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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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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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What is the true definition of Gauss law? [closed]

i found a question where there was a ring uniformly charged and a charge away at axis. i want to know the electric field at a point d distance away from centre it was an mcq where the answer confused ...
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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 ...
Quantum Wonder's user avatar
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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 ...
CuSO4 NaOH's user avatar
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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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Question on electric flux (jee advanced) [closed]

I am unable to find the necessary symmetry in the figure in order to find flux through this surface...please share your solutions @johnrennie
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Understanding of flux [closed]

Q1. The question: to find flux through a “half sphere with top cut off” (closed surface) with point charge at sphere’s center For this question- flux as I understand it is the number of field lines ...
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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 ...
Charu _Bamble's user avatar
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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 ...
Alok Jha's user avatar
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Gauss law and spherical cavity [closed]

Q) In a solid uniformly charged dielectric sphere where charge is uniformly distributed through the volume exept the cavity find the flux through any point P inside the cavity and also find the ...
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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 ...
Kshitiz Katiyar's user avatar
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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 ...
Madly_Maths's user avatar
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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:
petit beauté's user avatar
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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 ...
MathSolver's user avatar
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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?
ARYAN KUMAR PANDEY Class 12th 's user avatar
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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/...
佐武五郎's user avatar
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2 answers
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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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Why is the differential form of Gauss's Law equivalent to the integral form?

I can understand the Differential form of Gauss's Law ∇⋅𝐄= $\frac{ρ}{ɛ_0}$ as saying that the source of electric field vectors or flow disperse(The divergence of the electric field) is equal to the ...
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Uniform electric field. Find the flux of this field through a square side of 20 cm, parallel to the $y$-$z$ plane?

A uniform electric field has: $$\bar{E} = 2 \times 10^3 \ \hat{i} \ \ \mathrm{N/C}$$. Find the flux of this field through a square side 20 cm, whose plane is parallel to the $y$-$z$? I'm fairly new ...
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Volume Distribution of Bound Charge in an Isotropic Dielectric: when does $ \nabla \cdot \vec{E }=0$?

In Electricity and Magnetism by Bleaney & Bleaney (3rd Ed.) pg 18 they state: In a dielectric where $ \chi_e $ (the susceptibility) is uniform, isotropic and independent of field strength there ...
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Electric potential inside a conductor due to a point charge outside the conductor

I am a highschool student. I recently learned about conductors with cavity in school. How does a point charge outside the cavity, kept at a certain distance from the conductor, affect the potential of ...
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Understanding Gauss' Law on Charged Sheets and Oppositely Charged Plates

I'm grappling with understanding Gauss' Law as applied to charged sheets and oppositely charged plates. From what I've gathered, when using a Gaussian pillbox encompassing both sides of an infinite ...
Tom Cajot's user avatar
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1 answer
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Field due to an infinite sheet of charge with dielectric on one side

Suppose you have a surface charge density $\sigma$ on a conducting plane $z=0$. The region $z<0$ is filled with a dielectric of permittivity $\varepsilon$. What is the field everywhere? I tried ...
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General Formula for electric flux

I've noticed that most of Physics 2 courses highlight the fact that the surface is closed before giving the electric flux formula. Is the following formula only valid for closed surfaces? If yes, are ...
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How does the electric field behave at the surface of a realistic conductor?

So I am taking my University Electromagnetism course and we are currently learning about gauss's law and gaussian surfaces. A common question involves point charges inside of a hollow sphere that has ...
William Banquier's user avatar
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Electric fields around plates of charge vs sheets of charge, and then made into a capacitor

I've read over several other discussions on the topic of "electric field of a sheet of charge vs electric field of a charged plate", on this very site, but I still haven't gotten the answer ...
Brian Ellis's user avatar
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Factor of 2 discrepancy in electric field on the surface of a uniformly charged spherical shell

I recently came across this topic in electrostatics and saw derivations using Gauß's law of how the electric field on the surface of a uniformly charged shell is: $$|\vec E|=\frac1{4\pi\varepsilon_0}\...
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Electric field due to bound charge on surface of dielectric material

I got stuck on a step in Example 4.8 of Griffiths. It places a charge $q$ a distance $d$ above an infinite linear dielectric material. The Problem It states the the field due to the bound charge $σ$ ...
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Field outside a hollow conductor

Feynman shows in his Lectures on physics, Volume 2, Section 5.10 that in a hollow conductor there can be no electric fields inside the cavity. But he also says that no static charge distribution Q ...
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Actual definition of electric flux [duplicate]

I am currently studying electrostatics and I've come across confusing definitions of electric flux. One definition is the number of field lines crossing a surface. However, I have a hard time making ...
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6 answers
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Derivation of Coulomb's law from Maxwell's equations

I'm trying to find sufficient additional conditions to derive Coulomb equation for the electric field generated by a steady point charge in free space from Maxwell equations in said conditions. I know ...
Lorenzo Vanni's user avatar
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4 answers
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Charge distribution and voltage

The dependence of the electric potential can be obtained from Poisson equation and in one dimension is, $$ \nabla^2 V(x)=-\frac{\partial \mathrm{E}}{\partial x}=-\frac{\rho(x)}{\epsilon \epsilon_0}, $$...
Tomi's user avatar
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Gauss law does not look right for a flat volume

When thinking of gauss laws, it states that the net outflow of the electric field through a closed surface is proportional to the enclosed charge. This for the most surfaces is understandable, but not ...
Niclas's user avatar
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2 answers
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Does the divergence theorem imply an underlying symmetry?

The divergence theorem connects the flux (through surface) and divergence (in a volume) for any vector field. This theorem expresses continuity. It isn't clear (to me) whether there is a conserved ...
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How do we realistically calculate the monochromatic flux of an object in space?

If the collecting area of a telescope is ∆A, and it collects light for a time interval of ∆t, do we just build a telescope with a very small ∆A and make ∆t and ∆λ very small as well? Also, how do we ...
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Do conductor plates encloising charged particles exert a force on one another due to the charges induced on them? How to calculate in a 1D model

I would very much appreciate some guidance on the below. Consider a one-dimensional world as depicted in the attached figure. We have two (lets say positively charged) particles enclosed by two ...
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