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How does a changing magnetic flux induce an EMF, and what sets its size and direction?

Magnetic flux and flux linkage, Faraday's law, Lenz's law, and applications in generators and transformers.

A focused answer to WJEC A-Level Physics Unit 4 electromagnetic induction, covering magnetic flux and flux linkage, Faraday's law for the induced EMF, Lenz's law for its direction, and applications in generators and transformers.

Generated by Claude Opus 4.811 min answer

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

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  1. What this dot point is asking
  2. The answer
  3. Examples in context
  4. Try this

What this dot point is asking

WJEC wants you to define magnetic flux and flux linkage, state and use Faraday's law for the induced EMF, apply Lenz's law for its direction, and relate both to generators and transformers. Induction is the principle behind almost all electricity generation, so this dot point links a compact pair of laws to the technology that powers the grid.

The answer

Flux and flux linkage

When the field is perpendicular to the coil's plane (the normal aligned with the field), cos⁡θ=1\cos\theta = 1 and the flux is at its maximum BABA.

Faraday's law

Faraday's law states that the magnitude of the induced EMF equals the rate of change of flux linkage. A faster change of flux (a stronger field, larger area or quicker movement) induces a larger EMF.

Lenz's law

Generators and transformers

A generator rotates a coil in a magnetic field, continuously changing the flux linkage and inducing an alternating EMF. A transformer uses an alternating current in a primary coil to create a changing flux in an iron core, which links a secondary coil and induces an EMF, changing the voltage in the turns ratio VsVp=NsNp\dfrac{V_s}{V_p} = \dfrac{N_s}{N_p}.

Examples in context

Example 1. A bicycle dynamo. A small magnet spins past a coil as the wheel turns, so the flux linkage through the coil rises and falls continuously, inducing an alternating EMF that powers the lamp. Pedalling faster spins the magnet faster, increasing dΦ/dtd\Phi/dt and so the EMF and brightness. You also feel extra resistance because, by Lenz's law, the induced current opposes the motion.

Example 2. Induction cooktops. An alternating current in a coil beneath the hob creates a rapidly changing magnetic flux. This induces eddy currents directly in the metal pan, which heat it by their resistance. No flux change means no heating, which is why glass and ceramic dishes stay cool. The whole device is Faraday's law transferring energy without contact.

Try this

Q1. A coil of 200200 turns has the flux through it change from 00 to 4.0×10−3 Wb4.0\times10^{-3}\,\text{Wb} in 0.020 s0.020\,\text{s}. Find the average induced EMF. [3 marks]

  • Cue. ε=NΔΦΔt=200×4.0×10−30.020=40 V\varepsilon = N\frac{\Delta\Phi}{\Delta t} = 200\times\frac{4.0\times10^{-3}}{0.020} = 40\,\text{V}.

Q2. State Lenz's law and the conservation principle it expresses. [2 marks]

  • Cue. The induced current opposes the change producing it; conservation of energy.

Exam-style practice questions

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

WJEC 20195 marksA square coil of 150150 turns and side 5.0 cm5.0\,\text{cm} lies with its plane perpendicular to a magnetic field. The field increases uniformly from 0.20 T0.20\,\text{T} to 0.80 T0.80\,\text{T} in 0.30 s0.30\,\text{s}. Calculate the magnitude of the induced EMF, and state the direction of the induced current relative to the increasing field.
Show worked answer →

Find the area, then the change of flux, then apply Faraday's law.

Area: A=(0.050)2=2.5×10−3 m2A = (0.050)^2 = 2.5 \times 10^{-3}\,\text{m}^2.

Change of flux: ΔΦ=A ΔB=2.5×10−3×(0.80−0.20)=1.5×10−3 Wb\Delta\Phi = A\,\Delta B = 2.5 \times 10^{-3} \times (0.80 - 0.20) = 1.5 \times 10^{-3}\,\text{Wb}.

Induced EMF: ε=NΔΦΔt=150×1.5×10−30.30=0.75 V\varepsilon = N\dfrac{\Delta\Phi}{\Delta t} = 150 \times \dfrac{1.5 \times 10^{-3}}{0.30} = 0.75\,\text{V}.

By Lenz's law the induced current flows so as to oppose the increase, creating a magnetic field opposite to the increasing applied field inside the coil. Markers reward the flux change, the EMF from Faraday's law, and the opposing direction.

WJEC 20214 marksExplain, using Faraday's and Lenz's laws, how an alternating EMF is generated when a coil is rotated at constant speed in a uniform magnetic field.
Show worked answer →

As the coil rotates, the flux linkage NΦ=NBAcos⁡θN\Phi = NBA\cos\theta varies with the angle θ\theta between the coil's normal and the field. By Faraday's law the induced EMF equals the rate of change of flux linkage, so it depends on how fast the flux is changing.

The flux change is fastest when the coil's plane is parallel to the field (the coil is cutting field lines most rapidly), giving the peak EMF, and momentarily zero when the plane is perpendicular to the field. Over one rotation the EMF therefore varies sinusoidally, reversing direction every half turn, which is an alternating EMF.

Lenz's law fixes the direction at each instant so the induced current opposes the change in flux. Markers reward linking the varying flux linkage to a sinusoidal EMF and identifying the peak and zero positions.

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