# Eddy Current solver

Eddy currents (also called Foucault currents) are currents induced in conductors, when a conductor is exposed to a changing magnetic field due to relative motion of the field source and conductor; or due to variations of the field with time. This causes a circulating flow of electrons, or a current, within the body of the conductor. These circulating eddies of current then induce magnetic fields. These fields generate a force called the Lorentz force that can cause repulsive, attractive, propulsion and drag effects. The stronger the applied magnetic field, or the faster the field changes, then the greater the currents that are developed and the greater the fields produced.

The Eddy current solver available in the electromagnetism module allows to solve problems in the so-called “eddy-current” approximation, which is valid for good enough conductors with low frequency varying fields such that the displacement currents can be neglected compared to the current density. This approximation implies a divergence free current density and no free charge accumulation (see Maxwell equations). Some of the industrial applications involve electric metal forming, metal cutting, metal welding or high magnetic pressure generation. The Joule heating is also taken into account for coupling with the LS-DYNA thermal solver.

The Maxwell equations are solved using a Finite Element Method (FEM) for the solid conductors coupled with a Boundary Element Method (BEM) for the surrounding air (or insulators). Thus, no air mesh is necessary.