  We examine the equilibrium configurations of a nematic liquid crystal with an
immersed body in two-dimensions. A complex variables formulation provides a
means for finding analytical solutions in the case of strong anchoring. Local
tractions, forces, and torques on the body are discussed in a general setting.
For weak (finite) anchoring strengths, an effective boundary technique is
proposed which is used to determine asymptotic solutions. The energy-minimizing
locations of topological defects on the body surface are also discussed. A
number of examples are provided, including circular and triangular bodies, and
a Janus particle with hybrid anchoring conditions. Analogues to classical
results in fluid dynamics are identified, including d'Alembert's paradox,
Stokes' paradox, and the Kutta condition for circulation selection.
