A two-dimensional eddy current model using thin inductors

We derive a mathematical model for eddy currents in two dimensional geometries where the conductors are thin domains. We assume that the current flows in the x3direction and the inductors are domains with small diameters of order O(ǫ). The model is derived by taking the limit ǫ → 0. A convergence rate of O(ǫα) with 0 < α < 1/2 in the L–norm is shown as well as weak convergence in the W 1,p spaces for 1 < p < 2.