The self-capacitance of the Sun isn't very large--its radius is about
700,000 km. The Gaussian unit of capacitance is the centimetre (which
is close to a picofarad), and the self-capacitance of a sphere equals
its radius in centimetres.
Thus the capacitance of the Sun is about 7E10 cm, or 0.08 F.
Wiki says that the number of particles ejected by the Sun is about
1.3E36 per second, which is about 2E17 coulombs/s, counting both
positive and negative, and ignoring alpha particles having a charge of +2.
The maximum energy of the ejected particles is around 10 keV, so if the
Sun's voltage with respect to the rest of the universe reached +- 10 kV,
one sign of free particle would be unable to escape.
With 10**17 amps worth of the other polarity continuing to stream out,
and only 80 mF of capacitance, this would be corrected in about 10**-18
seconds. ;)
>
> If earth has a net charge, it is probably not many volts. Aren't
> cosmic rays almost all positive?
I don't know about the ones outside the atmosphere. The positive ones
are much more massive than electrons, and so have more momentum per unit
energy, which helps them penetrate the atmosphere.
>
> Most of the earth's surface is conductive, but dry sand might be a
> good enough insulator to have local surface potentials. Sounds like a
> good science project. Maybe make a drone that could scan a region and
> map gradients.