In simple magnetized toroidal plasmas, field-aligned blobs originate from ideal interchange waves and propagate radially outward under the effect of $\grad B$ and curvature induced $E \times B$ drifts. We report on the first experimental two-dimensional measurements of the field-aligned current associated with blobs, whose ends terminate on a conducting limiter. A dipolar structure of the current density is measured, which originates from $\grad B$ and curvature induced polarization of the blob and is consistent with sheath boundary conditions. The dipole is strongly asymmetric due to the nonlinear dependence of the current density at the sheath edge upon the floating potential. Furthermore, we directly demonstrate the existence of two regimes, in which parallel currents to the sheath do or do not significantly damp charge separation and thus blob radial velocity.