Eddy Current — CAE Glossary

In short, eddy current is a closed-loop current induced in a conductor when placed in a time-varying magnetic field. Based on Faraday's law, when there is a time-varying magnetic flux $\partial \mathbf{B}/\partial t$, an electromotive force is induced in a direction that opposes this change, causing a looping current. Unlike ordinary circuit current created by wiring, eddy current flows in a swirling vortex pattern through the bulk of a conductor—hence the name "eddy" current.

That's correct. With a completely constant DC magnetic field, eddy current is zero. However, if the conductor itself moves through the magnetic field, the situation is different. From the conductor's perspective, the magnetic flux is changing with time, so eddy currents will flow. For example, when you move a copper plate near a magnet, you feel resistance—that's the effect of eddy current.

Eddy current flows through the electrical resistance of the conductor, so Joule heating occurs ($P = \int \sigma^{-1} |\mathbf{J}|^2 \, dV$). This is called eddy current loss. In transformer cores and motor cores, it becomes a major cause of efficiency loss. The standard design approach is to laminate thin silicon steel sheets to break the eddy current loops into smaller ones.

Yes, they're directly related. When alternating current flows through a conductor, the time-varying magnetic field created by that current induces eddy currents within the conductor. These induced eddy currents flow in a direction that opposes the original current in the center of the conductor, causing current density to concentrate near the surface. This is the skin effect. The skin depth $\delta$ is calculated from:

For copper ($\sigma \approx 5.8 \times 10^7$ S/m, $\mu \approx \mu_0$) at commercial frequency 50 Hz, $\delta \approx 9.3$ mm. So for thin copper wire a few millimeters in diameter, the effect is small. However, as frequency increases, skin depth decreases rapidly. At 1 MHz, $\delta \approx 0.066$ mm, or 66 μm. This is why thick solid conductors become inefficient at high frequencies—that's why Litz wire (stranded conductor) is used, bundling fine wires together to increase the effective surface area.

Exactly—that's induction heating (IH). A coil is supplied with high-frequency current to create a strong alternating magnetic field, which induces large eddy currents in the metal workpiece, heating it by Joule dissipation. Since it's non-contact and by exploiting skin effect can selectively heat the surface, it's widely used for hardening, brazing, zone refining of semiconductors, and more.

Yes, exactly the same. The cooktop generates an alternating magnetic field at 20–90 kHz, which induces eddy currents in the metal pot to heat it. That's why aluminum and ceramic cookware don't work—they don't support eddy currents well. Iron and stainless steel, with high conductivity and permeability, are ideal. In CAE, we often run coupled electromagnetic-thermal analysis to predict temperature distribution in induction heating processes.

A probe coil carrying alternating current is brought close to the test specimen, inducing eddy currents near the surface. If a crack or flaw exists, the eddy current path is disrupted and must detour around the defect, changing the current pattern. This changes the coil's impedance (both resistance and reactance components). The impedance change is plotted on an impedance plane to detect defects.

Detection depth is limited by skin depth. Since eddy currents concentrate near the surface, we can typically detect flaws up to about 3 times the skin depth. Lower frequency gives larger skin depth and deeper penetration, but reduces resolution. In practice, multi-frequency ECT is used—combining multiple frequencies for better detection. It's used in critical applications like fatigue crack inspection around aircraft rivets and corrosion detection in nuclear steam generator tubes.

Yes. When a conducting disk or rail moves through a magnetic field, eddy currents are induced, and Lorentz force $\mathbf{F} = \mathbf{J} \times \mathbf{B}$ acts to oppose the motion. Since there's no mechanical contact, there's no wear. The braking force varies with speed. Bullet trains use it as a supplementary disk brake; it's also used on roller coasters as end-of-line brakes and on truck retarders.

Good observation. Eddy current requires time-varying magnetic flux to be induced, so at zero velocity, there's no braking force. Eddy current braking alone cannot bring a vehicle to complete stop and hold it. In practice, friction brakes are used in combination for final stopping and parking. In CAE, we simulate these speed-dependent braking characteristics using coupled electromagnetic-mechanical analysis.

A-V formulation solves Maxwell's equations using magnetic vector potential $\mathbf{A}$ (where $\mathbf{B} = \nabla \times \mathbf{A}$) and electric scalar potential $V$ as unknowns in finite element analysis. A major advantage is that the divergence-free condition $\nabla \cdot \mathbf{B} = 0$ is automatically satisfied. The governing equation in the conductor region is:

JMAG, ANSYS Maxwell, COMSOL Multiphysics, Opera, and Flux (Altair) all adopt A-V formulation (or variants combined with T-Ω formulation) as standard. In practice, a critical issue is meshing fine enough to resolve skin depth. At minimum, you need 3–4 element layers within the skin depth. Failing to do this is a common pitfall leading to underestimation of eddy current loss.

Absolutely. For example, at 100 kHz copper has $\delta \approx 0.2$ mm, so element size must be below 50 μm. That's computationally expensive. In practice, the standard technique is to use a boundary layer mesh, with fine elements near the conductor surface and coarser elements deep inside. Another technique is to use impedance boundary conditions, which remove the interior region entirely and greatly reduce computational cost.