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.
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Contradiction about electrostatic equilibrium following Gauss' Law [closed]
Confusion about Gauss' Law for electrical electrostatic equilibrium
My textbook says if there is an external charge, then a conductor will have 0 net charge anywhere inside it, because for any point ...
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Does the force of gravity equation include only one dimension?
Been in a debate with someone who is claiming the force of gravity equation describes three dimensions. I was under the impression there is only one dimension relevant in the equation, that being the ...
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What counts as the Earth's mass? At which point would it increase or decrease?
I get that gravity depends on the mass of an object: more mass = higher gravity. But over time humans have been doing stuff to the total amount of stuff on the Earth due to space travel. At which ...
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How to use this 'charge exist radially' information to find vale of k [closed]
I tried to solve this in Cartesian co-ordinate system but couldn't not solve it. Then tried solving in polar coordinate system. I'm getting n as -1/6 but give is 0(zero).
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Coulomb atraction inside a charged sphere
There is a hollow metallic sphere, positively charged. And inside of it there is a much smaller sphere, negatively charged. The question is: will the walls of the bigger sphere attract the smaller ...
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Why does gravity obey an inverse square law? [duplicate]
I am reading Martin Rees' Just Six Numbers, and came across this paragraph, where the author explains why a three-dimensional universe implies an inverse square law.
I understand the argument, but my ...
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Why doesn't mass accumulate on surfaces like charge does?
When calculating the total charge of a body, one should not only take into account the charges inside it but also those located on its surface, such that:
$$Q=\int_V\rho dV + \int_\Omega\sigma dA$$
...
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Why electric field inside a hollow sphere on points except centre is 0? [duplicate]
Why electric field inside a hollow sphere on points except centre is 0
I got the explation through the gauss law but I can mannually see at points except centre the field is non zero
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Gauss law, gauge and global symmetries
I am reading Witten's paper on the confinement/deconfinement phase transition in $\mathcal{N}=4$ $\mathrm{SU}(N)$ SYM theory. I am a bit stuck at section "Confinement" at Finite Volume, page ...
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Can field effect transistor s channel s varying depletion layers generate electric flux and control output current indirectly
Since magnetic field lines without need of contact attracts iron filing and drag them closer so that magnetic field line remain smallest.same analogy applied to field effect transistor ions in the ...
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Electrostatic potential outside of a charged ball [closed]
To preface, I have never solved Maxwell's equation or his resulting Poisson's equation in any coordinate scheme, nor am I a physics major. I'm entirely teaching myself how to do this, so I don't know ...
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Does the geometric shape of the cross-section of an infinitesimally thin conducting charged thread (wire) affect its electric field?
Assume that a solid conducting torus (toroidal ring), with a cross-section of a circle of (minor) radius $r$, is negatively charged. Solving Poisson's equation, we can find the charge distribution of ...
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How does this proof of Gauss’ law generalize from $1$ to $n$ charges?
I am having trouble seeing how the proof of Gauss’ law for one charge generalizes to hold for multiple charges in Griffiths’ introduction to electrodynamics.
Gauss’ law is proved for one charge (for ...
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Derivation of the Noether current (Gauss law operator) in anomalous chiral gauge theory
I am reading Fujikawa-Suzuki's Path Integrals and Quantum Anomalies, §6.3. The Lagrangian I am looking at is
\begin{equation}
\mathcal{L}=-\frac{1}{4g^2}\left(\partial_\mu L_\nu^a-\partial_{\nu}L_\mu^...
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Why is flux of magnetic field always zero for closed surfaces?
I'm having troubles accepting that the magnetic flux through a closed surface is always zero. I understand the fact that no magnetic monopoles exist , therefore all the 'lines' of magnetic flux that ...
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Does cutting out the surfaces with no surface charge affect the charge distribution on the remaining parts of a conducting surface of arbitrary shape?
Assume that we have an arbitrary conducting surface being charged positively/negatively. Also, assume that we have extracted charge distribution by solving the Poisson's equation with proper boundary ...
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Total charge within a sphere
Consider an electric field in free space with
$$
\mathbf {D} = -3z\mathbf {a_r} μCb/m^2
$$
I need to calculate the total charge within a 3mm sphere centered at (0,1,1).
I calculate the charge ...
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Induced charge on conducting sphere sliced by a plane
We are given a conducting solid sphere, and it is cut by a plane as shown.
A charge $Q$ is given to the smaller part of the conductor, and it is required to find the induced charge on the surface of ...
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Can the $r^2$ in gravity be seen as signifying the distance of object 1 to 2 times distance from object 2 to 1 [closed]
If the formula for gravity multiplies the mass in the numerator and the distance in the denominator is this akin to saying the multiplied masses over the multiplied distances times the gravitational ...
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Gauss's Law vs Image charges
Consider a grounded shell of radius $R$, inside is a point charge $q$ at a distance $a$ from the centre. Now, this charge would induce an amount of charge $-q$ on the conductor, whose field would be ...
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Total charge on a polarized neutral dielectric
I'm going through Griffith's EM book right now and from problem 4.14 we can see that the total charge on a polarized neutral dielectric is 0 (since it is neutral) the polarization may move around some ...
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Why do multiply electric field by the area? [closed]
I have a question about why we multiply e field by the surface area. When finding the total of something in a given area we need to take how much there is in one unit and multiply it by the area. If i ...
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Confusion regarding a statement regarding conductors [duplicate]
While discussing conductors, our lecturer told us that,
UNDER ELECTROSTATIC CONDITIONS, electric field is zero in the "meat" of the conductor.
Using this assumption (and using Gauss law), ...
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Does the distance between two objects of mass not matter when measuring strength of gravity in one-dimensional space?
From all that I have heard about Newton's Law of Universal Gravity, one fact, which I find quite interesting, is that the distance between the two objects of mass is squared and not cubed due to our ...
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Charged plate between two different dielectrics
Imagine a charged plate, placed in between two DIFFERENT dielectrics of susceptibilities $\chi _1\:and\: \chi _2$ .
From Gauss's law, We can conclude that the sum of the magnitude of the electric ...
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Why does the electric field only depend on the rod?
In the following exercise:
We are asked to calculate the electric field at a certain distance from an exis where a rod is located. Previously, we are asked to calculate the charge density a ...
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How does space charge stop a Geiger discharge?
It seems common in the literature (e.g. McGregor and Shultis) to say that the accumulation of space charge from positive ions around the anode wire lowers the electric field below the critical field ...
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Series Solution of Laplace Equation in Spherical Coordinates
I was recently Studying Griffiths Electrodynamics after a long time and there I saw the Laplace equation. Because it was my second time going over Griffiths so I thought maybe I should try to derive ...
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Are there exceptions to Gauss's law?
The textbook I am reading claims that Gauss's law is a fundamental law of nature, however is that really true? For example, would it hold up if inside the closed surface there was a negative charge ...
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Uniqueness Theorem and boundaries conditions
I was recently studying Jackson Electrodynamics and faced some issues directly. I have studied Griffiths Electrodynamics and I knew about the uniqueness Theorem from it. But in Jackson, they proved it ...
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When should we use $\sigma/\epsilon$ and $\sigma/2\epsilon$? [closed]
I was doing a question, in this i have to find distance between proton and plate.. so i use work energy theorm ie change in ke is net work done..
so as for electric field i use gauss law and taken ...
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What is the flux associated with the flat surface of a uniformly charged hemispherical shell?
Let us assume a uniformly charged hemispherical shell with net charge $Q$ uniformly distributed over the curved surface of the shell.
Now charge density $= σ = Q/2πR^2$
Now I wish to find out the flux ...
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What is the difference between conducting and non-conducting shells in electrostatics?
I've been taught electric field lines do not exist inside the volume of the conductor. An internal field is created inside its volume which cancels the external field, hence suggesting the net charge ...
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Plane angle subtended by a segment at a point such that the line joining the point to the segment is not perpendicular to it
I am studying a chapter on Gauss's Law from Concepts of Physics - Volume 2 by HC Verma. There is a discussion about the notion of a solid angle in the chapter. While going through it, I encountered a ...
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Unable to derive electric field of uniformly charged hemispherical shell using gauss law [closed]
I followed the below methodology to arrive at an answer,
Let the net charge on the hemispherical shell of radius $r$ be $Q$, then
Surface charge density = $Q/2πr^2 = σ$
Now, let us assume a spherical ...
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$\int \vec{E} \cdot \vec{dA} = (E)(A)$?
I've seen this kind of simplification done very frequently in Gauss's law problems, assuming E is only radial and follows some "simple" geometry:
$$\oint\vec{E}\cdot\vec{dA}=\frac{Q_{enc}}{\...
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Why are all the Gaussian surfaces very long or infinite?
I want to know why every Gauss's law question starts with an assumption that a rod, cylinder, plane, etc. is very/infinitely long.
Examples:
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Why is the cylindrical Gaussian surface constructed inside the cylindrical shell? Doesn't it enclose no charges?
I have looked up all the lectures, articles, and stackexchange questions for the last 2 hours and am still having difficulties understanding the cylindrical Gaussian surface constrcuted inside a ...
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Potential difference between two non-grounded equipotential plate
I am attempting to solve for the potential difference between two non-grounded equipotential plates using Poisson's PDE. The relevant Maxwell equation considered is $∇⋅E=\rho$, where $E$ represents ...
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Deriving everything from Gauss Law [duplicate]
I have a doubt in electordynamics,
I was learning Electrodynamics (last major topic) ,
and I learned about Maxwell's Equation, which can explain everything in Electrodynamics (actually according to my ...
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Where does $4\pi$ come from in electromagnetism?
We know that in Coulomb's law, the constant $k_e$ is $\frac{1}{4\pi \epsilon_0}$. Where does $4\pi$ come from? Why is it related to the force between two charges?
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Why is the electric field inside a conducting filled/hollow sphere is zero? [duplicate]
why is the electric field inside a conducting filled/hollow sphere is zero, when a charge emits electric field lines radially?
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Equation of a equipotential surface
I have been trying to find a equation for the equipotential surface of a dipole , so I started with a simpler system of a singular charged particle , here are few things I know about the equipotential ...
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How do I calculate the flux passing through a closed cone (with charge placed at vertex) with Gauss Law?
I know that for a point charge placed at the vertex of a cone, the formula for flux passing through the (closed) cone will be equal to :-
$\phi$ = $\frac{q}{2\epsilon_0}\times[1-cos\theta]$ where $\...
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Do electric field lines exist inside a charged conducting shell of infinitesimally small thickness?
A conducting shell, on the inside, is hollow and by using gauss law we calculate the electric field inside the shell. While using gauss law we use flux = charge inside / permittivity of free space = ...
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Doubt regarding proof of Earnshaw's Theorem using Gauss's theorem
While proving Earnshaw's theorem using Gauss's theorem, we consider a small sphere surrounding our test charge, and apply Gauss law on this sphere, stating that field from all external charges must ...
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Why charges reside only on the surface on conductor?
I wonder why charges reside only on the surface on conductor?
And I read this question and the answer to it:
Why charges reside on the surface on conductor?
https://physics.stackexchange.com/a/210634/...
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Wrong solution for Green function of one-dimensional Poisson equation
An old electrodynamics exam question asks:
"Find the Green function (for the one-dimensional Poisson equation) that solves the equation
$$
\frac{d^2}{dx^2}G(x,x') = -\delta(x-x').
$$
Choose the ...
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Problem with one of the premises in electrostatic pressure theory
I was watching a video and he was trying to derive a result in electrostatic pressure. He was deriving the pressure on a differential area element of a hollow conducting sphere. He did it two ways, ...
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What exactly does charge density mean in Gauss's law?
I am familiar with Gauss's law, how it can be derived and, and how it can be applied (when in integral form)
$$\nabla \cdot \mathbf{E}=\frac{1}{\epsilon_0} \rho$$
But I do not feel I really understand ...
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