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How does a changing magnetic field generate an electromotive force?

Magnetic flux and flux linkage, Faraday's law and Lenz's law, the emf induced in a moving conductor, and the emf induced in a rotating coil.

A focused answer to AQA A-Level Physics 3.7.5.4, covering magnetic flux and flux linkage, Faraday's law and Lenz's law, the emf induced in a conductor moving through a field, and the emf produced by a rotating coil.

Generated by Claude Opus 4.810 min answer

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  1. What this dot point is asking
  2. Magnetic flux and flux linkage
  3. Faraday's law and Lenz's law
  4. EMF in a moving conductor
  5. EMF from a rotating coil
  6. Try this

What this dot point is asking

AQA specification point 3.7.5.4 wants you to define magnetic flux and flux linkage, state and use Faraday's law and Lenz's law, calculate the EMF induced in a moving conductor, and find the EMF produced by a coil rotating in a magnetic field.

Magnetic flux and flux linkage

Flux is a measure of how many field lines thread through the area. Flux linkage accounts for the fact that each of the NN turns is threaded by the same flux, so the effect on the induced EMF is multiplied by NN. The weber is equivalent to a tesla square metre, or a volt second.

Faraday's law and Lenz's law

Faraday's law states that the magnitude of the induced EMF is equal to the rate of change of flux linkage. There are three ways to change the flux linkage and so induce an EMF: change the flux density BB, change the area AA, or change the angle θ\theta between the field and the coil.

Lenz's law, shown by the minus sign, states that the induced current flows in a direction such that its effect opposes the change producing it. This is a direct consequence of conservation of energy: if the induced current aided the change, it would amplify itself and create energy from nothing.

EMF in a moving conductor

A straight conductor of length ll moving at speed vv perpendicular to a field BB sweeps out area at a rate lvlv, so it cuts flux and induces an EMF:

This follows from Faraday's law: in time Δt\Delta t the conductor sweeps area ΔA=l vΔt\Delta A = l \, v \Delta t, so the flux cut is ΔΦ=Bl vΔt\Delta\Phi = B l \, v \Delta t, and dividing by Δt\Delta t gives BlvBlv.

EMF from a rotating coil

The EMF is greatest when the coil's plane is parallel to the field (the flux is changing fastest) and zero when the plane is perpendicular to the field (the flux is momentarily at its maximum and not changing). Increasing the rotation speed raises both the peak EMF and the frequency.

Try this

Q1. State Faraday's law of electromagnetic induction. [1 mark]

  • Cue. The induced EMF is equal to the rate of change of flux linkage.

Q2. A wire of length 0.25 m0.25 \text{ m} moves at 6.0 m s−16.0 \text{ m s}^{-1} perpendicular to a 0.40 T0.40 \text{ T} field. Calculate the induced EMF. [2 marks]

  • Cue. ε=Blv=0.40×0.25×6.0=0.60 V\varepsilon = Blv = 0.40 \times 0.25 \times 6.0 = 0.60 \text{ V}.

Q3. State the conservation law that underlies Lenz's law. [1 mark]

  • Cue. Conservation of energy.

Exam-style practice questions

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

AQA 20184 marksA coil of 150150 turns and cross-sectional area 2.5×10−3 m22.5 \times 10^{-3} \text{ m}^2 lies with its plane perpendicular to a magnetic field. The flux density falls uniformly from 0.80 T0.80 \text{ T} to zero in 40 ms40 \text{ ms}. Calculate the average EMF induced in the coil.
Show worked answer →

The flux linkage changes from NΦ=NBAN\Phi = NBA to zero. Initial flux linkage =150×0.80×2.5×10−3=0.30 Wb turns= 150 \times 0.80 \times 2.5 \times 10^{-3} = 0.30 \text{ Wb turns}.

Faraday's law gives the magnitude of the average EMF as ε=NΔΦΔt=Δ(NΦ)Δt=0.3040×10−3\varepsilon = N\dfrac{\Delta\Phi}{\Delta t} = \dfrac{\Delta(N\Phi)}{\Delta t} = \dfrac{0.30}{40 \times 10^{-3}}.

ε=0.300.040=7.5 V\varepsilon = \dfrac{0.30}{0.040} = 7.5 \text{ V}.

Markers reward calculating the change in flux linkage, converting the time to seconds, and dividing to get the EMF.

AQA 20224 marksA bar magnet is dropped north pole first through a horizontal copper ring. Use Lenz's law to explain the direction of the induced current as the magnet approaches, and state what this implies about the force on the magnet.
Show worked answer →

As the magnet approaches, the downward flux through the ring increases. By Lenz's law the induced current opposes this change, so it flows in a direction that makes the top face of the ring a north pole, repelling the approaching north pole of the magnet.

This means the induced current creates a force on the magnet that opposes its motion (upward, decelerating the fall). The magnet therefore falls more slowly than in free fall.

This opposition is required by conservation of energy: the work done against the retarding force supplies the electrical energy dissipated in the ring's resistance.

Markers reward identifying the increasing flux, applying Lenz's law to get the opposing pole, the retarding force, and linking it to conservation of energy.

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