Role of spatial dispersion in defining the image of a point charge near the dielectric surface

Influence of spatial dispersion on the point charge image near the surface of dielectric or metal is estimated. The polarization field generated by the point charge is calculated. Especially the longitudinal and transverse components of polarization force applied to the point charge moving in the conducting tube are considered. It is shown that the cut-off of the Fourier components of dielectric function in the wave vector space leads to the cut-off in the angular momentum space.