The ratio of the electromagnetic force to the gravitational force between a proton (M) and an electron (m) is just
2
K e G M m
------ = ------
2 2
R R
or
2
K e = G M m
so
2
42 K e
10 = ------
G M m
approximately. In terms of the densities of these particles in the universe, N and Rho,
2 2 2
K e N = G Rho
-29
so that for a cosmological density of matter of 10 gm/cc you get
-24
N = 10 protons/cc
But the cosmological density of matter divided by the mass of a proton
is just 10^-5 atoms/cc with is 10^19 times higher than the density needed
in charges so that the electrostatic forces contribute as much as the
gravitational forces between particles. So, this means that if in 10^19
atoms in the universe, you have exactly 1 unit of charge ( 1 electronic
charge), the net effect as an electrostatic force equals the gravitational
force from these 10^19 atoms! That's how close we have to be to exact
neutrality in the universe before non-gravitational forces predominate!
In fact, no non-gravitational forces have ever been confirmed in the dynamics of galaxies or galaxy clusters, so we know that, on average, matter in the cosmos has even less net charge than 1: 10^19.