  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 obstacle's 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 obstacle's potential
increases, which can be directly tested in current experiments.
