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 $x\_3$-direction and the inductors are domains with small diameters of order $O(\epsilon )$. The model is derived by taking the limit $\epsilon \to 0$. A convergence rate of $O({\epsilon }^{\alpha })$ with $0<\alpha <1/2$ in the $L^2$--norm is shown as well as weak convergence in the $W^{1,p}$ spaces for $1<p<2$.