The bold part above is quite clear intuitively, and I believe the mathematics required to demonstrate it would be very straightforward.
Ziggurat has already cited the current Wikipedia article on the Shell theorem
WP, which contains a derivation based on Gauss's law for gravity
WP, ∇∙
g=-4
πGρ.
I can't say for EM off the top of my head, but if there were a perfect sphere of matter, no matter how thick, gravity is completely neutral for any location within the sphere. Zero.
For the electric field, Gauss's law is ∇∙
E=4
πρ. Apart from a multiplicative constant -
G, that's just like Gauss's law for gravity, so you can take exactly the same proof, substitute
E for
g, and remove the factor of -
G from every equation in which it appears.
One of the many ironies here is that it's been less than a week since
Michael Mozina accused us of loving "pseudoscience" because he, Michael, had placed his faith in some ludicrous pseudo-mathematical dogma he had invented about magnetic reconnection being somehow forbidden by Gauss's law for the magnetic field, ∇∙
B=0. Now, when a similar form of Gauss's law is actually relevant, and that relevance is backed up by hundreds of years of laboratory experiments, Michael refuses to see the connection.
Just as I was about to post this, I see he has once again stuck his fingers in his ears and kicked off another of his Gish gallops.
It would appear that some "outside of the observable universe" force pulling on the universe to accelerate the cosmological expansion can be ruled out mathematically, by the simple geometry of the situation.
Consequently, it must be something within the observable universe that we can't see and can't feel or test in a laboratory because of the scale involved. Hey, I have an idea; let's call it "dark energy" and try to figure out what it is!
Sounds like a plan, but we might have to proceed without Michael.