A coil of 100 turns experiences a flux change of 2.0 × 10^-3\ Wb per turn in 0.040\ s. Find the induced e.m.f. [2 marks]

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How does a changing magnetic flux induce an e.m.f., and what determines its size and direction?

Define magnetic flux and flux linkage, apply Faraday's law and Lenz's law, and explain the operation of a simple generator

A focused answer to the H2 Physics learning outcome on electromagnetic induction. Magnetic flux and flux linkage, Faraday's law of induction, Lenz's law and energy conservation, and the simple a.c. generator.

Generated by Claude Opus 4.89 min answerUpdated 2026-06-06

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

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What this dot point is asking
The answer
Examples in context
Try this

What this dot point is asking

SEAB wants you to define magnetic flux and flux linkage, to apply Faraday's law (the induced e.m.f. equals the rate of change of flux linkage) and Lenz's law (the induced effect opposes the change), and to explain a simple generator. Induction is the basis of electrical power generation and the transformer.

The answer

Magnetic flux and flux linkage

Magnetic flux through an area $A$ in a field of flux density $B$ is:

\Phi = BA\cos\theta

where $\theta$ is the angle between the field and the normal to the area. Flux is maximum when the field is perpendicular to the area ( $\theta = 0$ ). Its unit is the weber (Wb).

For a coil of $N$ turns, the flux linkage is $N\Phi$ (the flux multiplied by the number of turns), measured in weber-turns.

Faraday's law of induction

The magnitude of the induced e.m.f. equals the rate of change of flux linkage:

\mathcal{E} = \frac{\Delta(N\Phi)}{\Delta t}

So an e.m.f. is induced whenever the flux linkage changes, whether by changing the field, the area, or the orientation. A faster change, a stronger field, a larger area or more turns all increase the induced e.m.f.

Lenz's law and direction

Lenz's law gives the direction: the induced current always opposes the change that produces it. This is a statement of conservation of energy: the induced current creates effects (a magnetic field, a force) that resist the change, so work must be done to maintain the change, supplying the electrical energy. The minus sign in $\mathcal{E} = -\dfrac{\Delta(N\Phi)}{\Delta t}$ encodes this opposition.

The simple generator

A coil rotated in a magnetic field has a continuously changing flux linkage, so it induces an alternating e.m.f. For a coil of $N$ turns and area $A$ rotating at angular frequency $\omega$ in a field $B$ :

\mathcal{E} = NBA\omega\sin(\omega t)

The e.m.f. is greatest when the coil is parallel to the field (the flux is changing fastest) and zero when the coil is perpendicular to the field (the flux is momentarily at a maximum, so its rate of change is zero). The output is sinusoidal alternating current.

Worked example

A square coil of $50$ turns and side $0.10\ \text{m}$ lies with its plane perpendicular to a field that increases uniformly from $0.20\ \text{T}$ to $0.80\ \text{T}$ in $0.30\ \text{s}$ . Find (a) the change in flux linkage and (b) the induced e.m.f.

Step 1: Find the coil area

A = (0.10)^2 = 1.0 \times 10^{-2}\ \text{m}^2

Step 2: Find the change in flux linkage

The flux linkage is $N\Phi = NBA$ (field perpendicular to the plane, so $\cos\theta = 1$ ).

\Delta(N\Phi) = NA\Delta B = 50 \times 1.0 \times 10^{-2} \times (0.80 - 0.20) = 50 \times 1.0 \times 10^{-2} \times 0.60 = 0.30\ \text{Wb}

Step 3: Apply Faraday's law

\mathcal{E} = \frac{\Delta(N\Phi)}{\Delta t} = \frac{0.30}{0.30} = 1.0\ \text{V}

Step 4: State the result

The induced e.m.f. is $1.0\ \text{V}$ . By Lenz's law, the induced current would flow so as to oppose the increasing flux, creating a field that resists the rise.

Examples in context

Example 1. Power station generators. A turbine spins a coil (or set of coils) in a strong magnetic field, continuously changing the flux linkage and inducing an alternating e.m.f. The mechanical energy of steam or falling water is converted to electrical energy, with Lenz's law ensuring the generator resists the turbine, so more fuel is needed to draw more power.

Example 2. Eddy-current braking. A metal disc moving through a magnetic field has changing flux through it, inducing circulating eddy currents. By Lenz's law these oppose the motion, producing a braking force without contact. Trains and roller coasters use eddy-current brakes for smooth, wear-free stopping.

Try this

Q1. Define magnetic flux and state its unit. [2 marks]

Cue. $\Phi = BA\cos\theta$ , the product of flux density and the area perpendicular to the field; unit weber (Wb).

Q2. A coil of $100$ turns experiences a flux change of $2.0 \times 10^{-3}\ \text{Wb}$ per turn in $0.040\ \text{s}$ . Find the induced e.m.f. [2 marks]

Cue. $\mathcal{E} = \dfrac{\Delta(N\Phi)}{\Delta t} = \dfrac{100 \times 2.0 \times 10^{-3}}{0.040} = 5.0\ \text{V}$ .

Q3. Explain how Lenz's law is a consequence of conservation of energy. [3 marks]

Cue. The induced current opposes the change, so work must be done against this opposition; that work is the source of the electrical energy, and if the current instead aided the change, energy would be created from nothing.

Exam-style practice questions

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

Original5 marksA coil of

200

turns and area

4.0 \times 10^{-3}\ \text{m}^2

is in a magnetic field perpendicular to its plane. The flux density falls uniformly from

0.50\ \text{T}

to zero in

0.020\ \text{s}

. (a) Find the initial flux linkage. (b) Find the magnitude of the induced e.m.f.

Show worked answer →

(a) Flux linkage: $N\Phi = NBA = 200 \times 0.50 \times 4.0 \times 10^{-3} = 0.40\ \text{Wb}$ (weber-turns).

(b) Faraday's law: $\mathcal{E} = \dfrac{\Delta(N\Phi)}{\Delta t} = \dfrac{0.40 - 0}{0.020} = 20\ \text{V}$ .

Markers reward the flux linkage as $NBA$ , recognising the final flux is zero, and the induced e.m.f. as the rate of change of flux linkage with the correct time.

Original4 marks(a) State Lenz's law. (b) A bar magnet is pushed north-pole-first into a coil connected to a galvanometer. Explain, using Lenz's law, the direction of the induced current and how this illustrates conservation of energy.

Show worked answer →

(a) Lenz's law: the direction of an induced current is always such that it opposes the change producing it.

(b) As the north pole approaches, the flux through the coil increases. The induced current flows so that the coil's near face becomes a north pole, repelling the incoming magnet and opposing the increase in flux.

This illustrates conservation of energy: work must be done against the repulsion to push the magnet in, and that work is the source of the electrical energy dissipated in the coil. If the induced current instead attracted the magnet, energy would be created from nothing.

Markers reward Lenz's law as opposition to the change, the coil face becoming a north pole to repel the magnet, and the energy-conservation argument (work done against repulsion supplies the electrical energy).