Plasma clouds can enhance the collection of current to a charged body in the ionosphere in two ways. The first is by providing a large collection area for inosphere electrons to be collected. The second is by ionization of neutral gas in the vicinity of the plasma cloud. The collection of electrons across a magnetic field is examined, and it is shown that the effective collection area is limited to the region of the cloud where the magnetic field effects are overwhelmed by the electric field effects from the charged body. Upper and lower bounds are obtained for the radius of the core region where the electric field influence dominates. From these, upper and lower bounds are obtained for the current collection. ¿ The American Geophysical Union 1989