Questions tagged [gauss-law]
A law in classical electromagnetism and Newtonian gravity which relates (charge) density to the divergence of a field, or alternatively the charge in a volume to the flux through the bounding surface.
221
questions
11
votes
2
answers
3k
views
Why $1/r^2$ and not another power of $r$ in Newton's law of gravitation?
My book introduces the force of gravitation as a non-contact force between two bodies of mass $M_1$ and $M_2$ separated by a distance $r$ . Then it says it is directly proportional to the product of ...
user36790
9
votes
2
answers
2k
views
Is Gauss's law wrong, or is it possible that $\int_s{\vec E} \cdot d\vec{s}=0$ does not imply $\vec E = 0$?
This is a question from David J Griffith's Introduction to Electrodynamics.
A specified charge density $\sigma(\theta)=k\cos(\theta) $ is glued over the surface of a spherical shell of radius $R$. ...
- 2,000
9
votes
1
answer
8k
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 ...
9
votes
5
answers
8k
views
Why is electric field of an infinite plate constant at all points?
I know from Gauss law, it is $\vec{E}=\dfrac{\sigma}{2 \epsilon_0}(\hat{n})$ at all points. But it doesn't make sense because of the inverse square nature of electric field which suggests if you move ...
- 772
7
votes
3
answers
2k
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 ...
- 784
6
votes
4
answers
11k
views
Infinitely charged wire and Differential form of Gauss' Law
I have tried calculating the potential of a charged wire the direct way. If lambda is the charge density of the wire, then I get
$$\phi(r) = \frac{\lambda}{4 \pi \epsilon_0 r} \int_{-\infty}^\infty \...
- 214
6
votes
4
answers
11k
views
Electric Flux - What is the point?
Electric flux is a defined quantity that is proportional to the no. of field lines passing through a given area element for a given electric field. It is not proportional to the relative density of ...
4
votes
2
answers
2k
views
Gauss' law and an external charge
Gauss' law states that the net outward normal electric flux through a closed surface is equal to $q_{total, inside}/\epsilon_0$. However, I'm a bit confused of why the presence of an external charge ...
- 685
4
votes
1
answer
3k
views
Gravity force strength in 1D, 2D, 3D and higher spatial dimensions
Let's say that we want to measure the gravity force in 1D, 2D, 3D and higher spatial dimensions.
Will we get the same force strength in the first 3 dimensions and then it will go up? How about if ...
- 75
4
votes
2
answers
8k
views
Electric field inside a conductor and induced charges
My textbook says two different things and I'm not sure how to reconcile these two:
electric field inside a conductor is always 0.
for a conductor with a cavity with a charge q inside it, the field ...
3
votes
1
answer
294
views
Formal Connection Between Symmetry and Gauss's Law
In the standard undergraduate treatment of E&M, Gauss's Law is loosely stated as "the electric flux through a closed surface is proportional to the enclosed charge". Equivalently, in differential ...
- 130
3
votes
3
answers
11k
views
Electric flux due to external charge
Why is electric flux due to external charge i.e a charge outside a closed surface equal to 0?
P.S:Moreover I found this statement confusing:-
Electric field appearing in the Gauss' law is the ...
- 897
3
votes
1
answer
29k
views
Charge inside conductor
I know that the $E$ field inside a conductor is zero. What happens if I put a source of charge inside the conductor?
Say the conductor was spherical centered on the origin and there exists a charge ...
- 3,569
2
votes
1
answer
570
views
Gauss's law not making sense
If we have a point charge and outside of it we have a non-conducting Gaussian sphere, then Gauss's law says that the net flux should be zero. I agree that the total field lines coming in are equal to ...
- 221
0
votes
1
answer
294
views
Electric field inside conductor with a cavity
Suppose I have a neutral spherical conductor with a cavity inside. Suppose there's a $+q$ point charge inside the cavity.
I know that the electric field $\vec{E}$ is zero within the conductor, also ...
- 15