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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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Why Electric field inside the spherical shell is zero?

electric field in and out of the spherical shell Why the field inside the conducting spherical shell is zero? Professor Lewin said and I quote," there is NO charge inside the conductor because any ...
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Find electric field for a hemispherical shell using Gauss law [closed]

The hemispherical shell has charge density $σ$ find electric field at its centre I know how to do it by integration but I tried to do it using Gauss law and answer I got was correct but I am not sure ...
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Point charge inside a hollow conductor, does the exterior field changes when the charge moves?

Suppose that I have a hollow conductor with no specific format. I know that if I put a charge inside it, it will induce charge in the inner surface and on the outer surface a charge with a opposite ...
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Electrostatic in 2D: dimensional analysis

After reading this very interesting post about the electric field and the electric potential of a point charge in 2D and 1D, I've understood that, for the $2D-$case, the following formulas hold: $$ \...
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What is the electric flux through the flat and curved surfaces? [closed]

My question is from Physics For Scientists And Engineers 7th: A particle with charge Q is located immediately above the center of the flat face of a hemisphere of radius R, as shown in the figure. ...
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Electric field in center of non-conducting sphere with non-uniform charge distribution from Gauss's law

I'm currently reviewing electricity for the AP Physics C exam, and came across a problem or general topic I don't really understand that has to do with Gauss's law. The general form of Gauss's law we ...
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Why the electric field of an infinity line is dependent on distance? [duplicate]

A very common question about Gauss law is being asked in schools or Internet: Why the electric field of an infinite plane is independent on distance? Actually I was one of who asked this ...
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51 views

Earnshaw's Theorem in Chemical Bonds

Earnshaw's theorem says that: A collection of point charges cannot be maintained in a stable stationary equilibrium configuration solely by the electrostatic interaction of the charges. I also know ...
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39 views

Electroshielding in asymmetric conductors

Consider the textbook problem of a spherical conductor, with a concentric spherical cavity and a charge of +Q located in the center. By constructing a suitable Gaussian surface, we can deduce that the ...
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Finding electric displacement $\mathbf D$ for a parallel-plate capacitor filled with two slabs of linear dielectric material

This problem refers to Griffiths Problem 4.18: According to my solutions, my lecturer wrote: Only free charge is on plates. $$\mathbf D = -\sigma \hat z \ \text{between the plates and $0$ ...
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Please give the answer with proper explanation [duplicate]

How to find the electric flux of a point placed at the vertice of a cube.
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Flux received by a negative charge

Consider two charges $+q$ and $-Q$ placed at a distance, note- charge q and Q are different In terms of magnitude. My question: is number of flux lines received by $-Q$ proportional to its own charge,...
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Why is electric field inside a cavity of a non-conducting sphere not zero? [closed]

Consider a charged non conducting solid sphere of uniform charge density, and it as hole of some radius at the centre. Now suppose I apply Gauss law. As there is no charge inside the cavity, no ...
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Calculating flux through a spherical Gaussian sir surface

Three uniformly charged wires with linear charge density $\lambda$ are placed along $x,y$ and $z$. What is the flux of the electric field through Gaussian surface given by $$x^2 + y^2 + z^2 = 1;\, x&...
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Relationship between polarization charge density and free charge density

I have concluded that in a uniform dielectric, volume free charge density $\rho_0$ and volume polarization charge density $\rho'$ satisfy $$ \rho' = \frac{-(\epsilon - \epsilon_0)}{\epsilon}\rho_0 $$ ...
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Principle of superposition in spherical shells

If I have a spherical shell with a uniform positive charge desnity on its surface is near a positive point charge q (sitting in quadrant II area) In consideration of the electric field strength and ...
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Gauss divergence theorem (GDT) in physics

Some of the statements for $GDT$ which I find in modern textbooks (both electromagnetism and multivariable calculus textbooks) are: (1) Calculus: Several variables Adams Let $D$ be a regular, ...
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element of surface area versus vector element of surface area

In the context of calculating electric flux, is there a difference between element of surface area versus vector element of surface area? Thanks
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Physical example of line charge

Electric field due to an infinite line charge, sheet of charge, point charge, etc are popular problems solved in most text on Gauss's law of electromagnetism. My question: does an (exact or ...
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Why are the two outer charge densities on a system of parallel charged plates identical?

One of the ways examiners torture students is by asking them to calculate charge distributions and potentials for systems of charged parallel plates like this: the ellipsis is meant to indicate any ...
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What is the difference between Closed and Bounded surface?

When I was going through "The Feynman's Lecture on physics" Volume-2 , I found the line "It is useful to speak of the flux not only through a completely closed surface, but through any bounded ...
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Charged enclosed by the sphere

I'm reviewing the book "Conquering the Physics GRE" for my upcoming Physics GRE. I came across this problem which I'm having trouble with understanding. In particular, I understand the solution that ...
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1answer
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Integrating Laplace's equation over a sphere

The Wikipedia page on Laplace's equation states that if the Laplacian of $u$ is integrated over any volume that encloses the source point, $$\iiint_V \nabla \cdot \nabla u \, d^3V =-1.$$ I can'...
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Electrostatics and Gauss law [duplicate]

How can we prove that surface integral of the electric fieldfor a point charge that is outside a gaussian surface, $$\int\mathbf E\cdot\,\mathrm d\mathbf S,$$ without actually using the concept of ...
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Why don't the electric field vectors cancel each other out in a non-conducting infinite plane sheet?

Why do these vectors not cancel each other out in spite of their being in the opposite directions?
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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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1answer
69 views

Are charges outside a conducting shell relevant to electric field inside the shell?

Assume there is a thin conducting shell with a fixed point charge in the center, Q. Scattered outside the shell (not on its surface) there are more fixed point charges. If I would like to know the ...
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1answer
66 views

Physical meaning of electric field flux

I need to test my understanding regarding the physical meaning of the electric field flux. First of all, the electric flux is found by the surface integral of the field dot product a differential ...
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The correct way to use Gauss law to calculate an electric field (electrostatics)

While studying electrodynamics on my own I stumble with a problem involving the electric field inside a charged spherical shell. I understand that the electric field inside equals zero but I don't ...
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Electrostatic field-Field lines relationship [duplicate]

How is the $\frac{1}{r^2}$ dependence of the electric field intensity due to a stationary point charge consistent with the concept of field lines?
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Why is the electric flux of a point charge inside a sphere not 0 since its a vector and all the field lines point outward?

I know that the magnitude of the total flux of a point charge is $\frac{q}{ϵ_0}$, and can follow the maths and reasoning behind it. But since flux is a vector, shouldnt it also have a direction? I ...
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How to calculate the electric field using Gauss' s Law in this example? [closed]

Suppose we have an infinite cylinder (infinite in the z-direction) with radius $a$. Inside it, there is free charge density given by $\rho = \rho_o \cos (kz - \omega t)$ and current density given by $\...
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1answer
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How is the area vector larger by a factor of $\frac{1}{cos \theta}$ for proving the gauss law?

So I was reading Electricity and magnetism by Purcell and I came across the Gauss law. Now in here its said I quote "The area of the patch $A$ is larger than that of the patch $a$ by two factors: ...
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Gauss's Law and Superposition Principle [closed]

Hi I am doing the homework in MIT 8.02 by Dr.Lewin, I doubt that the answer provided online for Problem set is wrong, here is the problem. For question(a)(b)(c) it answers For me, I think the ...
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Flux density via Gauss' Law inside sphere cavity

There are many similar questions on here but most seem to deal conceptually with electric field, not the mathematics behind it. The setup is this: there is some sphere of radius b which has a volume ...
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Why do outside charges not contribute to net flux through a surface, pt 2

The question I have is a succession from the ones below. Why do outside charges do not contribute to net flux of a Gaussian Surface? Gauss' law and an external charge The responses to these ...
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Knowing when Gauss's Law is useful

I'd like to know whether my sense of Gauss's Law is correct here. Suppose I have a cube of side length $L$ filled uniformly with electric charge. Let's say I use as my integration surface a cube ...
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Total charge in electron cloud in a hydrogen atom

Essentially, the problem I'm trying to solve is The potential at a distance $r$ from the nucleus that is generated by an electron in a hydrogen atom is given by: $$V(r) = \frac{q}{4\pi\...
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Gauss' Law- Hollow Sphere with Non-Uniform Charge Distribution

I am confused about the solving for the E field inside of a hollow sphere with a non uniform charge distribution. I understand conceptually that the unbalanced charge distribution would lead to an E-...
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Physical Interpretation of $\nabla \cdot \vec{E} = \frac{\rho}{\epsilon_0} $

The differential's form of Gauss' Law is $$\nabla \cdot \vec{E} = \frac{\rho}{\epsilon_0}. $$ This suggests that at every point in space, the the electric field $\vec{E}$ is determined by the charge ...
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Charge Distribution on a perfectly conducting hollow shell

As shown in the figure, I have a hollow shell which contains a charge at its centre and another charge is placed outside the shell (some distance apart). I know that the situation this figure depicts ...
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Divergence of magnetic field

Consider a point near one of the poles of a bar magnet. The magnetic field lines do appear to spread, but according to Maxwell's equations the divergence of a magnetic field is always zero. So what's ...
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Will it be complicated to use Gauss's Law in this problem? [closed]

The electric field strength depends only on the $x$ and $y$ coordinates according to the law $\vec{E}=a(x\hat{i}+y\hat{j})/(x^2+y^2)$ where $a$ is a constant. Find the flux of the vector$\vec{E}$ ...
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Starting from Gauss's law, prove that the Electrostatic potential satisfies Poisson's equation [closed]

If we start from differential form of Gauss Law and take out divergence of E , I am getting it to be zero. How's is it possible? So how do I proceed further in order to prove that Electrostatic ...
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Gauss theorem and inverse square law [duplicate]

I know that the gauss law states that the Flux of the electric field through a closed surface is Q/ε , but does the gauss theorem works also for non inverse square law Fields?
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How calculate work from an electric field on a $+q$ particle without the curve? [closed]

Well,i've a workout for home,and it is asking me to calculate the work from the electric field with equation: $\hat E=6xy \hat x+(3x^2-y^2)\hat y$ I tried to solve the line integral but it doesn't ...
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Question on capacitance

I am recently trying to learn electrics on my own but am a bit confused with regard to capacitance. By Gauss law, I understand that the electric field from a single parallel plate results in: $$ E = \...
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Why do we not have devices like inductors or capacitors to hold gravitational field? [closed]

I know that a capacitor can store electric field and an inductor can store magnetic field. So is there a way that gravitational field field can be stored in any such device. Also we do not have a law ...
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If Ampere's law implies the Biot-Savart law, which implies Gauss's law for magnetism, does that mean Maxwell's equations are redundant?

Studying electromagnetism, I came across the following fact: Maxwell's third equation (divergence of magnetic field is zero) can be derived from the Biot-Savart Law. The Biot-Savart Law can be ...
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Electric field inside a cylinder containing a grounded wire?

Say we have a hollow cylinder at 100V. I understand that if this cylinder were empty, you would have no electric field inside because if you drew a Gaussian surface, it would contain no charge. ...