# What is the orgin of Gauss' law?

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• feynman1
feynman1
Was Gauss' law originally derived from theory or discovered by experiment?

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Experiment, otherwise known as Coulomb's law.

pinball1970 and (deleted member)
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The answer is both theory and experiment:

It all starts with the experimental discovery of Coulomb's law but then it requires some mathematical processing in which we use Gauss's theorem (which is a theorem of vector calculus more widely known as divergence theorem) to show that if ##\vec{E}## is the field we get by integrating Coulomb's law that is ##\vec{E}=\int \frac{\vec{r}-\vec{r'}}{|\vec{r}-\vec{r'}|^3}\rho(\vec{r'})d^3\vec{r'}## then it satisfies $$\oint_{A} \vec{E}\cdot \vec{dA}=\frac{q_{enclosed}}{\epsilon_0}$$ for any closed surface A.

For more details check https://en.wikipedia.org/wiki/Gauss's_law#Relation_to_Coulomb's_law

After that we generalize this result to include not only electrostatic E-field but time-varying (dynamic)E-field.

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etotheipi, vanhees71 and feynman1
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"Was Gauss' law originally derived from theory or discovered by experiment?"
I take your question to be about history, where it is difficult to be sure.

Wikipedia says:
"The (Gauss) law was first[1] formulated by Joseph-Louis Lagrange in 1773,[2] followed by Carl Friedrich Gauss in 1813,[3] both in the context of the attraction of ellipsoids."

This suggests its derivation was more about any 1/r^2 force. It's a matter of taste whether that is called 'experiment' or 'theory'. I am pretty sure that Gauss's law in its integral form was derived without recourse to experimental measurement of E_normal around a closed surface.

The dates overlap Coulomb:

"The quantity of electrostatic force between stationary charges is always described by Coulomb's law.[4] The law was first published in 1785 by French physicist Charles-Augustin de Coulomb."

One interesting note: Almost no named law is named for its first formulator. Next time, be second.

feynman1
Gold Member
"The Tortured History of Gauss's Law"
of Spencer Ross,
that asserts the origin of Gauss law is due to J.Priestly (1733-1804).
Ssnow

Delta2 and feynman1
feynman1
"The Tortured History of Gauss's Law"
of Spencer Ross,
that asserts the origin of Gauss law is due to J.Priestly (1733-1804).
Ssnow
thanks but all I see is an aps meeting abtract, is there a paper?

Gold Member
thanks but all I see is an aps meeting abtract, is there a paper?
Hi, I asked directly to the author, I am waiting ...
Ssnow

vanhees71 and feynman1
feynman1
Hi, I asked directly to the author, I am waiting ...
Ssnow
look forward to it!

vanhees71 and Ssnow