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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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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582 views

Question on Gauss's law

This question is from Griffiths' Electrodynamics, Chapter 2, question 49, part e). The question is as follows: Problem 2.49 Imagine that new and extraordinarily precise measurements have revealed ...
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400 views

Is Gauss electric flux law valid in all coordinate systems?

The derivation of Gauss electric flux is as follows : $$\iint{\vec{E}}\cdot{\vec{dS}}=\iint E \, dS \cos\theta \, .$$ The projection of infinitesimal area on the surface $\vec{dS}$ on the radial ...
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Electric field of a capacitor in dielectric medium with weird size

I have been learning gauss's law in capacitor recently, recently I come up with this problem that I couldn't solve myself. If we have a capacitor,and a dielectric medium with half the volume between ...
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601 views

Flux through a conduting cylinder?

A point charge of magnitude $Q$ is placed inside a conducting cylinder of length $L$ and radius $R$ at its centre. What is the flux through the cylinder? I know that I have to use Gauss Law here but ...
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60 views

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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25 views

How can I calculate the $D$ field when all the free charge is on a conductor embedded in a dielectric?

Let $K$ be a bounded piece of conductor, embedded in an isotropic, homogeneous, uniform dielectric of permittivity $\epsilon$. Let $ \vec r$ be a point in the exterior of the conductor. Let $\rho_f$ ...
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34 views

Is principle of superposition valid for extended conducting objects whose charge distribution is affected by presence of other charges nearby?

let me explain my question with an example. Say we put a charge at the centre of an metallic hollow charged sphere and measure electric field at a distance larger than the radius. It is easy to ...
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59 views

A point charge near a conducting cylinder

As we could figure out the point charge induced image charge on a conducting sphere in Jackson's book. Is there any way to figure out the point charge induced image charge form on a conducting ...
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3answers
623 views

How is the $E$-field getting canceled between outer and inner surface of a neutral conducting spherical shell?

I am reading Purcell's E&M book and in one of the example questions, it shows that there is no E field between outer and inner surface after a a point charge is located at an arbitrary position ...
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65 views

A solution of an electrostatic problem without definition of flux

I have this problem: The figure shows the electric field lines around a system of three charges $q_1$, $q_2$ and $q_3$. The central charge have a value of $q_2=-10.0\,\mu\mathrm C$. Find the value of ...
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273 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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396 views

Analogies between electrostatics and steady state heat equation?

In electrostatics we have $$\nabla \cdot E = \rho/\varepsilon$$ and using the divergence theorem we get $$\int_{\partial\Omega} E \cdot \hat{n} dS = \int_\Omega \rho/\varepsilon dV.$$ This states ...
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Is the gravitational field $\mathbf{g}(x)=-G\int_{\Bbb R^3}\rho(y)\frac{x-y}{|x-y|^3}\,\mathrm{d}y$ continuously differentiable?

I apologize for mathematician-style question, but I was wondering if for continuous mass density $\rho:\Bbb R^3\to\Bbb R$ with compact support, the gravitational field $$\mathbf{g}(x)=-G\int_{\Bbb R^3}...
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Eletrical field Mobius strip

I had this question in my mind for months, is there a way to calculate the Electric Field ( Gravitational field as well) generated from a non orientabile Surface ?
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Divergence theorem and discontinuous vector fields in electrostatics

Wikipedia defines Gauss Divergence Theorem for a continuously differentiable vector field; but in many idealized physical situations, we use it for non-differentiable fields. For example, the electric ...
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357 views

insulator based gauss law questions

My book is incredibly scarce on insulator based Gauss law questions. Conductors seem to handle themselves pretty simply. Here's a question I'm working on that isn't part of my book. where the radii ...
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1answer
120 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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1answer
30 views

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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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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1answer
131 views

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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1answer
45 views

Electric Field Divergence

I found a statement written in Introduction to Electrodynamics which mentions that if "Electric field lines terminate somewhere midway in the air, then divergence of Electric field will not be 0&...
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58 views

What are the “derivations” of the inverse-square law?

Besides the derivation mentioned in this Wiki article, I want to know if there exists any other derivation of the inverse-square law based on some profound physical/philosophical concepts.
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Gauss Law for infinite objects - Components

For an infinite rod, the formula would be $E=2k\lambda/R$ using a cylinder. If we have a point in space and wanted to only calculate the $z$-component, I assume we would do $E_z=\cos\theta$. How ...
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Confusion over Gauss' law for an ideal electric dipole

To find the charge density of an ideal electric dipole centred at the origin, I can evaluate the divergence of $\vec{E}(\vec{x})$ which equates to evaluating the laplacian of the potential. Working ...
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Electric flux through Solid non-conducting sphere placed in uniform electric field

What would be the electric flux through a Solid non-conducting sphere placed in uniform electric field and how?
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37 views

Gauss's Law with Periodic Boundary Conditions- Why No Electrical Charges?

So I've read quite a few papers recently claiming that if you have a system with periodic boundary conditions, there are no electrical charges. I'm trying to better understand why this is the case. ...
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51 views

How do we know that we have taken all factors into consideration while deriving Coulomb's Law?

It was experimentally deduced that $$F_e \propto q_1q_2$$ $$F_e \propto \dfrac{1}{R^2}$$ where $F_e$ denotes the electrostatic force between two charged particles with the magnitude of their charges ...
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36 views

How actually magnetic flux change explains inducing of current.?

If a bar magnet is moved towards a coil, current is induced as there is a flux change. Consider a circular coil where magnetic field is there only inside the coil covering a concentric area of less ...
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2answers
71 views

How to find integral's bounds - calculating electric field using Gauss's law?

This is the original question: The space between two parallel infinite planes $ x=0 $ and $ x=L $ is filled with charge of the density $ \rho\left(x\right)=ax^{2}\left(L-x\right) $ where $ a $ is a ...
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4answers
124 views

Why is electric field inside a conductor non-zero even if there is point charge placed inside it?

If I place a point charge q inside a conductor, The electric field at any point inside it will be non zero (Kq/x²). If we draw a Gaussian surface inside the conductor, the net enclosed charge will be ...
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49 views

Net Electric field on a Gaussian surface

While applying Gauss' Law, the electric field at a point on the Gaussian surface has to come from superposition of electric fields of all the charges, whether outside or inside the Gaussian surface. ...
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Charge density inside dielectric with conductivity

Consider the figures I and II , they consist of similar circuits with identical batteries. There are two different slabs connected in the circuit, both are geometrically identical and have the same ...
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95 views

Using Gauss's law to calculate flux

I don't see how using Gaussian surfaces can help me to calculate flux for example if there is a disk with radius R and center at (0,0,0) and a point charge at random (a,0,b). If I consider an ...
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Can we have a Non-Gaussian Likelihood and which are the conditions or examples?

I am working on Fisher formalism and MCMC method. It seems that Fisher formalisme assumes that posterior is always Gaussian. So if I find with MCMC a gaussian posterior, I validate the results of ...
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112 views

Gauss law use not in free space

Gauss' law specifies permitivity for free space. what happens if electric field is not in free space. does the law apply?
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The electric field of conducting and non conducting sheets

When a non conducting sheet is charged , the electric field due to it is half the electric field due to a charged conducting sheet. How exactly do they differ? When we use gauss law using a Gaussian ...
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287 views

Maxwell's equations UPML in FDTD with inhomogeneous media

I'm looking at matching the UPML (uniaxial perfectly matched layer) defined in Taflove&Hagness' Computational electrodynamics to an inhomogeneous media (inhomogeneous w.r.t. both $\varepsilon$ and ...
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101 views

Unstable equilibrium due to an arbitrary electrostatic configuration

Suppose n charges are put in an arbitrary electrostatic configuration and a small test charge is placed at a null point (i.e., where $\vec{E}=0$ ) of the configuration. The task is to show that the ...
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How is the third case obeying integral form of Maxwell's second equation?

Let $m$ denote pole strength. In the diagrams: (1) Sky blue: Closed Gaussian surface (2) Red: North pole of magnet (3) Green: South pole of magnet (4) Yellow: Part of magnet cutting Gaussian surface ...
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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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399 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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316 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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450 views

Spherical conducting shells behaviour

My textbook provides the following problem: Consider a spherical conducting shell with inner radius $R_2$ and outer radius $R_3$, that has other spherical conductor inside it with radius $R_1$ (...
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How to apply Gauss' Law given charge?

How I approached this question is by adding the two charges and dividing by epsilon zero. (Gauss' Law) Is this the correct way to solve this problem?
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Electric displacement clarification

I'm reading Griffiths E&M book and I just need some clarification about the electric displacement $\mathbf{D}$ given by $$\mathbf{D}=\epsilon_0\mathbf{E}+\mathbf{P}$$ where $\mathbf{E}$ is the ...
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Generalised gauss's law

Considering a particle can produce a field with potential, $$\phi=1/r^n$$ where n is a positive integer, If the particles density distribution in space is $\rho(r)$, then the potential, $$\phi (r)=\...
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How can we find the surface density on the surface of the conducting plate nearest to a point charge without using image method?

The problem I'm having trouble with is this. If a point charge Q is located a distance y from the surface of an infinite conducting plane, what is the surface density on the surface of the conductor ...
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416 views

Gaussian surface difference between conductor and non-conducting sheet for calculation of eletric field

For non-conducting sheet we select gaussian surface as cylinder with its end at the two opposite side of the sheet, but for conductor we select cylinder with one end inside the conductor. I know the ...
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Can Maxwell's Equations in differential form be viewed as equalities of measures?

What I have in mind is the following - Suppose we choose to model the universe as a 3 dimensional flat Euclidean space $\mathbb{R}^3$ equipped with the standard topology and the Borel-sigma algebra. ...