Linked Questions

8
votes
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 ...
3
votes
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 ...
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 ...
2
votes
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?
2
votes
1answer
450 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 ...
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}...
1
vote
1answer
143 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 ...
1
vote
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 ...
1
vote
1answer
208 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 ...
0
votes
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 ...
0
votes
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 ...
-1
votes
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 ...
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 ...
1
vote
0answers
681 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 ...
0
votes
0answers
100 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.

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