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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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Electric flux of a cube with charge at the center [on hold]

I've known gauss' law that any closed surface with some net charge inside, the electric flux would be q/ε0 , but some professor told us that a cube cannot be a gaussian surface and that the electric ...
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Electric field due to an infinite plane slab

So the solution says that in the x z plane, E = 0 by symmetry that is my problem, how is E = 0, maybe I can't visualize it correctly, however if I assume that that's really the case, I can continue ...
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Electrostatics: Charge Distribution and Energy - Confusion

Consider the following situation: Between two metallic plates, are two dielectrics of dielectric constants $K$1 and $K$2. The surface charge density on the upper metallic plate is $\sigma$, and that ...
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Can $E=\frac{q}{4\pi\epsilon_0 r^2}$ be directly derived from differential form of Maxwell equations?

The electric field of a point charge $q$ is well known to be $$\mathbf E=\frac{q}{4\pi\epsilon_0 |\mathbf r|^3}\hat{\mathbf r}$$ This can be derived easily from integral form of Gauss’s law. Taking $...
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Notion of flux and field lines

I am curious about the origin of electric flux and field lines. -Flux- I am aware of the fact that flux is a mathematical concept, but how did it find its way into physics? Was it just introduced ...
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Closed field lines in case of a Bar magnet

Field lines in case of charges go from +ve to -ve but incase of magnet, they dont start or stop anywhere. They form closed loops. Is this consequence of the fact that single poles dont exist or ...
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Property of surface Green function in electrostatic field

Let's consider a 2D-square with 4 equal subsquares containing different dielectrics. Inside the square domain, the unknown electric potential function $\Phi$ satisfies the Laplace equation: $$\nabla^...
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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 ...
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Electric Field between two parallel plans of opposite charge density

So considering two infinite parallel plans of opposite charge density let's say +σ for the left plan and -σ for the right plan Why is the electric field calculated this way : $$ E = σ/2εo + σ/2εo ...
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Why the integral of Berry curvature over a closed surface is not zero?

I read [1,2] that for a spin-1/2 particle under magnetic field, the Berry curvature is a monopole, $$ \mathbf F_{\pm} = \mp\frac{\mathbf B}{2B^3}, $$ of which the integral over a closed surface is $2\...
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Confusion in deriving Gauss law for magnetism

I am deriving Gauss law for magnetism from Coulomb's law of magnetic poles. I have a cubical magnet as shown below and the Gaussian surface is inside the magnet: The magnet can be considered as a ...
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Gauss Law For Electrostatics [duplicate]

In Gauss Law for Electrostatics, Electric flux term contains Electric field due to charges that are both inside and outside the Gaussian surface. If we use Gauss Law to calculate electric field at a ...
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Two dimensional hyperbolic potential has no charge density but a surface charge density?

I am learning about electric potential, and I am confused about what exactly is going on in the following situation: Say we have a potential $V =- V_0 \frac{xy}{a^2}$ This means that $\nabla^2V=0$. ...
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Electric potential everywhere around an infinite slab

The problem: Consider an infinite slab with uniform charge density $\rho$ between two planes $z=\frac{d}{2}$ and $z=-\frac{d}{2}$. Find the electric potential $V$ in the entire space and plot $V$ ...
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I'm confused about electric flux?

In a previous physics class, I learned that the electric flux was $\vec{E}\cdot\vec{A}$ (dot product), and hence the unit is $Nm^2/C$. But in my electromagnetics book, it says the unit is Coulomb, and ...
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Flux through a cube of side length $l$

Let's say I have a cube sitting in the first octant with one corner at the origin and of side length $l=0.1$meters. The question from the text is as follows, "The electric field is uniform, has ...
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How to calculate the Electric field of an cylinder with length of infinity and given charge density of the surfac? [closed]

I know how to calculate the Electric field of this example if the given variable would be the charge density of the volume but since only the charge density of the area is given, I'm very confused ...
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Does a point charge inside a conducting shell cause redistribution of charge in the shell?

A point charge Q is placed inside a conducting spherical shell at a random place (non-centre). I have read that there is no force on Q from the shell no matter where Q is inside the shell ('there ...
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3answers
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Electric field of an infinite sheet of charge [closed]

I am trying to derive the formula for E due to an infinite sheet of charge with a charge density of $ \rho C/m^2$. I assumed the sheet is on $yz$-plane. I used Coulomb's law to get an equation and ...
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Space charge density of bound charges

This is a question from Irodov's Problems in General Physics. I can understand the physics but I think I am doing something wrong in the calculus. The problem is : Extraneous charges are uniformly ...
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2answers
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Proving electric field constant between two charged infinite parallel plates

It is known that the electric field intensity between two infinitely long charged parallel plates is constant. I had read that one explanation is that if a test charge is placed between the plates, ...
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Cavendish's experiment on concentric conducting shells

In a paper were there was a section addressing Cavendish's experiment on concentric conducting shells which was basically the following : Two conducting spherical shells were put together (like the ...
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How to derive Gauss' Law without divergence theorem or surface integral?

This is for a presentation I'm doing. So we know from Coulomb's Law, you can get $$E = \frac{Q}{4\pi r^2\epsilon_0}$$ We also know that $\Phi = E\Delta A\cos\theta$ where $\theta$ is the angle ...
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Generalization of the Gauss' Law to a lorentz-covariant law in Paper of Kobe: Is it “guessed”?

In the Paper Generalization of Coulomb's law to Maxwell's equations using special relativity by Donald H. Kobe, he tries to derive Maxwell's equations by trying to find covariant laws between tensor ...
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Can Newton’s law of gravitation be derived from Coulomb’s law? [duplicate]

I’m casually learning physics and have noticed that Newton’s law of gravitation and the electrostatic force formulas look similar. I’ve asked this question before but would really appreciate another ...
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Why is the constant of proportionality in Gauss's law exactly $1/\epsilon_0$

$\epsilon_0$ is epsilon naught, or permittivity of free space. Let me preface this by saying that I've just started to learn about electromagnetism. When I first saw Coulomb's law, I was incredibly ...
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Buoyancy: integrating over a region where the fluid isn't?

On both ProofWiki and Wikipedia, the article's respective authors manage to arrive at Archimedes' principle by applying the Gauss theorem to the surface integral of the fluid's stress tensor $\sigma$: ...
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Why there is a distance dependence in Coulomb's law if photons can travel to infinity?

Why there is a distance dependence in coulombs law if photons can travel to infinity? Why there is distance dependence at all?
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52 views

Flux is not coming zero, although charge inside it is zero!

In the figure, there are two capacitors connected in series. So, they have same charge on them. Since, the plates have same area, therefore they have same charge densities σ. Also, one capacitor have ...
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1answer
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What happens if I place a charge inside a hollow conductor and fix it? [duplicate]

So I know that when you put some charge inside a counter, it resides uniformly on the surface of the conductor in order to make the electric field zero everywhere inside the conductor.. But what if I ...
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Electric field in a spherical shell [duplicate]

Question mentioned like this find out the electric field inside and outside a spherical shell of radius r which carries a uniform surface charge density sigma. In the above question it is not ...
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Electric field generated by an infinite plane paradoxon

Every element of the distribution generates weaker electric field at a larger distancce. Although other arguments involving gauss' law or taking the limit of the field result it's constancy. How could ...
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Field inside a hollow sphere uniformly charged [duplicate]

How to prove that field inside a hollow sphere is zero anywhere inside that sphere using solid angle concept?
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592 views

Problem verifying Gauss's law

I am trying to verify Gauss's law, differential form, SI units, non-special relativity regime, ignoring time retardation, by performing the differentiation on the left-side of the equations to see if ...
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How gaussian surface and continous charge distribution overlap in 2D?

It is well known that Gauss's Law & Coulomb's Law are inter-dependent. Any violation of Gauss's Law will indicate departure from inverse square law and vice versa. Then how gaussian surface and ...
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2answers
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Is the gravitational potential a measurable physical quantity or an artifact of warped measures?

The Euler-Lagrange conditions for stationary points of $$L=m/2 v(\mathbf{\dot{x}})^2-U(\mathbf{x})$$ ($m$ is mass, $v()$ is velocity, $U()$ is the scalar potential, and the boldfaced arguments of ...
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Electrostatic force between half cylinder and dielectric plate

The problem is as follows: A half cylinder of radius $R$ and length $L>>R$ is formed by cutting a cylindrical pipe made of an insulating material along a plane containing its axis. The ...
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1answer
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Factor of 4 (or 2) in the gravitoelectromagnetic (GEM) Lorentz-force law. Which is correct? Why is it there?

I realize that the Gravitoelectromagnetic equations (GEM) are derived from the Einstein field equation (EFE) in the degenerate case of reasonably flat spacetime, which is the case for the propagation ...
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Applying Gauss's Law on a Non-Uniform Conductor [duplicate]

I've seen tons of examples of Gauss's Law applied to solve for electric field. However, the only shape its ever really applied to is a cylindrical or spherical Gaussian surface. I'm looking at a ...
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Why do we assume that Gauss' law of gravitation to remain same even when there are extra spatial dimensions?

Every kid knows that the magnitude of the gravitational force between two point masses is inversely proportional to the square of the distance $r$ between them i.e., $F\sim r^{-2}$. But experimentally,...
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Gauss's law on a stator winding (conductor)

I'm trying to perform Gauss's Law on a stator winding. Previously performing it on a circular conductor, is fairly simple. The goal for the circular conductor was to determine the electric field at a ...
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101 views

Charge distribution on Spherical conducting shells

For example we have very thin conducting spherical shells of radius R and 2R. Initially the smaller shell has Q and other shell has q charge of their own, now there will be charge induction in them ...
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How to derive Gauss's law for magnetism, $\nabla \cdot \vec{B}=0,$ if charge density is discontinuous?

I want to derive Gauss's law for magnetism,$$ \nabla \cdot \vec{B} = 0 \,.$$ The derivation in Griffiths Introduction to elecrodynamics uses$$ \nabla \cdot\vec{B} ~=~\frac{\mu_0}{4\pi} \int {\nabla \...
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1answer
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Is Gauss law applicable to image charges in electrostatics?

Take for instance the standard example with a charge in front (distance $d$ from middle) of a grounded conducting sphere of radius $a$. It is not hard to show that the relevant image charge will be $-...
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1answer
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Newton's “Shell theorem” in higher dimensions

In Newtons's shell theorem, the net gravitational force is zero inside a hollow sphere, if the gravitational force is proporional to $1/r^2$. In 2D, the net force is zero inside if the force is ...
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1answer
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Why does $\frac{1}{4\pi}$ appear in many formulas? [duplicate]

Why do most of the physical equations have $\frac{1}{4\pi}$ as constants? I have seen that many equations have $\frac{1}{4\pi}$ as constants like Coulomb, pendulum problems, etc. Can anyone tell me ...
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Gauss law in non-uniform electric field

I am trying to figure out how gauss law would hold in an electric field configuration that varies with space. For simplicity, let us assume the classic XYZ coordinate system. Consider an electric ...
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Confusion regarding Gauss law and capacitors

In book (Halliday Resnick Krane, 2nd Part, fifth edition), it's written that when you you put some charge in an isolated conductor, then within around $10^{-9}$ seconds the charges all go to the ...
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Boundary condition for electric field with addition of polarization

Comparing the boundary conditions for $E$ field and $D$ field, why does one of them E changes to D and the other E stays E? I am looking for physical intuitions, does it have to do with the direction ...
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Capacitors electic field

If we have the electric field on the surface of a conductor being $E=\sigma / \epsilon_0$ where $\sigma$ is the charge per unit area then why is the combined $E$ field from two parallel plates not 2x ...