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7 Electromagnetic induction: eddy currents & transformers

Checked against 2022-2025: eddy currents (2024) and transformers (2023) each appear at Merit-Excellence — real material, not an occasional extra.

Faraday’s law: EMF from a changing flux

Magnetic flux \Phi=BA Weber (Wb). B is the flux density (T, or Wb m⁻²) and A the area the field passes through, when the coil faces the field square on. Induced EMF \varepsilon=-N\frac{\Delta\Phi}{\Delta t} N turns, each with the same EMF, in series, so they add. The minus sign is Lenz’s law: the EMF opposes the change in flux.

Eddy currents

  • A CHANGING magnetic flux through the BULK of a conductor (not just a coil) induces circulating currents inside it — eddy currents.
  • By Lenz’s law, the eddy currents create their own magnetic field that OPPOSES the change producing them.
  • The opposing field exerts a retarding force on whatever is causing the change — e.g. a magnet falling through a conducting pipe is slowed, because its motion is the "change" the eddy currents oppose.
Worked example A magnet falling through a copper pipe A strong magnet is dropped down a vertical copper pipe. Explain why it falls much more slowly than it would in free fall, using the concept of eddy currents. As the magnet falls, the magnetic flux through any cross-section of the pipe near it is CHANGING. By Faraday’s law, this changing flux induces eddy currents circulating in the copper. By Lenz’s law, these currents create a magnetic field that OPPOSES the change — which means opposing the magnet’s motion. The opposing field exerts an upward retarding force on the magnet, slowing its fall. ✓ The induced eddy currents create a magnetic field that opposes the falling magnet’s motion, producing a retarding force — copper is not magnetic itself, so without a CHANGING flux there would be no effect at all.

Transformers

  • Two coils — primary (Np turns) and secondary (Ns turns) — wound on a shared IRON CORE.
  • An alternating current in the primary creates a CHANGING flux; the iron core guides that flux through the secondary coil, inducing an EMF there by mutual induction.
  • AC is essential — a STEADY DC current produces a constant flux, which induces nothing in the secondary. Only a CHANGING flux induces an EMF.
  • An iron core is used because it channels (concentrates) the magnetic flux between the two coils far more effectively than air, so almost all the flux from the primary reaches the secondary.

Transformer equation

Turns ratio \frac{V_s}{V_p}=\frac{N_s}{N_p} More turns on the secondary steps voltage UP; fewer steps it DOWN. Worked example Why raise the voltage for transmission A power station delivers 100 kW to a town. Compare the power LOST in the transmission line (resistance 2.0 Ω) if it is sent (a) at 240 V, versus (b) at 24 000 V (using step-up and step-down transformers at each end). P = VI, so I = P/V. (a) At 240 V: I = 100 000/240 = 417 A. Power lost = I²R = 417² × 2.0 ≈ 3.5×10⁵ W — far MORE than the 100 kW being delivered, which is why this is not done in practice. (b) At 24 000 V: I = 100 000/24 000 = 4.17 A. Power lost = I²R = 4.17² × 2.0 ≈ 35 W. ✓ Raising the transmission voltage by 100× drops the current by 100×, and since power loss depends on I², the loss falls by 100² = 10 000×. High-voltage transmission is only practical because transformers can step voltage up for the line and back down for consumers.

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