  We calculate the non-retarded dispersion force exerted on an electrically
polarizable quantum particle by a perfectly conducting toroid, which is one of
the most common objects exhibiting a non-trivial topology. We employ a
convenient method developed by Eberlein and Zietal that essentially relates the
quantum problem of calculating dispersion forces between a quantum particle and
a perfectly conducting surface of arbitrary shape to a corresponding classical
problem of electrostatics. Considering the quantum particle in the symmetry
axis of the toroid, we use this method to find an exact analytical result for
the van der Waals interaction between the quantum particle and the conducting
toroid. Surprisingly, we show that for appropriate values of the two radii of
the toroid the dispersive force on the quantum particle is repulsive. This is a
remarkable result since repulsion in dispersive interactions involving only
electric objects (and particles) in vacuum is rarely reported in the
literature. Final comments are made about particular limiting cases as, for
instance, the quantum particle-nanoring system.
