The development of a flow of a viscous conducting fluid over a rough spinning disk in the presence of a transverse magnetic field has been analysed for different patterns of surface roughness of the disk and different initial distributions of the height of the liquid lubricant. The numerical solution of the governing equation of motion subject to initial and boundary conditions has been obtained by a finite-difference method. The temporal evolution of the free surface of the fluid and the rate of retention of the liquid lubricant on the spinning disk have been obtained for different values of the two parameters M, the Hartmann number and Nratio, the ratio of the surface tension effect to the centrifugation effect. In the absence of the magnetic field, the results have been observed to agree with those of . It has been observed that the effect of surface roughness is to enhance the relative volume of the fluid retained on the spinning disk and this is further enhanced by the presence of the magnetic field.