  We calculate the bound state properties of $J/\psi$ in a hot and dense QCD
plasma using phenomenological potentials augmented by inputs from perturbative
QCD. The temperature and density region of study will be relevant in future
heavy ion collision experiments at FAIR. We find that the effect of baryon
density on the dissociation of $J/\psi$ is small in this regime. However we
indicate that if there is a critical end point in the QCD phase diagram then
strong density fluctuation will dissociate charmonia near hadronization. The
measurement of $J/\psi$ suppression can therefore signify the existence of the
critical point unambiguously.
