About Eddy Currents
Eddy currents are loops of electric current induced within a conductor when it is exposed to a changing magnetic flux, as described by Faraday's law of induction. By Lenz's law, these circulating currents generate their own magnetic field that opposes the change causing them, producing a braking force. This phenomenon is exploited in magnetic braking systems on roller coasters and high-speed trains, induction hobs, and metal detectors.
This simulation models a permanent magnet falling through a conducting tube. You can vary the tube's electrical conductivity and wall thickness to observe how the induced drag force changes and how much the magnet's fall is slowed compared to free fall.
Frequently Asked Questions
Why does a magnet fall slowly through a copper pipe?
As the magnet moves, its changing flux induces eddy currents in the pipe wall. By Lenz's law these currents create a magnetic field opposing the motion, resulting in an upward braking force. The magnet reaches a terminal velocity where this drag exactly balances gravity, which can be many times slower than free fall.
How does wall thickness affect the braking force?
For a thin-walled tube the braking force is approximately proportional to wall thickness squared and to the conductivity of the material. Doubling the wall thickness roughly quadruples the induced drag at low speeds, because more conductive material is available to carry eddy currents over a wider cross-section.
What is terminal velocity in this context?
Terminal velocity is reached when the electromagnetic braking force equals the gravitational force on the magnet, so its acceleration becomes zero. For a strong neodymium magnet in a thick copper tube, terminal velocity can be as low as a few centimetres per second, compared with the metres-per-second it would reach in free fall.
Which materials produce the strongest eddy-current braking?
Materials with high electrical conductivity produce the strongest eddy currents. Copper (58 MS/m) and aluminium (37 MS/m) are far better than steel (about 6 MS/m), which is why eddy-current brakes on trains use aluminium or copper fins rather than iron ones. However, ferromagnetic materials also concentrate magnetic flux, adding a separate contribution.
Are eddy currents always undesirable?
No. They are deliberately exploited in induction hobs (eddy currents in the pan base generate heat), magnetic braking systems, eddy-current dampers in seismometers, and electromagnetic flow meters. They are undesirable in transformer cores, where they cause power loss; laminating the core breaks the eddy-current paths and greatly reduces this loss.
How does frequency of flux change affect eddy currents?
Eddy-current power loss scales with frequency squared (P ∝ f²B²), which is why high-frequency transformers require very fine laminations or ferrite cores. The skin effect also confines eddy currents to a thin surface layer whose depth decreases as 1/√f, concentrating losses near the surface at high frequencies.
What is the skin depth and why does it matter?
Skin depth (δ) is the depth at which eddy currents fall to 1/e of their surface value: δ = √(2ρ/ωμ), where ρ is resistivity, ω is angular frequency, and μ is permeability. For copper at 50 Hz, δ ≈ 9 mm; at 1 MHz, δ ≈ 0.07 mm. This limits how effectively thick conductors can use their full cross-section at high frequencies.
Can eddy currents be used for non-destructive testing?
Yes. Eddy-current testing (ECT) is a standard non-destructive evaluation technique. A coil carrying alternating current induces eddy currents in a nearby conductor; cracks or voids alter the current patterns, changing the coil's impedance. ECT can detect surface cracks as small as 0.5 mm and is widely used to inspect aircraft fuselage panels and heat-exchanger tubes.
How do eddy currents relate to magnetic levitation?
If a conductor moves rapidly past magnets, the induced eddy currents can produce a repulsive lift force as well as drag. This principle underlies the electrodynamic (Halbach-array) suspension used in some maglev trains, such as Japan's SCMaglev, which achieves speeds over 600 km/h. The lift-to-drag ratio improves with speed, making it efficient only above about 100 km/h.
What energy is dissipated by eddy currents?
The kinetic energy lost by the falling magnet is converted to heat in the tube walls via Joule heating (P = I²R). In a typical demonstration with a neodymium magnet and copper pipe, the power dissipation is only milliwatts, but in industrial induction heating systems eddy currents can deliver tens of kilowatts to a workpiece within seconds.
How are eddy currents minimised in transformer cores?
Transformer cores are built from thin silicon-steel laminations (typically 0.3–0.5 mm thick) coated with insulating varnish. Each lamination is too thin for large eddy-current loops to form, so the total eddy-current loss is reduced approximately in proportion to the square of lamination thickness. High-frequency transformers use powdered-iron or ferrite cores instead.