This paper describes a numerical investigation of the influence of axial and dipolar magnetic fields on the stability of the convective flow of an electrically conductive Boussinesq fluid in a spherical gap for the radius ratios eta = inner radius/outer radius = 0.4, 0.5, and 0.6. The inner shell is warmer than the outer shell. We show that whereas the axial magnetic field stabilizes the flow for low Hartmann numbers, a destabilizing effect is detected if the magnetic field increases. On the other hand, numerical analysis shows that the dipolar magnetic field configuration stabilizes the flow. The critical wave number, mc, is much higher than that for the axial magnetic field. The critical Grashof numbers are presented as a function of the Hartmann number for both configurations of the B-field. The stability analysis is accompanied by calculations of the 3D flows. (C) 2016 Elsevier Ltd. All rights reserved.