Eddy Currents and Applications: Brakes, Heating, Meters

Eddy currents are loops of electric current induced inside a solid conductor, such as a metal plate or a transformer core, when the magnetic flux through it changes. They are called eddy currents because they swirl in circles like eddies in water. They are produced by electromagnetic induction, the same effect Faraday discovered, but instead of flowing in a neat wire they circulate inside the bulk of the metal.

Eddy currents matter for two opposite reasons. They waste energy as heat in transformers and motors, so engineers fight them. But the same heating and braking effects are extremely useful in induction cooktops, metal detectors and the smooth brakes of trains. Few phenomena are both a problem and a tool in so many everyday devices.

Key Concepts

• Electromagnetic induction: a changing magnetic flux through a conductor induces an EMF, and hence a current, in it.
• Eddy currents: closed loops of induced current flowing inside a conducting mass rather than in an external circuit.
• Lenz law: the induced currents oppose the change that produces them, which is why they create a braking force on moving conductors.
• Lamination: building a core from thin insulated sheets so the eddy current loops are broken into tiny paths, greatly reducing the loss.
• Skin effect connection: eddy losses rise with the square of frequency and with the square of the thickness of the conductor, which is why thin laminations work so well.

Formulas

Faraday law gives the induced EMF around any loop: ε = − dΦ/dt, where ε is the EMF in volts and Φ is the magnetic flux in webers. Inside a bulk conductor, many such loops exist at once. The eddy current power loss in a laminated core is approximately proportional to P ∝ B² f² t² V / ρ, where B is the peak flux density in tesla, f is the frequency in hertz, t is the lamination thickness in metres, V is the core volume and ρ is the resistivity of the material in ohm-metres. The practical lesson of the formula is that halving the lamination thickness cuts the loss to one quarter.

Worked Example

A transformer core is first built as a solid block. It is then rebuilt with laminations each one fifth as thick as the effective solid path, keeping everything else the same. By what factor does the eddy current loss change?

1. Eddy loss is proportional to t², the square of the thickness.
2. New thickness t₂ = t₁ / 5.
3. Loss ratio = (t₂ / t₁)² = (1/5)² = 1/25.

The laminated core has only one twenty-fifth of the eddy current loss of the solid core. This single trick is a major reason real transformers can reach efficiencies above 95 percent instead of overheating their cores.

Common Misconceptions

• Eddy currents flow only on the surface of metal. Wrong. They circulate throughout the volume wherever the flux is changing, though at high frequencies they concentrate near the surface due to the skin effect.
• Eddy currents are always harmful. Wrong. Induction heating, induction cooking and electromagnetic braking all depend on them. They are harmful only where they appear unwanted, as in transformer cores.
• Laminating a core removes eddy currents completely. Wrong. Lamination reduces them drastically by raising the resistance of the eddy paths, but a small loss always remains.

Real-World Applications

Induction cooktops pass high-frequency alternating current through a coil, eddy currents heat the base of the steel vessel directly, and the glass top stays comparatively cool. Electromagnetic brakes in trains, roller coasters and trucks use eddy currents to slow a metal disc smoothly without friction or wear. Induction furnaces melt metal by heating it with its own eddy currents. Metal detectors at airports and on beaches detect the eddy currents induced in hidden metal objects. Electricity meters traditionally used an aluminium disc whose speed was controlled by eddy current braking, and speedometers in older vehicles used the same principle to move the needle.

Eddy currents are induction acting inside solid metal. Unwanted, they heat transformer cores and are suppressed by lamination; harnessed, they cook food, melt steel, detect metal and brake trains without touching them.