When injected across an ambient magnetic field, a stream of collisionless plasma polarizes, and the resulting polarization electric field may allow the stream to penetrate the magnetic field. The polarization charge spreads from the stream sides along the magnetic‐field lines and any ambient plasma that is magnetically connected to the stream will be picked up to form Alfve´n wings of co‐moving plasma. As the stream and wing plasmas move across the magnetic field, their outer edges are continually stripped off. Because of these processes, the stream must expend charge, momentum, and kinetic energy in order to continue its cross‐field motion. These expenditures derive from five requirements of charge from the stream: charge is required (1) to polarize the stream plasma, (2) to replace the charge stripped from the stream’s edges as it propagates, (3) to set up the Alfve´n wings on the stream, (4) to replace the charge stripped from the sides of the wings as they propagate, and (5) to supply any conduction currents in the ambient plasma. By using idealized stream configurations, approximate limits on the propagation distance are obtained.