SAPhysicsSyllabus dot point

How does a changing magnetic field generate a voltage, and what determines its size?

Apply Faraday's law to relate induced EMF to the rate of change of magnetic flux through a coil.

The concept of magnetic flux, how a changing flux induces an EMF, and Faraday's law relating EMF to the rate of change of flux and number of turns, with worked examples.

Generated by Claude Opus 4.78 min answerUpdated 2026-05-29

Reviewed by: AI editorial process; not yet individually human-reviewed

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What this dot point is asking
Magnetic flux
Faraday's law
Ways to induce an EMF

What this dot point is asking

You need to define magnetic flux and apply Faraday's law to calculate the EMF induced when the flux through a coil changes.

Magnetic flux

Magnetic flux measures how much magnetic field passes through an area.

Flux changes if the field strength changes, the area changes, or the orientation of the coil relative to the field changes.

Faraday's law

The central law of induction states that the induced EMF equals the rate of change of flux linkage (flux times number of turns).

So you get a bigger induced voltage by:

changing the flux faster (smaller $\Delta t$ ),
using more turns (larger $N$ ),
producing a larger flux change (stronger field, larger area, or bigger orientation change).

If the flux is not changing, there is no induced EMF - induction needs change.

EMF from a changing field

A 200-turn coil of area $0.015 \text{ m}^2$ sits in a field that drops from 0.40 T to 0 in 0.10 s

Find the average induced EMF (the coil faces the field, $\theta = 0$ ).

Initial flux: $\Phi_i = BA = 0.40\times0.015 = 6.0\times10^{-3} \text{ Wb}$ .
Final flux: $\Phi_f = 0$ .

Change in flux: $\Delta\Phi = 0 - 6.0\times10^{-3} = -6.0\times10^{-3} \text{ Wb}$ .

Induced EMF (magnitude):

|\varepsilon| = N\left|\frac{\Delta\Phi}{\Delta t}\right| = 200\times\frac{6.0\times10^{-3}}{0.10} = 200\times0.060 = 12 \text{ V}

Ways to induce an EMF

Moving a magnet into or out of a coil changes the flux.
Rotating a coil in a field changes $\theta$ , hence the flux (the basis of generators).
Changing the current in a nearby coil changes the field and so the flux (the basis of transformers).
A conductor moving through a field cuts field lines, inducing a motional EMF $\varepsilon = BLv$ .

Exam-style practice questions

Practice questions written in the style of SACE Board exam questions on this dot point, with worked answer explainers. The year tag is the paper they imitate, not the source.

2024 SACE Stage 23 marksA square conductive loop leaves a region of uniform magnetic field of magnitude 0.900 T. The cross-sectional area of the loop is 1.35 x 10^-2 m2 and the loop leaves the field in 0.160 s. Calculate the average emf induced in the loop.

Show worked answer →

Faraday's law gives the magnitude of the average induced emf as the rate of change of magnetic flux: emf = N (change in flux) / (change in time), with N = 1 for a single loop.

The flux through the loop is flux = B A. As the loop leaves the field, the flux falls from B A to zero.

Change in flux = B A = (0.900)(1.35 x 10^-2) = 1.215 x 10^-2 Wb.

emf = (change in flux) / (change in time) = (1.215 x 10^-2) / (0.160) = 7.59 x 10^-2 V.

1 mark for the change in flux, 1 mark for applying Faraday's law, 1 mark for the answer of about 0.076 V.

2025 SACE Stage 23 marksIn a wind-turbine generator, as one magnet passes a coil the magnetic field through the coil decreases by 0.35 T in 0.048 s. The coil has 58 conducting loops and a cross-sectional area of 0.45 m2. Calculate the magnitude of the emf induced in the coil.

Show worked answer →

Faraday's law: emf = N (change in flux) / (change in time), where the flux change comes from the changing field, change in flux = (change in B) x A.

Change in flux = (0.35)(0.45) = 0.1575 Wb.

emf = N (change in flux) / (change in time) = 58 x 0.1575 / 0.048 = 9.135 / 0.048 = 190 V.

1 mark for the flux change, 1 mark for including the 58 turns via N, 1 mark for the answer of about 190 V (1.9 x 10^2 V).

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