A two-dimensional eddy current model using thin inductors

Abstract

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 x₃-direction and the inductors are domains with small diameters of order O(ε). The model is derived by taking the limit ε→0. A convergence rate of O(ε^α) with 0<α<1/2 in the L²-norm is shown as well as weak convergence in the W^1,p spaces for 1<p<2.