  We study the director field around a spherical particle immersed in a
uniformly aligned nematic liquid crystal and assume that the molecules prefer a
homeotropic orientation at the surface of the particle. Three structures are
possible: a dipole, a Saturn-ring, and a surface-ring configuration, which we
investigate by numerically minimizing the Frank free energy supplemented by a
magnetic-field and a surface term. In the dipole configuration, which is the
absolutely stable structure for micron-size particles and sufficiently strong
surface anchoring, a twist transition is found and analyzed. We show that a
transition from the dipole to the Saturn ring configuration is induced by
either decreasing the particle size or by applying a magnetic field. The effect
of metastability and the occurence of hysteresis in connection with a magnetic
field are discussed. The surface-ring configuration appears when the
surface-anchoring strength W is reduced. It is also favored by a large
saddle-splay constant K_24. A comparison with recent experiments by Poulin et
al. gives a lower bound for W, i.e., W > 0.6 erg/cm^2 for the interface of
water and pentylcyanobiphenyl (5CB) in the presence of the surfactant sodium
dodecyl sulfate.
