Can two charges with same sign atrract?

Question

Can two charges with same sign (++/--) separated by some finite distance attract each other ?

Answer 1

If you are talking about point charges then, as explained above, the answer is no.

But in the case of non-uniform charge distributions, it is possible for same-charge particles to attract, if they are sufficiently close.

As an example, the following two particles are identical, each having a net charge of -1. Plotted below them is their potential energy as a function of distance. As you can see, when far away they repel each other like ordinary point charges. But when sufficiently close, they attract.

These dipole-dipole interactions are important in many areas of physics and chemistry.

Answer 2

Be aware that the terminology on $\pm$ for the charges is nothing but a convention to distinguish between the way they move once they feel the electromagnetic field. In fact in nature you almost never measure the charge of a particle but you rather measure the direction it moves between two points at a different potential.

Coming to your question: take two any charges and place them one in front of another. If they attract, then you define the two charges to have different signs (no matter which is $+$ and which is $-$). Once you do so, you can take either of the two and test it against another random charge, and so on and so forth. It is experimentally true that in the universe exist (so far) only two types of electric charges, and you can assign each charge to one of the two sets $\pm$ using the above technique.

To conclude: the definition of $\pm$ for a charge comes after you have tested whether they attract to each other or not.

Answer 3

Certainly. At very short range, typically about a femtometer, the strong force becomes dominant, and (as an example) protons can clump together to form atomic nuclei. Of course, for any larger distance the answer is no.