For a smooth bounded domain G ⊂ R 3 we consider maps n : R 3 \ G → S 2 minimizing the energy E(n) = ´R3 \G |∇n| 2 + Fs(n ⌊∂G) among S 2-valued map such that n(x) ≈ n 0 as |x| → ∞. This is a model for a particle G immersed in nematic liquid crystal. The surface energy Fs describes the anchoring properties of the particle, and can be quite general. We prove that such minimizing map n has an asymptotic expansion in powers of 1/r. Further, we show that the leading order 1/r term is uniquely determined by the far-field condition n 0 for almost all n 0 ∈ S 2 , by relating it to the gradient of the minimal energy with respect to n 0. We derive various consequences of this relation in physically motivated situations: when the orientation of the particle G is stable relative to a prescribed far-field alignment n 0 ; and when the particle G has some rotational symmetries. In particular, these corollaries justify some approximations that can be found in the physics literature to describe nematic suspensions via a so-called electrostatics analogy.