In this paper we consider an incompressible viscous indefinite and electrically conductive fluid slowly moving under the action of a uniform magnetic field and body forces distributed with continuity in a fixed region of the medium. We give two procedures for reduction of this problem. In the case where the induced magnetic field is sufficiently small compared with the body forces, we determine solutions of the velocity field, induced magnetic field and pressure field. These solutions are expressed by definite integrals which, having an analogy with the Newtonian volume potentials, are called hydro-dynamic and magnetic potentials.