  Effective medium theory replaces a given fine-scale heterostructure with a
homogeneous one in such a way that the physically measurable quantities, e.g.
reaction fields and losses, remain approximately the same. This Letter shows
that the very nature of the physical problem may change upon homogenization. A
specific example is a stratified nonlinear magnetic and conducting medium,
where a low frequency excitation induces eddy currents. It is shown that the
appropriate coarse-scale (homogeneous) model is, counter intuitively,
magnetostatic, with an effective complex valued BH curve whose real and
imaginary parts represent active and reactive losses in the sample. Similar
situations may arise in other physical and engineering applications, notably,
in diffusion problems with boundary layers.
