# What is the orgin of Gauss' law?

• I
• 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 formulated by Joseph-Louis Lagrange in 1773, followed by Carl Friedrich Gauss in 1813, 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. 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