  Tactoids are spindle shaped-droplets of a uniaxial nematic phase suspended in
the co-existing isotropic phase. They are found in dispersions of a wide
variety of elongated colloidal particles, including actin, fd virus, carbon
nanotubes, vanadium peroxide and chitin nanocrystals. Recent experiments on
tactoids of chitin nanocrystals in water show that electric fields can very
strongly elongate tactoids even though the dielectric properties of the
co-existing isotropic and nematic phases differ only subtly. We develop a model
for partially bipolar tactoids, where the degree of bipolarness of the director
field is free to adjust to optimize the sum of the elastic, surface and Coulomb
energies of the system. By means of a combination of a scaling analysis and a
numerical study, we investigate the elongation and director field's behavior of
the tactoids as a function of their size, the strength of the electric field,
the surface tension, anchoring strength, the elastic constants and the electric
susceptibility anisotropy. We find that tactoids cannot elongate significantly
due to an external electric field, unless the director field is bipolar or
quasi bipolar and is somehow frozen in the field-free configuration. Presuming
that this is the case, we find reasonable agreement with experimental data.
