As you know from your physics days, the electric field of a dipole drops off to nothing right away but the magnetic field goes way out. Also, if there were a net charge on the sun it would be blowing off a lot of charged particles of either positive or negative charge depending on the net charge on the sun until the net charge balanced to zero.
Re: electric field dipole
You are correct unless the dipole forms into a Birkeland Current in a plasma. Birkeland Currents seem to have no such limits. The plasma, called the perfect conductor, allows the free flow of electrons along with their accompaning magnetic fields. Birkeland Currents are scalable from the micro to the macro to the astronomic... litterally.