  We investigate the lateral van der Waals (vdW) force between an anisotropic
polarizable particle and a perfectly conducting plane with a hemispherical
protuberance with radius $R$. We predict, via an exact calculation, a sign
inversion in the lateral vdW force, in the sense that, instead of pointing to
the protuberance, in certain situations this force points to the opposite
direction. In the literature, predictions of sign inversions in the lateral vdW
force were based on perturbative solutions, valid when the height of the
protuberance is very small when compared to the distance $z_0$ between the
particle and the plane. Here, taking into account exact formulas, we
investigate how such nontrivial geometric effect depends on the ratio $R/z_0$,
and how the particle orientation and anisotropy affect this sign inversion.
