  In this paper, based on the numerical calculation of total energy utilizing
the Green's function method, we found that the external electric field applied
to a microparticle-suspended nematic liquid crystal cell, if reaching a
critical value, combined with its direction, surface anchoring feature and
molecular dielectric anisotropy, is possible to create an anisotropic "bubble"
around the microparticle with a vertical fast "lane", in which the
microparticle can, driven by the asymmetric buoyant force, vertically move
swiftly from the cell's midplane to a new equilibrium position, triggering a
positional transition discovered by the author previously. Such a new
equilibrium position is decided via a competition between the buoyant force and
the effective force built upon the microparticle by the elastic energy gradient
along the "lane". The threshold value of external field, depends on thickness
$L$ and Frank elastic constant $K$ and slightly on the microparticle size and
density, in a Fr\'{e}edericksz-like manner, but by a factor. For a nematic
liquid crystal cell with planar surface alignment, a bistable equilibrium
structure for the transition is found when the direction of the applied
electric field is (a) perpendicular to the two plates of the cell with positive
molecular dielectric anisotropy, or (b) parallel to the two plates and the
anchoring direction of the cell with negative molecular dielectric anisotropy.
Except for the formation of a vertical fast "lane", when the electric field
applied is parallel to both the two plates and perpendicular to the anchoring
direction, the microparticle suspended in the nematic liquid crystal tends to
be trapped in the midplane, regardless of the sign of the molecular dielectric
anisotropy. Such phenomenon also occurs for negative molecular dielectric
anisotropy while the external is applied perpendicular to the two plates.
