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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Net flux = No lines leaving - No lines entering

Consider the following statement I found in a physics book : "The net flux through the surface is proportional to the net number of lines leaving the surface, where the net number means the ...
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Charge on a conducting sphere

As far as I know, to have a net flex through a closed surface there must be a charge inside it. However, what if I have for example a conducting sphere where the charge accumulate on the surface, will ...
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Gauss's Law for planes

Why when we apply Gauss's Law on a conducting plane we choose the Gaussian surface to be a cylinder which one end of it is inside the conductor, whereas when we apply Gauss's Law on an insulating ...
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Tricky thought on Gauss's law

When the charge enclosed by a gaussian surface is equal to $q/2$ nought shouldnt the number of field lines be equal to half which does not make sense at all.
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Why the electric field inside a solid sphere is non-zero according to gauss while we know that the electric field inside a conductor is zero?

We know that the electric field inside a conductor is zero, but in my book, according to Gauss' law, the electric field inside a solid sphere (it's not mentioned if it's a conductor or non-conductor) ...
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Electric field due to a large, non-conducting plate and factors of 2

I'm trying to derive the electric field due to a single large, thin, non-conducting plate at a point (see figure). I'm solving it using 2 methods, and arriving at a different answer using both. I've ...
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Version of Olber's Paradox for gravity [closed]

Olber's Paradox is a famous problem in cosmology. In astrophysics and physical cosmology, Olbers' paradox, named after the German astronomer Heinrich Wilhelm Olbers (1758–1840), also known as the &...
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How did Gauss, Ampere and Biot-Savart derive their laws? [migrated]

Gauss' law for electricity and magnetism, Ampere's law and Biot-Savart's law — all of these laws are crucial for understanding electromagnetism and Maxwell's equations. But I want to know how each of ...
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How gauss law is not applicable here?

I am a high school student and I am very confused in how to use Gauss law, when we have to calculate electric field due to infinite sheet or wire, and for spherical surfaces, I know how we do that, we ...
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Help decipher the notation said to denote a common pattern in various branches of science in Prelude to Mathematics by W. W. Sawyer

In Section 1.2 - Nature's Favorite Pattern? (excerpted below) of Prelude to Mathematics by W. W. Sawyer (1982), he said mathematicians used the notation $\nabla^2 V$ to denote a pattern that occurs &...
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Purpose of A Closed Surface in Gauss's Theorem

Why is it necessary to consider a closed surface while dealing with Gauss's Law? From the mathematical point of view, it is pretty clear that since we need to calculate the area of the Gaussian ...
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Electric field inside a conductor using gauss theorem

The electric field inside a conductor is supposed to be zero, but if we take a hollow conductor and place a charge inside it, isn't an electric field present at point $P$ (through Gauss theorem)? So, ...
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Poisson equation of point charge using Fourier transformation

i have problems applying the fourier transformation. all these integrals confuse me. so here is my calculation: $$ \Delta\phi(r)=-4\pi\delta(r) $$ $$ \text{Left hand side}:-\frac{1}{(2\pi)^{3/2}}\int_{...
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Why the any point has uniform electric field outside the plate of dielectric of infinte area?

The uniform electric field $E_{0}$ has been existed through infinite area. As the infinite area dielectric plate is placed in the uniform electric field, the polarization occurs and the bound charges ...
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Field inside hollow sphere with gauss law

Gaussian surface of radius $r$ in a non-conducting charged sphere of radius $R$ By using gauss law with the gaussian surface depicted above we should get a result as follows: $$\int{E \cdot ds} = \...
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Gauss law and electric field

In the above image there are two charges kept away from a point P, electric field at point P is non-zero according to couloumbs law but is zero if we consider a gaussian sphere enclosing the charges. ...
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Potential inside a sphere using Poisson's equation

I have trouble calculating the potential of the inside of a hollow sphere (with radius $R_1,R_2$ and $R_1<R_2$) with the help of the poisson equation. When I'm trying do solve this differential ...
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Why is electric field independent of the surface?

I was studying about electric flux and Gauss' Law, and I saw the following case of a spherical surface And the form to solve the problem where I saw that is $$\begin{align*} \iint_S\vec{E}\cdot d\vec{...
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What is the number of electric lines of force originating from a charge of 1 Coulomb

This is a question from SL Arora, so don't bash me. My initial thoughts were "Number of Field lines? well it should be infinity, You can draw how much ever field lines you want" However the ...
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A strange electric field, can it exist? [duplicate]

If the electric field strength is $E_x=x, E_y=E_z=0$, then by $\nabla\cdot E=\frac1{\epsilon_0}\rho_e$ where $\rho_e$ is the density of charge, we get $\rho_e=-1$ for any point in the space. But if $\...
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4answers
104 views

Electric field inside a conductor non zero

I have a spherical conductor with a charge $+q$ place inside the cavity, now the charges redistribute as shown, If I apply gauss law where my guassian surface is such the $q$ inside is non zero now , $...
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What went wrong with the nuclear boy scouts breeder reactor?

If I recall correctly the Nuclear boy scout tried to build a breeder reactor but the experiment gave him radiation poisoning because the neutron emitter was to emitting to many neutrons. Does anyone ...
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A uniform electric field $\bar{E}$ penetrates a surface having the shape of a cylinder of radius $R$ [closed]

A uniform electric field $\bar{E}$ penetrates a surface having the shape of a cylinder of radius $R$ cut in half. The field lines enter perpendicularly through the base which has a flat rectangular ...
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1answer
42 views

Electric field between two parallel plates

In my class we derived an expression for an electric field due to an infinitely long plane of charge and it given as: $$\bf{E} = \frac{\sigma}{\epsilon_0}\hat{\bf{r}}$$ where $\sigma$ it is the ...
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Relation between flux through a cone vs through a disc due to a charge

Find the flux through the uncharged disc of radius R due to point charge '+q' at a distance x from the center of disc and on its axis. So I tried to solve this by gauss law. First I started by ...
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How to calculate Electric field due to an uniformly charged infinite sheet without Gauss Law?

Electric field due to an uniformly charged infinite sheet at a distance $x$, if we calculate using Gauss Law, is ${\bf \frac{σ}{2ε_0}}$. But, How to calculate the electric field without using Gauss ...
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Why is the electric field inside a conductor zero at every point?

There are a couple of arguments on how the electric field inside a conductor is zero. Some of them appear to me to be unreasonable; I will explain. Let's consider a charged conducting sphere. I ...
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Flux through a surface as a limit of shrinking volume [closed]

Two point charges $q$ and $—q$ are separated by the distance $2L$. Find the flux of the electric field strength vector across a circle of radius $R$. Now, I don't understand the answer given by the ...
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Gauss law for gravitation [closed]

Assume earth as a solid sphere of radius R with volume mass density K varies with radial distance as $P = P_or$. A tunnel is dug along the radius up to a depth $R/2$ and a body is projected from the ...
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Electric field flux through the cubic with surface density of charge [closed]

first of all I want you to excuse me for my level of English. I'm doing a homework on Gauss's law, specifically on how to calculate electric flux through a cubic surface. Below I put the complete ...
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Density of flux lines [closed]

In the given figure flux through surface $\,\rm S_1\,$ is $\,\Phi_1\,$ and through surface $\,\rm S_2\,$ is $\,\Phi_2$. Which option is correct? (A) $\quad \Phi_1\boldsymbol{=}\Phi_2$ (B) $\quad \...
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When do we use the formula $E=kQ/r^2$?

A cube of side 20 cm has its center at the origin and its one side is along the x-axis, so that one end is at x = +10cm and the other is at x = -10cm. The magnitude of electric field is 100 N/C and ...
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Compute the variance of the squared ratio of 2 observables with noise

I have to compute the variance of the squared ratio of 2 observables (here cosmological bias $b_1$ and $b_2$). The random variable represented by this squared ratio is noted "observable O". ...
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How to find the electric flux by a point charge place at an edge of an infinitely long triangular prism?

I know that the solution will require for us to either a)Use symmetry and somehow create a closed gaussian surface and then apply gauss' law or b)use geometry to find the portion of charge which can ...
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Gauss' law in matter and the macroscopic electric field

Is the $\mathbf{E}$ in this equation the average macroscopic electric field? $$\epsilon_{0} \nabla \cdot \mathbf{E}=\rho=-\nabla \cdot \mathbf{P}+\rho_{f}$$ If yes, then how does the average get into ...
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Eletric Field of a induced sphere

Suppose I have a conductor sphere, and a point charge at a distance x away from the center of the sphere. The sphere will be polarized, but what about it field lines of that sphere? Is zero? I would ...
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Paradox in 1D Gauss Law [duplicate]

If we assume a 1D world, then the divergence of the electric field would read $\nabla\cdot\vec{E} = \partial_xE_x$, since $\partial_yE_y = \partial_zE_z = 0$ in a 1D world. Therefore, Gauss Law reads $...
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Justifying Gauss Law in 1D

From Maxwell equations, Gauss Law read: $\nabla\cdot\vec{E} = \rho/\epsilon_0$ Integrating this divergence over some volume and applying the Divergence theorem leads to: $\int \vec{E}\cdot d\vec{S} = ...
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Conductor with two cavities

I am going through the last example discussed in this site which discusses a conductor having charge in two cavities inside as given by the following set up: The only rule obeyed is that when the ...
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Electric potential on a non-uniform distribution - hollow sphere

I've been trying to solve this problem: The electric potential on the surface of a hollow spherical shell of radius $R$ is $V_0 cos\theta$, where $V_0$ is a constant. In this problem we use spherical ...
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Cylinder gravitational potential

I have a question about infinite cylidner. I wanted to calculate a gravitational potential that it creates, but I've stumbled across some difficulties. From Gauss's Law we know, that force on an ...
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Does the electric field in 1D exist in nature?

This is a question related to: Electric field and electric potential of a point charge in 2D and 1D Let's study in more detail the 1D case. In the 3D case we integrate a sphere of radius $r$ and get $...
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What strategy should one use to solve this problem? [closed]

Is it possible to solve this using Gauss law choosing a cylinder around one of the plates or should I something else?
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Gauss law for positive charge densities

I am trying to write a PIC (Particle In Cell) code to simulate plasma physics. I am starting with the simplest case, which is a 1D system with a longitudinal field $E = E(x)$. I am using this article ...
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Electric field outside a full sphere

I'll glad for help how can be proven without using Gauss's law that the electric field outside a sphere with continuous charge distribution equals (when $Q$ is total charge of the sphere and $d$ is ...
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What conditions are necessary for an inverse square law of a quantity?

Explanations for why forces like gravity obey an inverse square law usually refer to flux lines which decrease in density $\propto \frac{1}{4 \pi r^2}$. However there are many other cases of ...
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Why is $ \text{div}(\vec{r}/r^3) = 0 $?

Let's begin with some context. I was reading Griffiths's introduction to electrodynamics. This makes sense given all the content one can find online in order to understand visually the divergence. ...
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Why the each endpoint has the same electric field at infinity as applying Gauss law of 2 plates?

The 2 conductive plates of infinite length have been placed as above . $\sigma_{1}:=\text{surface charge density of the left plate}$ $\sigma_{2}:=\text{surface charge density of the right plate}$ $\...
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1answer
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Determining the behavior of the electric field due to a sphere of charge inside a conducting shell

I was recently given a question that went something like this: A spherical conductor is suspended within a hollow, conducting shell. The shell carries $0$ total charge, while the sphere carries a ...
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43 views

Quantisation of gauge field in temporal gauge

Whenever we use temporal gauge and quantise gauge field we implement Gauss law. I have seen some papers but the point is not cleared to me that why we implement Gauss law there. Please explain this if ...

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