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feynman1

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

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- #1

feynman1

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

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Experiment, otherwise known as Coulomb's law.

- #3

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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.

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.

Last edited:

- #4

Meir Achuz

Science Advisor

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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.

- #5

Ssnow

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"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

- #6

feynman1

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thanks but all I see is an aps meeting abtract, is there a paper?

"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

- #7

Ssnow

Gold Member

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

Ssnow

- #8

feynman1

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look forward to it!Hi, I asked directly to the author, I am waiting ...

Ssnow

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