We present the mathematical theory and its numerical validation of a method tailored to include eddy-current effects only in a part of the domain. This results in a heterogeneous problem combining an eddy-current model in a subset of the computational domain with a magneto-static model in the remainder of the domain. We adopt a two-domain two-step approach in which the primary variables of the problem are the electric scalar potential and the magnetic vector potential. We show numerical results that validate the formulation.