  Molecules of a nematic liquid crystal respond to an applied magnetic field by
reorienting themselves in the direction of the field. Since the dielectric
anisotropy of a nematic is small, it takes relatively large fields to elicit a
significant liquid crystal response. The interaction may be enhanced in
colloidal suspensions of ferromagnetic particles in a liquid crystalline
matrix---ferronematics--- as proposed by Brochard and de Gennes in 1970. The
ability of these particles to align with the field and, simultaneously, cause
reorientation of the nematic molecules, greatly increases the magnetic response
of the mixture. Essentially the particles provide an easy axis of magnetization
that interacts with the liquid crystal via surface anchoring.
  We derive an expression for the effective energy of ferronematic in the
dilute limit, that is, when the number of particles tends to infinity while
their total volume fraction tends to zero. The total energy of the mixture is
assumed to be the sum of the bulk elastic liquid crystal contribution, the
anchoring energy of the liquid crystal on the surfaces of the particles, and
the magnetic energy of interaction between the particles and the applied
magnetic field. The homogenized limiting ferronematic energy is obtained
rigorously using a variational approach. It generalizes formal expressions
previously reported in a physical literature.
