Why do atoms have an overall neutral charge ?
They don't
Well, unless it's an ion
They have the same number of protons and neutrons
and they have same magnitude of charge but opposite signs..
Overall neutral charge as the number of protons (which carries a +1 each) equals number of electrons (which carries a -1 each).
From a sufficient distance, the particles that make up an atom can be seen as a single entity with a charge averaged over the constituent charges of the individual particles. This is similar to how we can treat a complex gravitational n-body system, from far enough away, as a single particle with a point mass equal to the total mass at the centroid. But, this is a simplification -- let's call it the point-charge simplification of an atom -- and to more fully account for all the intricate behavior of atomic systems, one must consider the charges of individual particles and their respective (probabilistic) positions.
Hi! I'm just going to combine the answers so far. queelius outlined an important principle, and others identified that the charges are balanced. There are many charges in an atom. Protons have a +1 charge and electrons have a -1 charge, like dauspex said. The atom is commonly thought to be organized like this:|dw:1373518343734:dw|Uh, that's a rough representation...
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