The Science Behind Eddy Current Testing

Eddy current testing is rooted in Faraday’s law of electromagnetic induction, discovered in 1831. When a magnetic field near a conductor changes — either because the magnet is moving or the conductor is moving — an electromotive force (EMF) is induced in the conductor. This EMF drives circulating loops of current within the metal, known as eddy currents.

The name “eddy current” comes from their resemblance to the eddies that form in flowing water when it passes an obstruction. These currents flow in closed loops within the conductor. At high frequencies they crowd near the surface; at the slow speed of a pendulum they fill the whole thickness of a coin.

The magnitude of the induced eddy currents depends on three factors: the strength and rate of change of the magnetic field, the electrical conductivity of the metal, and the volume of metal available for current flow. Higher conductivity and larger volume both produce stronger eddy currents.

Lenz’s law states that the eddy currents will always flow in a direction that opposes the change that created them. When a magnet approaches a conductor, the eddy currents create a magnetic field that repels the approaching magnet. When the magnet recedes, the eddy currents create a field that attracts it, trying to maintain the original magnetic flux.

The practical effect is electromagnetic braking. A magnet swinging freely in air will oscillate for many cycles before stopping. But when the same magnet swings past a conductive metal, the opposing field created by the eddy currents extracts kinetic energy from the magnet, converting it to heat in the conductor. The pendulum comes to rest much more quickly.

This is the same principle used in electromagnetic braking on high-speed trains, rollercoasters, and industrial machinery. The EON pendulum applies it at a smaller scale, using the amount of braking to measure the metal beneath the magnet.

For a coin under a swinging magnet, the braking can be worked out from first principles. The force is proportional to the magnet’s speed, and its strength is the coin’s electrical conductivity (σ) times its thickness (t) times a factor set by the field geometry: the magnet’s strength and shape, the gap, and the coin’s diameter. The dependence on conductivity is exact, not fitted.

The coin’s edge matters. The currents cannot flow out through the rim, and a uniform field drives no current at all; only the change in field across the coin does. So a small coin under the flat centre of a large magnet is braked far less than a simple “infinite sheet” rule suggests. In the fitted model, leaving the edge out doubled the error.

At the Coin Cradle’s speeds, each pass over the coin is a half-cycle at about 40 Hz, where the skin depth in gold or silver is 10–12 mm. The coins are 1–3.3 mm thick, so the test reads the whole thickness of the coin, not only its surface. That is why a gold plating does not hide a tungsten core.

The pendulum is released from 50°, which gives it a fixed amount of energy (about 36–37 mJ). Each pass over the coin removes a share of it, so the swing dies away over several passes. The more strongly the coin brakes, the sooner it stops.

The dial is ratcheted and cumulative: it advances only while the pendulum swings outward on the side away from the release, and it adds up those strokes. That the dial counts only outward swings is known from the device; that it counts only those on the far side is inferred from the readings. The reading is therefore a total travel, and it falls roughly as one over the coin’s conductivity.

Built from the measured hardware, following the pendulum’s exact motion, and with nothing fitted, this model predicts the 38 readings on Coin Cradle #0001 to 12.4% rms. The full derivation is in the article “The Physics of the Coin Cradle”, with the technical report.

The spacers are 3 mm gauge blocks. With S spacers the magnet face sits 3S mm above the deck; the spacers are then removed. The gap between the magnet and a coin of thickness t is 3S − t.

More spacers mean a larger gap, a weaker field at the coin, less braking and a higher reading. In the Cradle #0001 readings each extra spacer raised the reading by a factor of 2.4–3.1. The field does not follow a simple power of the distance at these gaps, so the model computes it from the magnet’s shape rather than assuming one.

Fine gold conducts at about 44.7 MS/m and tungsten at about 18.9 MS/m. No cheap metal is both denser and more conductive than tungsten, so a gold-plated tungsten fake of a fine-gold coin brakes much less: in the model it reads about 2.4 times a genuine coin.

22-carat coins are different. The copper or silver in the alloy lowers the conductivity to about 9.7–11.1 MS/m, below tungsten’s. An engineered stack of tantalum and tungsten of the same size and weight can read within about 10% of a genuine Krugerrand, and adding rhenium can match it exactly. Testing both faces of the coin catches stacks that are not symmetric, and the ping test and weight checks remain part of the workflow.

These separations are modelled from handbook values. No fake has yet been measured on the device.

Before the first-principles model, the readings were described by a power law fitted to 38 readings on Coin Cradle #0001:

D_avg = 488 × 2.90^S / (σ^0.998 × V^1.431)

The constants 488 and 2.90 belong to that one unit. The σ^0.998 is what the physics requires. The exponent 1.431 on the volume is not a physical law: it stands in for three effects, the coin’s thickness, the thicker coin sitting closer to the magnet, and the coin’s diameter through the edge.

This four-number fit reaches 13.9% out of sample. The physics model fits nothing and reaches 12.4% on the 38 readings, and what it gets wrong points to something specific to measure.

A ±5% band applies only when the reading is compared with a genuine reference coin of the same type, measured on the same unit. Against the formula alone the error is about 15–21%, so a formula-only comparison cannot confirm a coin. On this site’s multi-factor score and certificates, an eddy-current pass needs a reference coin; a formula-only reading is shown as inconclusive.

For the most confidence, combine the eddy-current result with dimensions, weight and the acoustic ping. Each independent test measures a different property of the metal.