The steady‐state flow of a conducting fluid between two coaxial rotating disks in the presence of an axial magnetic field is considered for the following conditions: (1) the gapdbetween two disks is very small compared with the radial extension of the disksR; (2) the angular velocity of the disks is not too high, so that the thickness of the Eckman layer &dgr; is still larger than the gapd, (d/&dgr;)1/4≪1; and (3) the magnetic fieldBis moderate so that the corresponding Hartman numberM≪R2/d2. Under these conditions asymptotic solutions to the problem are obtained in terms of the small parameter &Egr;=d/R. The results show that to the lowest‐order approximation, the electric properties of the disks are not important to the flow field, while the magnitude of the magnetic field plays an important role in the equilibrium flow profile.