This paper presents the solution to the problem of determining the flow field and the fluctuating torque necessary to sustain the motion of a torsionally oscillating plate in a viscous conducting fluid subjected to a uniform axial field under the assumptions that the amplitude of the oscillation is small and that the magnetic Prandtl numberPr m(μσν) is small enough to justify the neglect of induced fields. The analysis reveals that the field decreases the flow velocities, but increases the magnitude of the fluctuating torque.