We investigate a computing procedure for the unbounded eddy current model put under a coupled finite elements/integral representation form. The exact and non-local artificial condition, enforced on the boundary of the truncated domain, is derived from the simple/double layers potential and the critical point is: how to handle it numerically? An iterating technique, based on the Cauchy fixed point technique, allows us to approximate accurately the solution. The advantage of it is that, at each step, only a bounded eddy current problem with a local condition has to be solved, which is currently carried out by most of the nowadays computing codes conceived to handle value problems on bounded domains.