Quote by DaleSpam
As I said above, the math guarantees that if you use the correct equations for the potential then all of your "positive contributions" and "negative contributions" work out correctly so that Gauss' law holds.

When passing through the surface of the sphere (0=thickness), is change in the integrated flux instantaneous from one end of the sphere to the other, or is it gradual (per synchronized time)? In other words, could the integral * freespace permittivity be onehalf a charge at one point, or does it "jump of a cliff" and go from 1 unit of charge down to 0, while skipping all values in between?
Does the field near the charge, if made stationary after displacement, continue for 1 year to change in a way compensating exactly the field far of it as it updates the far end of the sphere 1 light year away to reflect that the charge had been moved outside the sphere 1 year before?
EDIT: I guess I couldn't stop asking questions :D