  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 $1< p <2$.
