I read somewhere that if we pack a proton and an electron together in a small volume, the combination does not attract or repel another electron or proton placed at a distance.

But my problem is that force on a charged particle due any other charged particle is not affected by any other placed near latter,i.e, the force between charged particles follows superposition rule. Then why the combination of a electron and an proton does not attract or repel any other charged particle?