Today in class we were discussing the strong nuclear force, and our teacher was explaining about how the strong nuclear force counteracts the repulsion force between protons in a nucleus.
When asked about the relative strength of the two forces in question, she said that "The strong nuclear force is the strongest force of nature, and is infinitely stronger than the repulsion force between the protons". Now, if that were true, how would the atom remain in equilibrium, because if I'm correct, Equilibrium is achieved when the net force on a body is zero. However, in this situation, that doesn't seem to be the case. Could someone elaborate on this apparent contradiction?
Best Answer
First, the strong force acts on scales where our classical idea of forces as something that obeys Newton's laws breaks down anyway. The proper description of the strong force is as a quantum field theory. On the level of quarks, this is a theory of gluons, but on scales of the nucleus, only a "residual strong force", the nuclear force remains, which can be thought of as being effectively mediated by pions.
Now, a force mediated by pions is very different from one mediated by photons, for the simple reason that pions are massive. Massive forces do not, in their classical limit, follow a pure inverse square law, but yield the more general Yukawa potential, which goes as $\propto \frac{\mathrm{e}^{-mr}}{r^2}$ where $m$ is the mass of the mediating particle. That is, massive forces fall off far faster than electromagnetism.
So this makes it already difficult to tell what the "strength" of a force exactly is - it depends on the scale you are looking at, as Wikipedia's table for the strengths of the fundamental forces rightly acknowledges. However, in no sense is the strong force "infinitely stronger" than the electromagnetic force - it is simply much stronger than it, sufficient to keep nuclei together against electromagnetic repulsion.
Now, the person who said that it is "infinitely stronger" might have had something different in mind which is not actually related to the strength of the force but to its fundamentally quantum mechanical nature: Confinement, the phenomenon that particles charged under the fundamental (not the residual) strong force cannot freely exist in nature. When you try - electromagnetically or otherwise - to separate two quarks bound by the strong force, then you will never get two free quarks. The force between these two quarks stays constant with increasing distance, it does not obey an inverse square law at all, and in particular the energy to being on of the two quarks to infinity is not finite. At some point, when you have invested enough energy, there will be a spontaneous creation of a new quark-antiquark pair and you will end up with two bound quark systems, but no free quark. In this sense, one might say that the strong force is "infinitely stronger", but crucially this is not the aspect of the strong force that keeps nuclei together; the theory of pions shows no confinement.