7.1 Introduction

Wave scattering by small bodies is of great interest in theory and applications. An incomplete list of problems for which wave scattering by small bodies is of prime importance includes: radio wave scattering by rain and hail, light scattering by cosmic dust, light scattering in colloidal solutions, light propagation in muddy water, wave scattering in a medium consisting of many small particles, ultrasound mammography, finding small cracks and holes in metals and other materials, detecting mines and other subsurface inhomogeneities from the scattered field, measured on the surface, etc. We will show that the skin effect for thin wires and radiation from small holes are a particular examples of the the theory of wave scattering by small bodies. The number of examples is practically unlimited. The theory was originated by Rayleigh (1871) who contributed to this field until his death (1919). Rayleigh understood that the main term in the scattering amplitude in the problem of wave scattering by a small body with diameter much less than the wavelength of the incident field is the dipole radiation. J. J. Thomson (1893) realized that for a small perfect conductor the magnetic dipole radiation is of the same order as the electric one. Some efforts were made in order to develop an algorithm for finding the expansion of the scattered field in powers of ka, where k is the wave number and a is the characteristic dimension of the scatterer, ka ? 1 ([151], [50]). Since in...