on the HSC data sheet?: Not as words, but it is there: the minus sign in Faraday's law, ε = −NΔΦ/Δt, is Lenz's law. It says the induced emf acts to oppose the change in flux. The flux equation Φ = BA cos θ and both transformer equations are also on the 2019 data sheet.
What is the difference between Faraday's law and Lenz's law?: Faraday's law gives the size of the induced emf: it depends on the rate of change of flux and the number of turns. Lenz's law gives its direction: the induced current's field opposes the change in flux.
Why is Lenz's law an example of conservation of energy?: If the induced current helped the change, a magnet moving towards a coil would be pulled in faster and faster, creating kinetic and electrical energy from nothing. Because the induced current opposes the change, work must be done to keep the motion going, and that work is the electrical energy produced.
Do transformers work with DC?: No. A transformer needs a changing flux in its core, and a steady direct current makes a steady flux, so no emf is induced in the secondary (apart from a brief pulse when the current is switched on or off).
Why is electricity transmitted at high voltage?: For the same power, a higher voltage means a smaller current, and the heat lost in the lines is I²R. Ten times the voltage gives one tenth of the current and one hundredth of the loss.

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