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, concentrated near the surface closest to the magnetic source.

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 precise amount of braking to identify the metal beneath the magnet.

Through empirical regression analysis on a 38-sample dataset of authentic coins and known counterfeits, a mathematical relationship was established between the coin’s physical properties and the pendulum’s resting angle. The formula, with an R² of 0.985, is:

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

Where D_avg is the predicted average degrees of pendulum swing, σ is the electrical conductivity in MS/m, V is the volume in cm³, and S is the number of spacers (distance setting). The constants 488 (machine constant K) and 2.90 (spacer multiplier C) are specific to the EON pendulum’s geometry and magnet strength.

The spacer setting adjusts the vertical distance between the pendulum magnet and the coin surface. Each spacer adds approximately 3 mm of separation. As the magnet moves further from the coin, the magnetic field at the coin surface weakens following an inverse-cube relationship, reducing the eddy current intensity.

Fewer spacers place the magnet closer to the coin, producing stronger eddy currents and more damping (lower swing angle). More spacers produce weaker interaction and higher swing angles. This range allows the device to handle coins from small quarter-ounce pieces to large 10-ounce bars.

The formula captures this relationship through the 2.90^S term. Each additional spacer roughly triples the resting angle, providing a wide dynamic range. Testing at multiple spacer settings provides multiple independent data points for the same coin, increasing confidence in the result.

The formula shows that the resting angle is inversely related to conductivity (σ^0.998 ≈ σ). A material with higher conductivity generates stronger eddy currents, more opposing force, and more damping. The pendulum stops sooner, giving a lower angle reading.

Pure gold (44.0 MS/m) damps very strongly. Tungsten (17.9 MS/m) damps much less. A 22-carat gold alloy like the Krugerrand (9.7 MS/m) damps even less because the copper atoms scatter the conduction electrons. Each material has a unique conductivity fingerprint that the pendulum can detect.

Crucially, conductivity is a bulk property of the material. A thin gold plating over a tungsten core does not change the reading significantly because the eddy currents penetrate into the full volume of the coin. The skin depth at the pendulum’s effective frequency ensures that the interior is probed, not just the surface.

The EON system uses a ±5% tolerance band around the predicted value. A reading within this band is classified as AUTHENTIC; outside it, ANOMALY DETECTED. The tolerance accounts for normal manufacturing variations between minting years, minor temperature effects on conductivity, and the inherent precision of the mechanical instrument.

The 5% tolerance is tight enough to catch tungsten substitution (which produces deviations of 30–60%) while being wide enough to avoid false positives from legitimate coins. In testing across hundreds of authentic samples, the false positive rate is effectively zero, and the false negative rate for tungsten-core fakes is also zero.

For maximum confidence, the EON multi-factor approach combines the eddy current result with dimensional, weight, and acoustic data. Each independent test that passes increases the overall authentication confidence, quantified by the EON Authentication Score.