Linked Questions

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1answer
25k views

What is the proof for Gauss's law? [duplicate]

What is the proof for Gauss's law? Can you give me some explanation and details with the proof?
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0answers
665 views

How to prove Gauss's law div(E) = rho/epsilon from Coulomb's law? [duplicate]

As we know from coulomb's law that: $$\vec{E} = \frac{q}{4\pi\epsilon R^2} \hat{R}$$ using the above equation, how can I verify that: $$\vec{\nabla}\cdot \vec{E}=\frac{q}{\epsilon}$$ I have tried to ...
-1
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3answers
140 views

How to prove Gauss law geometrically (without coordinates) from Coulomb's law? [duplicate]

Namely that the Flux of the electric field through any surface equals the charge enclosed/vacuum permittivity. Without any coordinates or reference to axis.
1
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1answer
139 views

Gauss' Law Generalization to all closed surfaces [duplicate]

I'm currently in an introductory physics class, and we've learned about Gauss Law defining the flux as $$\int d\phi = \oint EdA = \frac{q}{\epsilon_0} $$ and from what I understand the way to arrive ...
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0answers
99 views

Proof of Gauss' Law [duplicate]

How would you prove Gauss' law for an asymmetrical closed surface? I can find it for symmetrical surface but couldn't for Asymmetrical surfaces.
0
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1answer
62 views

Electrostatics and Gauss law [duplicate]

How can we prove that surface integral of the electric fieldfor a point charge that is outside a gaussian surface, $$\int\mathbf E\cdot\,\mathrm d\mathbf S,$$ without actually using the concept of ...
0
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1answer
41 views

Can Gauss Law for any arbitary closed surface be derived from Coulomb's Law? [duplicate]

As far as I know, Gauss' Law is useful for calculating the electric field where Coulomb's Law doesn't work. For example, it is used for calculating the field produced by a thin sheet of charge and ...
1
vote
0answers
35 views

Derivation of Gauss' Law of Gravitation [duplicate]

this question is simple, I was looking for a good derivation to Gauss' Law of gravitation $$\int \vec g.d\vec A=-4\pi GM $$ but was unable to find a good enough one online. Hence may I know its ...
22
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4answers
55k views

Divergence of a field and its interpretation

The divergence of an electric field due to a point charge (according to Coulomb's law) is zero. In literature the divergence of a field indicates presence/absence of a sink/source for the field. ...
13
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5answers
6k views

Laplacian of $1/r^2$ (context: electromagnetism and Poisson equation)

We know that a point charge $q$ located at the origin $r=0$ produces a potential $\sim \frac{q}{r}$, and this is consistent with the fact that the Laplacian of $\frac{q}{r}$ is $$\nabla^2\frac{q}{r}~...
3
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4answers
27k views

The relation between Gauss's law and Coulomb law and why is it important that the electric field decrease proportionally to $\frac{1}{r^{2}}$?

My question relates to the third MIT's video lecture about Electricity and Magnetism, specifically from $21:18-22:00$ : http://youtu.be/XaaP1bWFjDA?t=21m18s I have watched the development of Gauss's ...
8
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1answer
6k views

Deriving Coulomb's Law from Gauss's Law

I've been thinking about this for the past couple of days. I apologize if my explanation isn't very clear. I have already seen derivations of this, but I'm still not satisfied. In the derivations of ...
6
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4answers
2k views

If you could ride an elevator through the earth [duplicate]

What if it was possible to ride an elevator straight through earth. If we take all the heat and pressure problems away, and assume it would be possible: What would happen with gravity? Would gravity ...
2
votes
1answer
8k views

Zero divergence of Electric field

I'm trying to rigorously derive the integral form of Gauss's law from Coulomb's law and the divergence theorem. Arrive at $$ \oint\limits_{\partial V} E\cdot da = \begin{cases} \frac q\epsilon_{o}...
2
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2answers
5k views

Why does Gauss's law work for a charge off center in a spherical surface?

CASE 1: Consider an enclosed spherical surface with a charge $q$ at its centre. From Gauss' law we can say that the flux through this sphere is $q/\epsilon_0$. CASE 2: The charge is inside but off ...
-1
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1answer
3k views

Why is electric flux through any closed surface $q/\epsilon_0$?

Why is electric flux through any closed surface $q/\epsilon_0$? In schools we are only taught of its simplest case, i.e. flux through a sphere with charge centered at origin. And then it is ...
3
votes
3answers
2k views

What does the Dirac delta function physically do while deriving Gauss Law form Coulomb's law?

While doing this derivation, the the source coordinates are mentioned as "$s$" and the coordinate of the point at which field is to be calculated is mentioned as "$r$". Kindly follow this Wikipedia ...
1
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1answer
3k views

Surface density charge, divergence of the electric field and gauss law

It´s known that the divergence of the electric field at a certain point is given by this formula: $$\nabla \cdot E=\dfrac{\rho (r)}{\epsilon_{0}}$$ Being $\rho (r)$ the volume charge density at that ...
3
votes
1answer
2k views

Rigorous proof of Gauss' law for an arbitrary charge distribution from Coulomb's law

Most of the books about electromagnetism prove Gauss' law for a point charge in vacuum: $$ \Phi = \int_{\Sigma} \mathbf{E} \centerdot d \mathbf{S} = q/\epsilon_0 $$ and then simply state that for ...
1
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2answers
1k views

Proof that flux through a surface is independent of the inner objects' arrangement

$$\Phi=\iint_{\partial V}\mathbf{g} \cdot d \mathbf{A}=-4 \pi G M$$ Essentially, why is $\Phi$ independent of the distribution of mass inside the surface $\partial V$, and the shape of surface $\...
2
votes
1answer
447 views

Is it equivalent to derive Gauss's law from discrete and continuous source distributions?

I've seen two derivations for Gauss's law in electrostatics. The first assumes a discrete charge distribution, the second a continuous one: Use superposition $$\vec{E}=\sum_{i=1}^n\vec{E}_i,$$ so ...
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1answer
207 views

Regarding the proof of Gauss's law

I know that this question has already been asked multiple times but I´m still not getting on the mathematical details behind the answers... So I hope that this question doesn´t get closed. First I ...
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2answers
116 views

Derivation of Gauß' Law

I am reading a book about special relativity and the author derives Gauss law the following way: $$\int_{S_R}E\dot{}d\textbf{S}=\frac{q}{4\pi R^2\epsilon_0}\int_{S_R}dS=\frac{q}{\epsilon_0}$$ (where $...
3
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1answer
84 views

Prove that external charge has no net flux on a gaussian surface mathematically

I understand how the field lines enter and leave the gaussian surface. But my concern is that the field isn't constant everywhere on the gaussian surface, i.e, there exactly doesn't exist an $- E\cdot ...