How cluster of charges of same polarity remain stronger together ?

Question

These clusters of same polarity attract clusters of opposite polarity and repel clusters of same polarity . It is known that charges of same polarity repel while of opposite polarity attract. But how these clusters of same polarity them selves hold together ?

Answer 1

Let us assume clusters to be spherical.
We know that the charges in conductor materials are located at the outer shell. It's also true for atomic clusters.

There's a critical radius.

By adding a new same charged cluster to a big one its radius increased thus the area for dispersion of charges increases too. so the charges are located further and then this process is feasible from thermodynamical point of view.
But remember that this process also increases the charge so it the increase in surface area couldn't overcome this effect it's not stable.

There should be at least one critical point(s) from DFT calculations for this problem.

Answer 2

If you are talking about the protons in a nucleus, they are held together by the nuclear force, which is much stronger than the electrostatic repulsion at these extremely small distances.