  We study DC and AC electrophoresis of silica micro and nanorods in a thin
film of a nematic liquid crystal. These particles induce virtual topological
defects and also demonstrate nontrivial electrophoresis in a nematic liquid
crystal. We measure several nonlinear electrophoretic mobility coefficients and
compare with those calculated theoretically. We demonstrate a competing effect
of the elastic and electrostatic torques that arises due to tilting of the rods
with respect to the liquid crystal director. A basic theory describing this
effect allows us to measure the effective polarizability of the rods. Our
approach is simple and applicable to a wide variety of asymmetric and
polarizable particles.
