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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 ...
2
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1answer
75 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{\...
2
votes
1answer
91 views

Why do we assume that Gauss' law of gravitation to remain same even when there are extra spatial dimensions?

Every kid knows that the magnitude of the gravitational force between two point masses is inversely proportional to the square of the distance $r$ between them i.e., $F\sim r^{-2}$. But experimentally,...
1
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1answer
153 views

Newton's “Shell theorem” in higher dimensions

In Newtons's shell theorem, the net gravitational force is zero inside a hollow sphere, if the gravitational force is proporional to $1/r^2$. In 2D, the net force is zero inside if the force is ...
0
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0answers
20 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
56 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 ...
0
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2answers
226 views

Coulomb Potential in 1+1 and 1+2 dimensions?

It is know that in 1+1 dimensions, the Coulomb potential is of linear form: $$ V(x) = Cx$$ and in 1+2 dimensions, of the form: $$V(x,y) = - \ln\left(\frac{L}{\sqrt{x^2 + y^2}}\right).$$ And I am ...
28
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2answers
2k views

Basis for the Generalization of Physics to a Different Number of Dimensions

I am reading this really interesting book by Zwiebach called "A First Course in String Theory". Therein, he generalizes the laws of electrodynamics to the cases where dimensions are not 3+1. It's an ...
3
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0answers
47 views

Inverse square laws & dimensionality [duplicate]

I have been thinking about the famous Inverse square-laws and how they came out to be that way. Gauss's law elegantly describes the square law for electricity to spherical distribution. Now I am ...
1
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3answers
334 views

How would Newtonian gravity work in a 1-dimensional universe?

I have come across the idea of gravity in different dimensional space. From the standard formula for gravity $F=\frac{GMm}{r^2}$ I have found that the $1/r^2$ term is a result of a three dimensional ...
2
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2answers
293 views

The inverse square law [duplicate]

Why the nature has chosen the inverse square law. For instance, the gravitational force as well as the Coulomb force is inversely proportional to the square of distances. Why not these forces are ...
-1
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1answer
53 views

Is there a connection between Newton's law of universal gravitation and the area of a sphere? [duplicate]

According to Newton, the force between two objects of masses $m$ and $M$ is $$ F = \frac{GmM}{r^2}, $$ where $r$ is the distance between the two objects. Basically, if distance between the object ...
2
votes
1answer
76 views

Zero net charge in two space dimensions?

I recently came across the statement (without further explanation) that the net charge in a two dimensional system has to be zero. Obviously in two dimensions, the electric field $\vec{E}$ due to a ...
2
votes
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'...
0
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1answer
134 views

How come divergence of $\vec E$ is zero in this case where $\vec E=\xi\frac{\left[x,y\right]}{\sqrt{(x^2+y^2)^3}}\,?$

I hope you could help me clearing some doubts about Gauss' law of the electric field that states $\epsilon_0\nabla\cdot\vec E=\rho$. Take for instance the case of a point charge in the origin in empty ...
7
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4answers
438 views

How does superstring theory explain the inverse square gravity law, given that it requires 9 spatial dimension?

In superstring theory, the spacetime dimension is either 10, one of them is time, the rest are spatial dimensions. But based on geometrical argument, we can say that $F\propto r^{1-D}$, where $D$ is ...
3
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3answers
464 views

Does Gravity Depend on Spatial Dimension?

Consider a line containing two point masses, $m$ and $M$. The line is a $1D$ space. What's the gravitational force between the two masses? Newton's formula for the gravitational force $F$ between ...
6
votes
2answers
154 views

Significance of electrical fields of infinite objects

I've noticed a pattern with the electric fields of charged objects of infinite dimensions. A point charge, which can be considered a charge of 0 dimensions, has an electric field that goes as $r^{-2}$...
1
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1answer
86 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 ...
1
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0answers
67 views

In Newton's gravity, is the inverse square law related to the fact that our Universe has (apparently) 3 dimensions? [duplicate]

I read, long ago, a book, whose title I can't remember but I think the author was Carl Sagan. In the book was saying that gravity follows the inverse square law because of our Universe was 3 ...
1
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1answer
989 views

Inverse Square Law and extra space dimensions

Newton's famous Inverse Square Law says that in $n=3$ dimension of space, force is inversely proportional to the square of the distance between a source and a target. I understand that for higher ...
3
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6answers
6k views

2 dimensional Coulomb's law equation

We can notice that in the Coulomb's law equation, $$\begin{equation}\tag{1}F=\frac{1}{4\pi\epsilon}\cdot\frac{q_1q_2}{r^2}\end{equation} $$ $4\pi r^2$ factor in the denominator expresses directly ...
2
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2answers
3k views

Newtonian gravity equation in a 2 dimensional world [duplicate]

I am wondering if my line of thought is correct - and thus the resulting answer to the problem above would be correct. As we know the gravitational force (of two point masses) is given by $$F = G\...
36
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5answers
5k views

Why are so many forces explainable using inverse squares when space is three dimensional?

It seems paradoxical that the strength of so many phenomena (Newtonian gravity, Coulomb force) are calculable by the inverse square of distance. However, since volume is determined by three ...
5
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4answers
11k views

Electric field and electric potential of a point charge in 2D and 1D

in 3D, electric field of a piont charge is inversely proportional to the square of distance while the potential is inversely proportional to distance. We can derive it from Coulomb's law. however, I ...
3
votes
1answer
193 views

Scaling of Static Electric Field

The electric field of a point charge goes like $\displaystyle\frac{1}{r^2}$ The electric field of an infinite line goes like $\displaystyle\frac{1}{s}$ The electric field of an infinite plane is ...
71
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6answers
6k views

Does Coulomb's Law, with Gauss's Law, imply the existence of only three spatial dimensions?

Coulomb's Law states that the fall-off of the strength of the electrostatic force is inversely proportional to the distance squared of the charges. Gauss's law implies that a the total flux through a ...