In this paper, the combined effect of surface roughness and transverse magnetic field on the performance characteristic of the annular plates lubricated with conducting couple stress fluid (CCSF) has been studied. On the basis of the Christensen Stochastic model, the generalized stochastic Reynold’s equation is derived. Modified equations for the non-dimensional pressure, load-carrying capacity and squeeze film time are derived. The results are presented both numerically and graphically and compared with conducting smooth surface case. It is observed the surface roughness effects are more pronounced for couple stresses as compared to non-conducting Newtonian fluid (NCNF) in the presence of magnetic field.