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A close-form solution to the problem of the unsteady linear motion of an arbitrary current distribution past materials of constant permeability is presented. The application of Green’s functions technique to the field equations yields to integral representations of the induction, eddy currents, and electromagnetic forces. Due to interface coupling of the boundary conditions along the surface of the conductor and taking into account the initial conditions, Green’s functions are shown to satisfy integral equations. In the case of a slab conductor of finite depth, explicit solutions for the Green’s functions are derived. Applications to electromagnetic levitation of forces on moving coils are derived and discussed. This analysis shows and experiments confirm that forces as a function of velocity may be strongly dependent on acceleration, giving in some cases a sort of hysteresis cycle. © 1998 American Institute of Physics.