Space-charge flows and electric fields in the magnetospheres of rotating magnetic stars

We illustrate a method for determining self-consistently the spacial distribution of space-charge currents and electric fields close to the surface of a rotating magnetic star. The unique solution for simple geometries shows that the space-charge flow, required to maintain the surface potentials and to bring the surface electric field parallel to the magnetic field to zero, simultaneously sets E·B to zero at all heights above the surface. Thus this result questions the previous estimates of the parallel electric fields near pulsars.