$MgB_2$ superconductor is highly sensitive to the Mg content. Even if the samples are synthesized with the appropriate looking stoichiometric ratio, the heat treatment leads to the loss of Mg either to ambiance or to MgO. To avoid it, either excess Mg is added in the starting powder or sealed ampoule annealing is employed. In this paper the effect of open Mg sintering ambiance on the ex-situ $MgB_2$ was studied to enhance its superconducting properties. The open Mg ambiance was created to avoid any overpressure of Mg by providing a hole in Fe tube used as sample holder. The decrease in resistivity of the synthesized sample was observed through the increased temperature dependence of electron-phonon interactions. A clear enhancement in the superconducting cross-sectional area and hence the in-field critical current density is obtained.