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Electromagnetic induction

Calculate magnetic flux and flux linkage, use Faraday's and Lenz's laws to find induced e.m.f.s, and explain moving rods, generators, eddy currents and ideal transformers.

  • GCE A-Level H2 Physics 2027
  • 12 lessons
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Before you begin

A changing magnetic flux through a circuit induces an e.m.f. in it. The lessons start by measuring how much field passes through a coil, as magnetic flux and flux linkage, then use Faraday’s law for the size of the induced e.m.f. and Lenz’s law for its direction. They apply these to a rod moving through a field, a rotating generator coil, eddy currents in bulk metal and the ideal transformer.

Be comfortable with: electromagnetic forces, because Fleming’s left-hand rule and the grip rule are used throughout.

Learning goals
  • Use magnetic flux and flux-linkage relationships.
  • Apply Faraday's and Lenz's laws to induced e.m.f. and direction.
  • Explain simple applications of electromagnetic induction, including motional e.m.f. and eddy currents.
  • Explain simple iron-core transformer operation and apply ideal transformer ratios.
Syllabus statements covered
  • define magnetic flux as the product of magnetic flux density and the cross-sectional area perpendicular to the direction of the magnetic flux density
  • show an understanding of and use the concept of magnetic flux linkage
  • recall and use Φ = BA and NΦ = NBA to solve problems, where N is the number of turns
  • infer from appropriate experiments on electromagnetic induction: (i) that a changing magnetic flux can induce an e.m.f.; (ii) that the direction of the induced e.m.f. opposes the change producing it; (iii) the factors affecting the magnitude of the induced e.m.f.
  • recall and solve problems using Faraday’s law of electromagnetic induction and Lenz’s law
  • explain simple applications of electromagnetic induction
  • show an understanding of the principle of operation of a simple iron-core transformer and recall and solve problems using Nₛ/Nₚ = Vₛ/Vₚ = Iₚ/Iₛ for an ideal transformer

Lessons

Work through them in order.

Core lessons

  1. Magnetic flux and flux linkageCalculate magnetic flux and flux linkage for a coil at any orientation to the field.
  2. Induction experiments and Faraday's lawInfer the laws of induction from magnet-and-coil experiments, and use Faraday's law to find the e.m.f. from changing flux linkage.
  3. Lenz's law: direction and energyPredict induced-current direction from a changing flux and account for the energy transfer.
  4. Motional e.m.f. and energy in a moving rodExplain and calculate the e.m.f. induced in a moving rod, and trace the energy from the push to the heating.
  5. Rotating-coil generatorsConnect coil orientation to alternating flux linkage and e.m.f., and explain the mechanical energy input.
  6. Eddy-current braking and heatingExplain currents within a bulk conductor, account for braking energy and distinguish useful currents from core losses.
  7. Simple iron-core ideal transformersExplain how an ideal transformer works and use the turns ratio to find voltages and currents.

Further explanations and worked examples

  1. Power distributionExplain why power is transmitted at high voltage and calculate transmission current, I²R loss and efficiency.Supporting
  2. Induction stoveExplain eddy-current heating, cookware compatibility and the limits of a simple heating model.Supporting
  3. Electric guitar pickups: turning vibration into a signalExplain a magnetic pickup and relate small string motion to the frequency and amplitude of its induced signal.Supporting
  4. Movement sensors: from motion to an induction signalExplain how a movement sensor induces an e.m.f. that grows with the rate of change of flux linkage.Supporting
  5. Residual-current protection: detecting a leakage pathExplain residual-current sensing with a magnetic core and identify what its protective function can detect.Supporting

Beyond the syllabus

  1. Transformer losses and imperfect couplingDistinguish winding and core heating from imperfect coupling, and explain how design reduces losses.Beyond the syllabus

Practise and check

Recommended nextElectromagnetic induction topic check

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Topic reference

Quick reference

IdeaRelationNotes
magnetic fluxΦ = BAA perpendicular to the field; BA cos θ with θ to the normal
flux linkageNΦN turns each linking flux Φ
Faraday’s lawE = -d(NΦ)/dtthe minus sign is Lenz’s law
moving rodE = Blvrod, velocity and field at right angles
rotating coilE = NBAω sin ω tpeak NBAω
ideal transformerNₛ/Nₚ = Vₛ/Vₚ = Iₚ/Iₛalternating input; power in = power out

Core knowledge to remember

  • Magnetic flux is the product of the magnetic flux density and the cross-sectional area perpendicular to the direction of the magnetic flux density.
  • A changing magnetic flux linkage induces an e.m.f. A steady flux linkage, however large, induces none.
  • Faraday’s law: the induced e.m.f. is proportional to the rate of change of magnetic flux linkage.
  • Lenz’s law: the direction of the induced e.m.f. is such that it opposes the change producing it. This follows from the conservation of energy.
  • Eddy currents are induced currents circulating inside bulk conductors; laminated transformer cores reduce them.
  • In an ideal transformer, the same changing flux links every turn of both coils, so the voltages are in the ratio of the turns.

Solving an induction problem

  1. Identify what is changing: the field, the area facing it or the orientation.
  2. Find the flux linkage at the start and end, or its rate of change, with areas in m² and times in seconds.
  3. Use Faraday’s law for the size of the e.m.f.
  4. Use Lenz’s law for the direction: decide whether the flux is increasing or decreasing, choose the induced field that opposes the change, then apply the grip rule, saying which side you are viewing from.
  5. Check the circuit and the energy: an open circuit has an e.m.f. but no current, and any electrical energy delivered must come from work done or energy lost elsewhere.

Common mistakes

  1. Using the angle between the field and the plane of the coil in BA cos θ.
  2. Reading the e.m.f. from the height of a flux linkage graph instead of its gradient.
  3. Saying the induced field opposes the flux; it opposes the change in flux.
  4. Putting the peak e.m.f. of a generator where the flux linkage peaks.
  5. Expecting a transformer to work on steady D.C., or to increase the power.