  The circular motion of charged test particles in the gravitational field of a
Reissner-Nordstr\"{o}m black hole in Anti de Sitter space-time is investigated,
using a set of independent parameters, such as charge Q, mass M and
cosmological constant $\Lambda= -3/l^2$ of the space-time, and charge to mass
ratio $\epsilon=q/m$ of the test particles. Classification of different spatial
regions where circular motion is allowed, is presented, showing in particular,
the presence of orbits at special limiting values, $M=4/\sqrt{6} Q$ and $l=6
Q$. Thermodynamically, these values are known to occur when the black hole is
on the verge of a second order phase transition, there by, giving an
interesting connection between thermodynamics and geodesics of black holes. We
also comment on the possibility of such a connection for black holes in flat
spacetime in a box.
