Nucleus validation

Question

Inside the nucleus of an atom is the Coulomb's law valid? I mean that between proton, neutron and other elementary particles, i.e., meson etc. What will be the limit or validity of charges between them. I mean can Coulomb's law can be applied here?

Answer 1

Yes, however the predominant forces are much, much stronger than electromagnetism. That is, there is a "strong nuclear force" which will routinely hold protons side-by-side in a tiny space, and a "weak nuclear force" which will routinely turn a neutron into a proton plus an electron, and those two forces completely violate what you'd expect from electromagnetism (like charges repelling, opposite charges attracting & merging).

The electromagnetic effects mostly just mean that it's easier to hit a nucleus with a neutron than with a proton.

Answer 2

Coulomb's law is valid at all energies we have probed experimentally. There is a subtlety here because the fine structure constant changes with energy so the electrostatic force gets stronger with increasing energy, but it is still an inverse square law force.

However a proton is not a point particle, so the force between for example a proton and electron only obeys the inverse square law as long as the separation is greater than the proton radius. Once you get closer than this the force will cease to obey the inverse square law.

However this isn't any fundamental breakdown of Coulomb's law. For example the gravitational force due to the Earth also obeys an inverse square law as long as you are above the Earth's surface. Once you go below the surface the distance dependance of the force changes because now some of the Earth is above you. Likewise, once you probe inside a proton some of the charge density is outside you.