The surface current density, K, is defined as the the current through a unit width perpendicular to the flow. In particular: K = v[itex]\cdot[/itex]σ where σ is the surface charge density. Now I have a little trouble understanding this formula intuitively. Can someone describe in pictures how it is interpreted physically? Also as a side note: Why can you unambigously speak of the current through a ribbon of width dl parallel to the current - what if the current changes as we move parallel to it?