Experimental and numerical results on the effect of an external vertical magnetic field (MF) on the structure of the flow which occurs when an electric current passes through a conducting medium between two hemispheres are presented. The experiments on the velocity measurement were carried out on the eutectic alloy In-Ga-Sn with the unique fiber-optic transducers. The fiberoptic technique for measuring velocity is described. Results on influence of the axial external MF on the flow are presented. The boundary curve separating the one-vortex and two-vortices flow modes depending on the current values through the experimental setup and the external MF was obtained. These results can be used in electrometallurgy for a priori estimates of the flow structure in the direct-current-arc furnaces.