  The Green function method developed in Ref.[S. B. Chernyshuk and B. I. Lev,
Phys. Rev. E \textbf{81}, 041707 (2010)] is used to describe elastic
interactions between axially symmetric colloidal particles in the nematic cell
in the presence of the external electric or magnetic field. General formulas
for dipole-dipole, dipole-quadrupole and quadrupole-quadrupole interactions in
the homeotropic and planar nematic cells with parallel and perpendicular field
orientations are obtained. A set of new results has been predicted: 1)
\textit{Deconfinement effect} for dipole particles in the homeotropic nematic
cell with negative dielectric anisotropy $\Delta\epsilon<0$ and perpendicular
to the cell electric field, when electric field is approaching it's Frederiks
threshold value $E\Rightarrow E_{c}$. This means cancellation of the
confinement effect found in Ref. [M.Vilfan et al. Phys.Rev.Lett. {\bf 101},
237801, (2008)] for dipole particles near the Frederiks transition while it
remains for quadrupole particles. 2) New effect of \textit{attraction and
stabilization} of the particles along the electric field parallel to the cell
planes in the homeotropic nematic cell with $\Delta\epsilon<0$ . The minimun
distance between two particles depends on the strength of the field and can be
ordinary for . 3) Attraction and repulsion zones for all elastic interactions
are changed dramatically under the action of the external field.
