We study the spatial distributions of the spin and mass currents generated by a moving Gaussian magnetic obstacle in a symmetric, two-component Bose-Einstein condensate in two dimensions. We analytically describe the current distributions for a slow obstacle and show that the spin and the mass currents exhibit characteristic spatial structures resembling those of electromagnetic fields around dipole moments. When the obstacles velocity increases, we numerically observe that the flow pattern maintains its overall structure while the spin polarization induced by the obstacle is enhanced with an increased spin current. We investigate the critical velocity of the magnetic obstacle based on the local criterion of Landau energetic instability and find that it decreases almost linearly as the magnitude of the obstacles potential increases, which can be directly tested in current experiments.
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