Eddy Currents
When a solid conductor moves through a magnetic field — or sits inside a changing magnetic field — Faraday's law demands that an EMF be induced. Unlike a wire coil where that EMF drives current around a single loop, a bulk conductor has countless possible current paths through its interior. The result is a swirling pattern of induced currents called eddy currents (also called Foucault currents), circulating in closed loops entirely within the conducting material, much like eddies swirling in a river behind a rock. Eddy currents obey the same physics as any induced current: they flow in directions that, by Lenz's law, oppose the change in magnetic flux that created them. This opposition has two important consequences. First, a force is exerted on the conductor that resists relative motion — a braking effect exploited in everything from the regenerative braking of trains to the smooth deceleration of fairground rides. Second, energy is dissipated as heat inside the conductor (Joule heating, P = I²R), which is a loss in electric motors and transformers but a valuable feature in induction cooktops and induction furnaces. Understanding eddy currents requires connecting three big ideas from electromagnetism: Faraday's law of induction, Lenz's law, and Ohm's law applied to a three-dimensional conductor. Once you grasp how these principles combine, you can both predict where eddy currents arise and engineer solutions — such as laminating transformer cores or cutting slots into brake discs — to either minimise or maximise their effects depending on the application.
- Changing Magnetic Flux Through a Conductor
- Currents Circulate in Closed Paths
- Lenz's Law Determines Direction
- Energy Dissipation as Heat
- Reducing Eddy Currents with Lamination
Changing Magnetic Flux Through a Conductor
Faraday's law states that any change in magnetic flux Φ_B through a surface bounded by a conducting loop induces an EMF equal to −dΦ_B/dt. In a solid conductor, imagine slicing it into thousands of tiny loop-shaped cross-sections. Each tiny loop experiences a changing flux when the external field changes (or when the conductor moves), so each one has an EMF induced in it.
Currents Circulate in Closed Paths
Because the conductor is a continuous medium, these EMFs drive currents that close on themselves — they have no external circuit to travel through. The current paths are determined by minimising resistance, which in a uniform conductor means roughly circular loops centred on the axis of the changing flux. The pattern resembles water whirlpools, hence 'eddy' currents.
Lenz's Law Determines Direction
Lenz's law tells us each eddy-current loop generates its own magnetic field that opposes the change causing it. If the applied field is increasing into a conductor, the eddy currents circulate counter-clockwise (viewed from the field source) to produce a field opposing the increase. This is why a falling magnet descends slowly through a copper tube: the eddy currents create an upward force on the magnet.
Energy Dissipation as Heat
Eddy currents are real currents in a resistive material, so they dissipate power P = I²R. The induced EMF is proportional to the rate of flux change (∝ dB/dt or ∝ velocity v), so the eddy-current magnitude scales with how rapidly the field changes. Power dissipation goes as the square of the EMF, meaning higher frequencies or faster motion cause disproportionately larger losses — a key reason why transformer cores must be laminated at power-line frequencies.
Reducing Eddy Currents with Lamination
To reduce unwanted eddy currents, engineers cut the conductor into thin insulated sheets (laminations) stacked parallel to the magnetic flux. Each sheet is much thinner than the eddy-current loop would naturally be, so the resistance of each small loop is high and the current — and thus the I²R loss — is dramatically reduced. The thinner the laminations, the lower the losses. Transformer cores, electric-motor stators, and electromagnet poles are all laminated for this reason.
The Key Equation
- \mathcal{E} — Induced EMF (V): The electromotive force that drives eddy currents within the conductor.
- \Phi_B — Magnetic flux (Wb (Weber)): The total magnetic field passing through a given area; Φ_B = B·A·cosθ.
- B_0 — Peak magnetic field amplitude (T (Tesla)): The maximum value of the alternating or varying magnetic field.
- \omega — Angular frequency (rad s⁻¹): How rapidly the magnetic field oscillates; ω = 2πf.
- d — Lamination thickness (m): The thickness of each conducting sheet; thinner sheets mean less eddy-current loss.
- \rho — Electrical resistivity (Ω·m): A material property measuring how strongly it resists current flow; higher ρ means lower eddy currents.
Worked Example
Problem. A solid copper disc of radius 0.10 m spins at 50 rev/s inside a region where a uniform magnetic field of 0.30 T points perpendicular to the disc face. Estimate the order of magnitude of the braking power due to eddy currents, given that the effective resistance of an eddy-current loop of radius r ≈ 0.05 m in copper (resistivity ρ = 1.7 × 10⁻⁸ Ω·m, thickness t = 0.005 m) is approximately R_loop = ρ·(2πr)/(t·w) where w = 0.01 m is the effective loop width.
Answer. Approximately 5 kW dissipated per representative eddy-current loop, demonstrating the enormous braking power of eddy currents in solid conductors.
Origins · 1 minLéon Foucault and how this was discovered
Jean Bernard Léon Foucault first demonstrated eddy currents experimentally in 1851, showing that a copper disc rotating between the poles of an electromagnet experienced a strong retarding force proportional to the field strength. He correctly attributed this to induced currents circulating within the disc — now called Foucault currents in his honour. He is also famous for the Foucault pendulum, which demonstrated Earth's rotation. Foucault trained as a physician but never practised medicine; he turned to experimental physics after finding surgery too distressing — and went on to measure the speed of light with unprecedented accuracy using a rotating mirror.
Related Concepts
- Faraday's Law of Induction — Eddy currents are a direct consequence of Faraday's law — the changing magnetic flux induces the EMF that drives them.
- Lenz's Law — Lenz's law determines the direction of eddy currents and explains the braking force they exert on moving conductors.
- Transformers — Transformer cores are laminated specifically to minimise eddy-current losses, making this concept essential for understanding transformer design and efficiency.
- Joule Heating — The energy dissipated by eddy currents is Joule heating (P = I²R), connecting electromagnetic induction to thermal energy conversion.