  Expressions are obtained for force and couple densities and stress tensors in
macroscopic models for nematic liquid crystals subjected to electric fields.
The coupling between the liquid crystal orientational properties and the
electric field is taken into account via a free energy of Oseen-Frank type
expressed as an integral functional of the director field and the electric
potential field. The variational model here also allows for a gravitational
field and a magnetic field, and the differences among these three common types
of force fields (gravitational, magnetic, and electric) are discussed. Also
included in the free energy is a surface anchoring potential, and its effect on
boundary traction and couple stress is explored. The electric field is assumed
to arise from electrodes held at constant potential. Flexoelectric effects are
included, and as a consequence, the material is no longer a linear dielectric
medium. It is shown that the equilibrium solutions of the Euler-Lagrange
equations satisfy appropriate expressions of force balance and torque balance,
obtained from a virtual-work principle, and a connection is made between this
and ideas related to Noether's Theorem. The development here builds from
theories of Ericksen related to the notion of "variational compatibility," and
this connection is made. Comparisons are also made to the extensive literature
in physics and continuum mechanics on electromagnetic field/matter interaction.
