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Do the protons inside the nucleus repel each other by the electrostatic force? If they do, why doesn't the repulsion drive the protons apart so that the nuclei get disintegrated?

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There is an electrostatic repulsion between the protons in the nucleus. However, there is also an attraction due to another kind of force besides electromagnetism, namely the so-called "strong nuclear interaction".

The strong nuclear interaction ultimately boils down to the forces between the "colorful" quarks inside the protons - and neutrons. It is mediated by gluons, much like electromagnetism is mediated by photons, described by Quantum Chromodynamics (QCD), much like electromagnetism is described by Quantum Electrodynamics (QED), and it acts (almost) equally on protons and neutrons.

The attractive strong nuclear interaction inside the nuclei is 1-2 orders of magnitude stronger than the repulsive electrostatic interaction which is what keeps the nuclei together despite the repulsive electrostatic force.

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    $\begingroup$ Wow, awesome answer. So much information in so few lines! When forces are described in contrast to one another, you see how they resemble each other and distinguish themselves more easily. I keep waiting for some exciting and crazy news that the strong nuclear interaction is really gravity working through curled up extra spatial dimensions on the subatomic scale. And yes, as you can obviously tell I don't know much about physics :-). $\endgroup$ Commented Jun 29, 2011 at 1:51
  • $\begingroup$ @Luboš Motl. Did you ever think about the possibility that electrons and protons during their approach could partially lose their charge? $\endgroup$ Commented Jan 3, 2017 at 20:24
  • $\begingroup$ Dear @HolgerFiedler , the electric charge is quantized - at least in every region where the charge density vanishes at the boundary (and perhaps in a shell around it), so no elementary particle can "continuously" lose its charge, the values in between $+1e$ and $0$ are simply not allowed by the laws of Nature. $\endgroup$ Commented Jan 6, 2017 at 6:25
  • $\begingroup$ I agree with you for free electrons. For atoms I'm inclined more to the observed charge neutrality due to canceling out the protons and electrons fields. My approach is that the electric field is quantized. The implication is that it is built from two quanta, which form electric fields, magnetic fields and EM radiation. I could not see any inconsistency in such a model about One-dimensional structures of space. $\endgroup$ Commented Jan 6, 2017 at 6:39
  • $\begingroup$ physics.stackexchange.com/q/302727/46708 $\endgroup$ Commented Jan 6, 2017 at 6:41
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Since protons are positively charged we think that they repel.....yes they repel due to electrostatic force between the protons(coulomb's law). In the similar fashion there also exists nuclear force ( nuclear binding energy) in the nucleus which balances the repulsion between the protons....so totally protons are balanced by both electrostatic force and nuclear force inside the nucleus...

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Given two protons within the same nucleus, the two dominant interactions between them are: the residual strong nuclear interaction and electromagnetic interaction (weak and gravitational interactions would also exist, but they are negligible compared to the two main ones).

The electromagnetic interaction is always repulsive, obviously, while the strong interaction is measured by pi mesons of zero spin, which makes this second interaction always attractive (because 0 is an even number) and, in fact, of greater magnitude than the electrostatic repulsion.

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As every body attracts each other but due to earth, our attraction forces are negligible. Therefore, protons and protons, neutrons and protons attract each other We can calculate it by g=(G*m1*m2)/r*r

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