A closed‐form solution to the central problem of the steady linear motion of an arbitrary current distribution past materials of constant permeability is presented. The application of the Green’s function technique to the field equations yields integral representations of the induction, eddy currents, and electromagnetic forces. Due to interface coupling of the boundary conditions along the surface of the conductor, Green’s functions are shown to satisfy integral equations. In the case of a conducting slab, explicit solutions for the Green’s functions are derived. Application to magnetic levitation and the calculations of forces on moving coils are developed. Results are compared with experimental drag measurements.