# 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 calculation through a cube [closed]

Ans: Applying Gauss’s law the net ﬂux can be calculated. And for option (B), I guess the flux will be 0. But not sure. Can anyone explain all the 3 options? For left and rignt face, EA = 300*(0.05)^...
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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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### Electric field outside a sphere with a cavity

I have a sphere of radius $2a$ centered at the origin and made of a nonconducting material that has a uniform volume charge density $\rho$. A spherical cavity of radius $a$ eccentric to the right side ...
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### Physical interpretation of $\iiint (∇\cdot\vec E)\mbox{d} V$ [duplicate]

Can anybody explain the physical interpretation of Gauss's law $$\iiint (\nabla\cdot \vec E)~\mbox{d}V~=~\frac{Q}{\epsilon_0}?$$ Also, how is the differential form of Gauss's law obtained from the ...
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### Flux through side of a cube

I am looking at Griffiths introduction to Electrodynamics 3rd ED. Problem 2.10 asks for the flux of $E$ through the right face of the cube, when a charge $q$ is in the back left corner of the cube. ...
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### Intuition behind defining divergence as flux divided by volume?

For a continuously differentiable vector field $F$ the divergence theorem can be used to give $$(\nabla\cdot F)(a) = \lim_{r\to 0} \frac{3}{4\pi r^3}\int_{|x-a|=r} F \cdot n dA$$ This should mean that ...
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### Can someone give an intuitive way of understanding why Gauss's law holds?

Gauss' Law of electrostatics is an amazing law. It is extremely useful (as far as problems framed for it are concerned :D. I do not have a real world-problem solving experience of using Gauss' Law). ...
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### Potential of arbitrary charge distribution

Imagine this: You have a sphere of air where you have no charge and around this sphere you have a charge distribution $\rho(r,\theta,\phi)$. (For instance, this could be $\rho(r,\theta,\phi)=e^{-r}$)...
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### The relation between Gauss's law and Coulomb law and why is it important that the electric field decrease proportionally to $\frac{1}{r^{2}}$?

My question relates to the third MIT's video lecture about Electricity and Magnetism, specifically from $21:18-22:00$ : http://youtu.be/XaaP1bWFjDA?t=21m18s I have watched the development of Gauss's ...
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### Why is the radial direction the preferred one in spherical symmetry?

I am learning about electricity and magnetism by watching MIT video lectures. In the lecture about Gauss's law, while trying to calculate the flux through a sphere with charge in it, the lecturer ...
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### How to find electric scalar potential of infinite wire with Poisson/Laplace equation?

I though it will be easier then calculating the electric field and then integrating, but I am stuck. lets say we have an infinite wire, charged $\lambda$ per unit of length and its located at the ...
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### Why is electric flux defined as $\Phi = E \cdot S$?

Flux, as I understand it, is the amount of substance passing through a particular surface over some time. So, from a simple perspective, considering photons that go through some virtual surface $A$ (...
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### Coulomb potential

It is known that the Coulomb potential can be obtained by Fourier transform of the propagator from E&M. Is this because one of Maxwell's equations have the form $\nabla \cdot \mathbf{E}=\rho$?
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### In electrostatics total flux linked from the closed surface enclosing the charge is equal to $Q/\varepsilon_0$. This is according to Gauss Law

In electrostatics total flux linked from the closed surface enclosing the charge is equal to $Q/\varepsilon_0$. This is according to Gauss Law. Is this the experimental value or defined value. If ...
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### How are excess charges distributed over non-spherical conductors?

My textbook gives the following explanation on how excess charges are spread over conductors: The excess charge on an isolated conductor moves entirely to the conductor's surface. However, unless ...
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### Gauss's Law understanding

In the case of a point charge $q$ at the origin, the flux of $\vec{E}$ through a sphere of radius r is, \begin{equation} \oint \vec{E}\cdot d\vec{a} = \int \frac{1}{4 \pi \epsilon_0 }(\frac{q}{r^2}\...
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### What is the electric field in a parallel plate capacitor?

When we find the electric field between the plates of a parallel plate capacitor we assume that the electric field from both plates is $${\bf E}=\frac{\sigma}{2\epsilon_0}\hat{n.}$$ The factor of two ...
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### Charge inside conductor

I know that the $E$ field inside a conductor is zero. What happens if I put a source of charge inside the conductor? Say the conductor was spherical centered on the origin and there exists a charge ...
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### Gauss' law and an external charge

Gauss' law states that the net outward normal electric flux through a closed surface is equal to $q_{total, inside}/\epsilon_0$. However, I'm a bit confused of why the presence of an external charge ...
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### Gauss's Law with Moving Charges

My text claims that Gauss's Law has been proven to work for moving charges experimentally, is there a non-experimental way to verify this?
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### Charges lying on a Gaussian Surface

Let's say you have a spherical charge distribution of radius R. This distribution has some charge density as a function of radius. I know that I can determine the electric field outside of the charge ...
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### Electric field around charged cylinder

This is a homework question, so please don't give me the answer outright. I just need help conceptually. "A cylindrical shell of length 190 m and radius 4 cm carries a uniform surface charge density ...
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### Is Newtonian gravity consistent with an infinite universe? [duplicate]

Let us assume that we have have an infinite Newtonian space-time and the universe is uniformly filled with matter of constant density (no fluctuations whatsoever), all of it at rest. By symmetry, the ...
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### Finding Electric Field outside a Charged Cylinder

I'm trying to solve a problem that involves finding the electric field due to a uniformly cylinder of radius $r$, length $L$ and total charge $Q$. Well, my thought was: if I am to use Gauss' Law, I'll ...
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### Why doesn't a gaussian surface pass through discrete charges?

I have read that Gaussian surface cannot pass through discrete charges. Why is it so? I have even seen in application of Gauss' Law when we imagine a Gaussian Surface passing through a charge ...
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### Applying Gauss' Law to find Electric Field

I'm in doubt in the application of Gauss' Law to find electric fields when the charge distribution is symmetric. Well, first of all: I know how to find the magnitude of the field - we just enclose the ...
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$$\Phi=\iint_{\partial V}\mathbf{g} \cdot d \mathbf{A}=-4 \pi G M$$ Essentially, why is $\Phi$ independent of the distribution of mass inside the surface $\partial V$, and the shape of surface $\... 1answer 216 views ### Newtonian Gravity on a Riemannian$3$-Manifold To solve the Poisson equation for the Newton Potential, say$\phi$, one can use the divergence theorem, such that $$\int_U \nabla^2 \phi \sqrt{g}~ \mathrm dV= \int_{\partial U} \langle \nabla \phi,n\... 2answers 838 views ### Electric lines of force Why cant electric lines of force pass through the charged sphere? Well, basically that's how a Faraday cage works, but how can it be so? 3answers 5k views ### Why can we use Gauss' law to compute electric field? For simplicity I'm considering only the sphere case. In the Gauss' Law formulation we have some field E introduced by charges Q inside some sphere, then we compute flux and integrate, and we get ... 1answer 876 views ### Finding the electric field on a point (x,y,z) using Coulomb's Law Using Gauss' Law, the answer is$$\frac{Q}{4 \pi \epsilon R^2}.$$However if I were to do the integration using Coulomb's Law, I get$$ \int_0^{2\pi} \int_{0}^{\pi}\int_r^a \frac{\rho \sin\theta dR ... 1answer 2k views ### Gravity force strength in 1D, 2D, 3D and higher spatial dimensions Let's say that we want to measure the gravity force in 1D, 2D, 3D and higher spatial dimensions. Will we get the same force strength in the first 3 dimensions and then it will go up? How about if ... 5answers 2k views ### Intuitive explanation of the inverse square power$\frac{1}{r^2}$in Newton's law of gravity Is there an intuitive explanation why it is plausible that the gravitational force which acts between two point masses is proportional to the inverse square of the distance$r$between the masses (and ... 5answers 5k views ### Why are so many forces explainable using inverse squares when space is three dimensional? It seems paradoxical that the strength of so many phenomena (Newtonian gravity, Coulomb force) are calculable by the inverse square of distance. However, since volume is determined by three ... 1answer 5k views ### Electric field inside and outside a metallic hollow sphere 1) It is known that inside a metallic hollow sphere it will not experience outside electric field because of the charge separation of electrons and holes at the surface of sphere and creating an equal ... 2answers 5k views ### Would a gauss rifle based on generated magnetic fields have any kickback? In the case of currently developing Gauss rifles, in which a slug is pulled down a line of electromagnets, facilitated by a micro-controller to achieve great speed in managing the switching of the ... 1answer 341 views ### How does one come up with the Coulomb's law? My teacher mentioned that field line density = no. of lines / area and the total area of a sphere is$4\pi r^2$and so an electric force is inversely proportional to$r^2$. Actually, why can the total ... 1answer 2k views ### Gauss Law for Electric Fields What is the integral form for the Gauss Law for Electric Fields? or ? 4answers 11k views ### Electric field and electric potential of a point charge in 2D and 1D in 3D, electric field of a piont charge is inversely proportional to the square of distance while the potential is inversely proportional to distance. We can derive it from Coulomb's law. however, I ... 2answers 4k views ### Find the quantity of charge - given potential function A potential function is given by$V(r)=\frac{Ae^{-\lambda r}}{r}$Find charge density and hence charge. I first took the gradient of potential to get$\vec{E}(r)=\frac{Ae^{-\lambda r}}{r}[\lambda+\...
I have been trying to understand the last step of this derivation. Consider a sphere made up of charge $+q$. Let $R$ be the radius of the sphere and $O$, its center. A point $P$ lies inside the ...