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> You can just plug numbers into Coulomb's law

Not if you want to get correct answers in problems that involve moving charges.

> relativity is necessary when things start to move 'very fast'

In electromagnetism, relativity is necessary whenever charges are in motion. Whether or not they are moving "ver fast" is irrelevant. Coulomb's Law is only valid when you have a charge at rest.

That said, the post I originally responded to obviously was talking about charges moving "very fast" since it claimed an electron falling towards a proton could exceed the speed of light.



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