The polarization phenomenon, involved in the mechanisms of emission from carbon nanotubes, is investigated by means of a self-consistent resolution of Poisson's equation. We show that the field enhancement. responsible for the emission, varies in a logarithmic way with the nanotube length. This leads, for most of the nanotubes investigated, to a rapid saturation of the amplification of the field which does not allow for the recovery of experimental values for microscopic lengths, However, this saturation is less important with (n,0) nanotubes and values of the amplification factor around 2000 can be obtained with small diameter nanotubes of this kind. The case of nanotube films is also investigated, and the dependence of the amplification factor with the nanotube density is pointed out. Finally, the screening effect of the outer shells on the inner ones is investigated in the case of multiwall nanotubes.