Linked Questions

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0answers
52 views

What are the “derivations” of the inverse-square law?

Besides the derivation mentioned in this Wiki article, I want to know if there exists any other derivation of the inverse-square law based on some profound physical/philosophical concepts.
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1answer
81 views

'Generalized' Universal Gravitation & Coulomb's Law?

It is said that Coulomb's 'inverse-square' law (and Gauss's Law) are empirical facts. I'm wondering how do we know that Coulomb's law is inverse-square, and what are the possible consequences if it's ...
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3answers
919 views

Proof of Coulomb's law in two and higher dimensions

I have found that the Coulomb force in two dimension varies with $\frac 1 r$: \begin{equation}\tag{2}F=\frac{1}{2\pi\epsilon}\cdot\frac{q_1q_2}{r}\end{equation} But I was not able to prove it. I think ...
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0answers
18 views

Validity of Gauss Law [duplicate]

If the electric field due to a point charge varies as $r^{-2.5}$ instead of $r^{-2}$, then would the Gauss Law still be valid? I infer that the $r^{-2}$ term in the Electric field comes as a result ...
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1answer
64 views

Why Coulomb's law goes with inverse of square radius?

I've seen many similar questions, but none of them were appropriated to me. I was reading about an answer that used the Gauss' law. I don't think that's wise because, of course, the electrostatic ...
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1answer
118 views

If Coulomb's were to depend on $\frac{1}{r^n}$ instead of $\frac{1}{r^2}$ where $n\neq 2$,would Gauss's law still be the same?

What I think is that Gauss's law is an independent law of nature which shouldn't change on modifying Coulomb's law.Am I correct? Well the relation between Gauss's law and Coulomb's law is very strong ...
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1answer
49 views

The pair potential different that $r^{-1}$

As I know, the potential between two particles of the form ~ $r^{-1}$ ($r$ is distance between particles) is special, because it solves the Poisson's equation in 3D. My question is: If I consider for ...
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0answers
61 views

Does gravity exist in higher dimensions? [duplicate]

I’m very curious to know whether gravity exists in higher dimensions. Because it follows the inverse square law it seems to me that it should be 3D only (just intuition). Is there any mathematical ...
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0answers
90 views

Is there a higher-level reason why $\nabla\cdot(\hat{\bf r}/r^2) = 0$ in three dimensions but not two? [duplicate]

I am working through Griffiths, Introduction to Electrodynamics, and finding the divergence of the electric field generated by a single charge sitting at the origin. $$\mathbf{E}(\mathbf{r}) = \frac{\...
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0answers
29 views

Scepticism regarding the exponent of -2 in Coulombs law? [duplicate]

So lately I was speculating why nature choose the number 2 in Coulomb's law like why not 2.$10^{100}$ trailing zeros and then 1 or anything else. I find 2 a bit arbitrary the given explanation being ...
2
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2answers
74 views

References on how dimensionality relates to inverse square laws

https://en.wikipedia.org/wiki/Spacetime#Privileged_character_of_3.2B1_spacetime Does Coulomb's Law, with Gauss's Law, imply the existence of only three spatial dimensions? Why are so many ...
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2answers
243 views

How can we be certain our world has only three spatial dimensions? [duplicate]

It's common knowledge that the universe has three spatial dimensions, and one temporal. But how can we be so sure? Physics tells us that vector forces act independently along different dimensions, so ...
2
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1answer
3k views

Why is Coulomb's law is an inverse square law? [duplicate]

I read about Coulomb's law it says the force of attraction or repulsion between two charges is inversely proportional to the square of the distance between them. So generally if I say then Coulomb'...
2
votes
1answer
777 views

What is the significance of the Inverse-square law? [duplicate]

Considering its occurrences in various fields like Electrostatics, Gravitation, Acoustics etc. how does the law bind these topics together?
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1answer
89 views

Is there an underlying reason why some forces are inversely proportional to the square of the distance? [duplicate]

This is the first time I'm studying those subjects (I'm still in high school) and my teacher couldn't give me an answer. I'm referring specially to Newton's law of gravitation and Coulomb's law of ...

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