In the simple magnetized torus TORPEX, field-aligned blobs originate from ideal interchange waves and propagate radially outward due to del B and curvature induced drifts. Time-resolved two-dimensional measurements of the field-aligned current density J(parallel to) associated with blobs are obtained from conditionally sampled data from a single-sided Langmuir probe and a specially designed current probe. The profile of J(parallel to) exhibits an asymmetric dipolar structure, which originates from the polarization of the blob and is consistent with sheath boundary conditions. The asymmetry results from the non-linear dependence of J(parallel to) at the sheath edge upon the floating potential. Using internal measurements, we directly confirm 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. To investigate the effect of the observed asymmetry of J(parallel to) on the blob motion, we carried out numerical simulations of seeded blobs, using a two-field fluid model, which evolves electron density and vorticity. Simulations are performed spanning a wide range of blob sizes covering both regimes. We use either the complete or a linearized form for the sheath dissipation term in the vorticity equation. The structure of the parallel current density and plasma potential is found to be different in the two cases. Asymmetric profiles are observed in simulations with the complete form, while symmetric profiles are obtained when a linearized form is used. Negligible effects are, however, observed in terms of blob radial velocity. The relevance of the present results for fusion devices is also discussed.