# What is the orgin of Gauss' law?

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• feynman1
In summary, the discovery of Gauss' law was a combination of both theory and experiment. While it was initially formulated by Lagrange and Gauss in the context of attraction of ellipsoids, it was later generalized to include electrostatic and dynamic E-fields. Its derivation can be attributed to both experimental measurements and theoretical calculations. However, it is debated whether it should be considered a purely theoretical or experimental discovery. Additionally, it is worth noting that many named laws are not actually named after their first formulator.
feynman1
Was Gauss' law originally derived from theory or discovered by experiment?

Experiment, otherwise known as Coulomb's law.

pinball1970 and (deleted member)
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.

Last edited:
etotheipi, vanhees71 and feynman1
"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
"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
Ssnow said:
"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?

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

vanhees71 and Ssnow

## 1. What is Gauss' law?

Gauss' law is a fundamental law in the field of electromagnetism that relates the electric flux through a closed surface to the charge enclosed by that surface. It is named after the German mathematician and physicist Carl Friedrich Gauss.

## 2. What is the origin of Gauss' law?

The origin of Gauss' law can be traced back to the 19th century when Carl Friedrich Gauss first formulated the law in his work on mathematical physics. He developed the law as a way to mathematically describe the relationship between electric charges and electric fields.

## 3. How does Gauss' law work?

Gauss' law states that the electric flux through a closed surface is equal to the charge enclosed by that surface divided by the permittivity of free space. This means that the electric field at a point is directly proportional to the charge at that point and inversely proportional to the distance from the charge.

## 4. What is the significance of Gauss' law?

Gauss' law is significant because it is one of the four Maxwell's equations that form the basis of classical electromagnetism. It allows us to mathematically describe the behavior of electric charges and electric fields, and is essential in understanding and predicting the behavior of various electrical systems.

## 5. How is Gauss' law used in practical applications?

Gauss' law is used in many practical applications, including designing electrical circuits, calculating the electric field inside and outside of conductors, and analyzing the behavior of charged particles in electric fields. It is also used in the development of technologies such as capacitors, transformers, and electric motors.

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