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which one has been discovered earlier? Coulomb's law or Gauss's law?

I've read that Gauss's law is more fundamental and of course we can derive Gauss's law using Coulomb's law and vice versa.

But my question is that which one is discovered earlier?

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Cavendish verified the Coulomb's law in the early 1770s, but did not publish, Coulomb published it in 1785 in his first three reports on electricity and magnetism. For magnetic poles the law was established even earlier by Michell in 1750, explaining Newton's inverse cube law for the magnetic dipole in Principia (1687), see Is Coulomb's law the earliest mathematical formula describing electricity?

So when Gauss was born in 1777 Coulomb's law was already known. He only formulated Gauss's law in 1835, and it was not published until 1867, when Maxwell already stated it as one of his four equations in 1861-62. It is interesting however that the divergence theorem which relates one law to the other in modern expositions was discovered by Lagrange in 1762, and then rediscovered multiple times, by Gauss in 1813, Poisson in 1824, Ostrogradsky in 1826, and Green and Sarrus in 1828.

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It seems to me that there is some confusion here. Coulomb Law is a law of physics. It is about electricity. It was discovered experimentally and can be proved ONLY by experiment. It is a statement about REAL WORLD.

I am not completely sure what "Gauss Law" in the question is. But I suppose this is Gauss' THEOREM about flux. This is a mathematical theorem. Which is established by mathematical proof and logically speaking has nothing to do with electricity or anything in the real world.

I checked the Wikipedia article and it indeed shows the same confusion. These are two different things, from different realities, and one cannot follow from another. Gauss theorem applies to vector fields (which is a mathematical notion). Gravity field, electrostatic field, are described as vector fields (this is an experimental fact) and THEREFORE must satisfy Gauss' theorem (and all other theorems about vector fields).

And of course the chronological question has trivial answer: Gauss was too young when Coulomb law was discovered.

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    $\begingroup$ "Gauss's Law" also traditionally refers to the statement about electric flux specifically, which is separate from the corresponding mathematical theorem. This is the usage Wikipedia follows en.wikipedia.org/wiki/Gauss's_law Deriving flux laws from point laws mathematically is a relatively late development, in particular this is not how Maxwell got his equation. Vector fields do not explicitly appear until Heaviside in 1880s hsm.stackexchange.com/questions/3158/… $\endgroup$ – Conifold Mar 18 '16 at 3:17

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