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 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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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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Confusion regarding gauss law

Gauss law states that flux due to net electric field on a Gaussian surface is charge enclosed divided by permittivity. $$ \Phi = \oint _ { A } \vec { E } \cdot \mathrm { d } \vec { A } = \frac { Q } ...
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Gauss' Law and Electric Field Close to a Ball

So I've learned about Gauss' law and I have something in my head. Why does electric field that is very close to a ball is not close to infinity. Take a look at this image: As we can see, if we make a ...
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174 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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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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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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135 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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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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538 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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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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Why is the $\vec E$ field inside a sphere = 0?

I was taught Electric Field inside a sphere is 0, because of Gauss Law. But inside a uniformly charged sphere, if I go at a distance of $r$ from the centre, I will be closer to the +ve charge and ...
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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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Unstable equilibrium due to an arbitrary electrostatic configuration

Suppose n charges are put in an arbitrary electrostatic configuration and a small test 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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46 views

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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266 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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192 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
117 views

Electric field related to conducting materials containing charge containing cavity

In my physics class we were analyzing a scenario where a charge has been placed inside the cavity of a conducting material like this: What my teacher did was to assume a Gaussian surface in the ...
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287 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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184 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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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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292 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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1answer
185 views

Gauss Law Doubt

I have a doubt regarding whether or not I can take a spherical surface as a Gaussian surface when the taken Gaussian surface completely overlaps a symmetrical spherical charge distribution of same ...
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133 views

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. ...
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465 views

Why perpendicular component of Electric field is discontinuous across the boundary and parallel components continuous?

I was going through Griffith's electrodynamics boundary conditions and have a problem understanding the discontinuity of $E_\perp$ components. While deriving the electric field for an infinite sheet ...
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655 views

How to calculate the Electric field near a 2-D charged square sheet of conducting material with finite area?

The case for infinite sheets are simple enough, and also for a disk of finite size, which can be derived as in the picture. title edited to specify sheet is finite.
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644 views

Electric potential due to surface charge distribution on a conducting sphere

Let's consider a conducting sphere. If we charge the sphere, it is understood that there will form a surface charge distribution such that the surface of the sphere is an equipotential surface $ 0=\...
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226 views

Simulating the Electric Field inside a Hollow Sphere of Uniform Charge

I've recently been studying Gauss's Law and have come across some results that I want to verify. For one, I am trying to verify that the electric field inside a conductor (in this case it could be ...
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782 views

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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Gauss's law giving incorrect answer

Let's consider two concentric spherical shells, one of radius $R$ and one of radius $R - \Delta R$. The outer shell is negatively charged and the inner shell positively, but both the shells have net ...
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Charge per unit length and charge per unit area

In the Halliday and Resnick book, I am asked the find the linear charge density of the inner wall of a shell. This confuses me because the inner wall of a shell is an area, not a one dimensional line. ...
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conducting hollow sphere in magnetic monopole

if a hollow copper sphere(or any conducting hollow sphere) is connected to dc at points diametrical and a magnetic monopole is right at the center of the sphere then will there be any movement of the ...
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309 views

How can electric field representation be obtained from Enge representation using Maxwell's equations?

Suppose we have a long electric capacitor. Let $L$ be its length ($z$ coordinate), $W$ its width ($y$ coordinate), and $D$ its full height (full aperture; $x$ coordinate). Let $L\gg W\gg D$. The ...
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Do these steps demonstrate that acceleration of charged particle is proportional to current?

One formulation of Maxwell's Gauss Law for electric field is: $$\bigtriangledown E = 4 \pi k \rho $$ This can be worked into the Divergence Theorem as follows: $$\int\int_{A} F_\perp \:dA= 4\pi k \...
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Newton's Law of Gravitation, Gauss Law and GR

From One of My Unpublished Papers $$\frac{d^2 x^{\alpha}}{d\tau^2}=-\Gamma^{\alpha}_{\beta \gamma}\frac{dx^{\beta}}{d\tau}\frac{dx^{\gamma}}{d\tau} \tag{1}$$ For radial motion in Schwarzschild’s ...
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How does one apply Gauss's Law when dealing with two infinite planes?

If you have two parallel planes with one density of 1 C/m^2 and the other with -1 C/m^2 density and you need to find the electric field at a point in the middle, how do you use Gauss's Law? I drew a ...
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Electric field from the intersection of two spheres with different charges

This question is repeated a lot, but I for two spheres with different charge densities, sphere one with radius a centered at the origin and charge density $\rho_1$, and sphere two with radius centered ...
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What is the electric field between two coaxial conducting cylinders when a charged sphere is placed within the inner cylinder?

A long cylindrical capacitor of length $l$ consists of an outer conductor of radius $a$ and an inner conductor of radius $b$, where $l>>a$. The outer conductor is earthed, and the inner ...
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Electric field in capacitor arrangement with different dielectric media

Please consider the following arrangement of infinitely extended charged plates. In z-direction the system also extends to infinity. The charged plate in the middle of the figure is 2x negatively ...
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Can we use Gaussian pillbox method to determine electric field at a point just near the surface of a surface charge distribution?

I know we can use Gaussian pillbox method to find the discontinuity at the surface of a surface charge distribution. But can we use Gaussian pillbox method to determine electric field at a point just ...
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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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What is the physical significance of the complex solutions for the function of electric field inside and outside the solid non-conducting sphere?

Please consider this graph of electric field due to solid non conducting sphere inside and outside the sphere. If we consider the function by its graphical analysis then it is a surjective or many ...
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Why can't Gauss surface be a cube?

For calculating field outside a charged plane conductor, a gaussian surface of Cylinder is considered. I have been said that we consider cylinder because the circle in its upper end is in equal ...
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On the Electric Field of conductor under Electrostatic Conditions

Let us take a hollow conductor which has a charge Q uniformly distributed on its surface. Now, we know that the Electric field inside the conductor must be ZERO. But what happens when I bring ...