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Scattering of electromagnetic (EM) waves by many small particles (bodies),embedded in a thin layer, is studied. Physical properties of the particles aredescribed by their boundary impedances. The thin layer of depth of the order$O(a)$ with many embedded in it small particles of characteristic size $a$, isdescribed by a boundary condition on the surface of the layer. The limitinginterface boundary condition is obtained for the effective EM field in thelimiting medium, in the limit $a\to 0$, where the number $M(a)$ of theparticles tends to infinity at a suitable rate.

Electromagnetic wave scattering by a thin layer in which many small particles are embedded