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### 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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### 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 ...
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### 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.
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### 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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### 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.
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### 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 ...
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### 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 ...
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### 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 ...
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### 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. ...
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 $$\nabla^2\frac{q}{r}~... 4answers 26k views ### The relation between Gauss's law and Coulomb law and why is it important that the electric field decrease proportionally to \frac{1}{r^{2}}? My question relates to the third MIT's video lecture about Electricity and Magnetism, specifically from 21:18-22:00 : http://youtu.be/XaaP1bWFjDA?t=21m18s I have watched the development of Gauss's ... 1answer 6k views ### Deriving Coulomb's Law from Gauss's Law I've been thinking about this for the past couple of days. I apologize if my explanation isn't very clear. I have already seen derivations of this, but I'm still not satisfied. In the derivations of ... 4answers 2k views ### If you could ride an elevator through the earth [duplicate] What if it was possible to ride an elevator straight through earth. If we take all the heat and pressure problems away, and assume it would be possible: What would happen with gravity? Would gravity ... 1answer 8k views ### Zero divergence of Electric field I'm trying to rigorously derive the integral form of Gauss's law from Coulomb's law and the divergence theorem. Arrive at$$ \oint\limits_{\partial V} E\cdot da = \begin{cases} \frac q\epsilon_{o}...
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 ...