You’re right that the force of *electromagnetism* tries really hard to push those protons apart. But there’s another force at play here, called the *nuclear force* or the *strong nuclear force*, holds the protons together even more strongly than electromagnetism pushes them apart. But it only works at incredibly tiny ranges – the distance between atoms is so great that they can’t affect each other, but within a nucleus itself, the strong force is king.
Sort of like how at on our human scale, electromagnetism can be stronger than gravity. We can use magnets to lift heavy metal objects, even thought the force of gravity wants to pull them down – one force is overcoming the other. But at long ranges (like the distances in space), gravity is the only force that still holds power, and it controls the interactions between the planets. Just like how electromagnetism can beat gravity at the human scale, the strong nuclear force can beat electromagnetism at the tiny scale.
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