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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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1answer
780 views

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

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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1answer
171 views

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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38 views

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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1answer
42 views

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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2answers
37 views

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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0answers
45 views

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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4answers
811 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 ...
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2answers
640 views

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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161 views

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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1answer
63 views

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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2answers
286 views

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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69 views

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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1answer
167 views

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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1answer
91 views

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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294 views

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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167 views

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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4answers
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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
1k views

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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2answers
477 views

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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1answer
147 views

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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1answer
131 views

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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4answers
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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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1answer
125 views

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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2answers
89 views

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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1answer
70 views

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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1answer
65 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
116 views

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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0answers
51 views

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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2answers
43 views

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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1answer
212 views

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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1answer
612 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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1answer
137 views

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
60 views

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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1answer
192 views

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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1answer
92 views

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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250 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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1answer
106 views

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
86 views

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
169 views

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
185 views

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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1answer
400 views

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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2answers
94 views

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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1answer
39 views

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 ...
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1answer
170 views

Charge Distribution on Conductor - Uniform or Not?

Consider a hollow conducting spherical shell S1 inside an irregularly shaped conducting wall S2 (in the figure). The sphere S1 is somehow given a charge +Q. Will the charge distribution on S1 be ...
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1answer
349 views

Gauss' Law and Symmetry

While reading my lecture notes about Gauss' Law, here's what I found: Gauss' Law is obeyed by a wider range of fields, than those represented by the electrostatic field. In particular, a field that ...
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0answers
249 views

Laplacian of electric potential in inhomogeneous media

I am confused about a problem on capacitance of a lossless inhomogeneous dielectric sandwiched between conductors. The permittivity of the medium is expressed as $\epsilon = \epsilon_0(1 + sin\theta)$...
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1answer
528 views

Electric flux through finite width/ infinitely long plane due to a point charge

The question is as follows: Consider a point charge Q placed at $(0,h,0)$ (Cartesian coordinates). Find the flux in an area formed by $y=0$, $z\leq0$, $x\geq l$ and $x\leq a$ $( l\leq x\leq a )$. I ...
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1answer
68 views

Finding the electric field when the sphere has multiple charges

In this case, in part (d), why is the charge -Q on the surface of the sphere not taken into account?