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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42
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6answers
6k 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 ...
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Gravitational field intensity inside a hollow sphere

It is quite easy to derive the gravitational field intensity at a point within a hollow sphere. However, the result is quite surprising. The field intensity at any point within a hollow sphere is zero....
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Why does the density of electric field lines make sense, if there is a field line through every point?

When we're dealing with problems in electrostatics (especially when we use Gauss' law) we often refer to the density of electric field lines, which is inversely proportional to the radius in the case ...
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How is Gauss' Law (integral form) arrived at from Coulomb's Law, and how is the differential form arrived at from that?

On a similar note: when using Gauss' Law, do you even begin with Coulomb's law, or does one take it as given that flux is the surface integral of the Electric field in the direction of the normal to ...
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Does Coulomb's Law, with Gauss's Law, imply the existence of only three spatial dimensions?

Coulomb's Law states that the fall-off of the strength of the electrostatic force is inversely proportional to the distance squared of the charges. Gauss's law implies that the total flux through a ...
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Field between the plates of a parallel plate capacitor using Gauss's Law

Consider the following parallel plate capacitor made of two plates with equal area $A$ and equal surface charge density $\sigma$: The electric field due to the positive plate is $$\frac{\sigma}{\...
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4answers
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Divergence of $\frac{ \hat {\bf r}}{r^2} \equiv \frac{{\bf r}}{r^3}$, what is the 'paradox'?

I just started in Griffith's Introduction to electrodynamics and I stumbled upon the divergence of $\frac{ \hat r}{r^2} \equiv \frac{{\bf r}}{r^3}$, now from the book, Griffiths says: Now what is the ...
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3answers
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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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5answers
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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 ...
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3answers
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Gauss's law in a uniform charge distribution extending infinitely in all directions

Let us assume the universe filled with positive charge. About a particular point, all the positive charged particles will be symmetrical. Now consider a sphere of radius $r < \infty$ and apply ...
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2answers
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Divergence of Electric Field Due to a Point Charge [duplicate]

I am trying to formally learn electrodynamics on my own (I only took an introductory course). I have come across the differential form of Gauss's Law. $$ \nabla \cdot \mathbf E = \frac {\rho}{\...
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4answers
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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 electric field flux through the base of a cube from a point charge infinitesimally close to a vertex?

I'm having some trouble with the following problem: A charge $q$ is placed on the body diagonal of the cube very close to one of the corners (distance $\delta$ from the corner, $\delta$ tending to ...
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3answers
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What do we mean with magnetic monopole and dipole?

What do we mean with magnetic monopole and dipole? I can not find a way to relate magnetic monopoles and dipoles with electric ones. I do not understand their outcomes. Also,what is their role in ...
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Explanation for $E~$ not falling off at $1/r^2$ for infinite line and sheet charges?

For an infinite line charge, $E$ falls off with $1/r$; for an infinite sheet of charge it's independent of r! The infinitesimal contributions to $E$ fall off with $1/r^2$, so why doesn't the total $E$ ...
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1answer
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Inverse Square Law and extra space dimensions

Newton's famous Inverse Square Law says that in $n=3$ dimension of space, force is inversely proportional to the square of the distance between a source and a target. I understand that for higher ...
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8answers
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Paradox with Gauss' law when space is uniformly charged everywhere

Consider that space is uniformly charged everywhere, i.e., filled with a uniform charge distribution, $\rho$, everywhere. By symmetry, the electric field is zero everywhere. (If I take any point in ...
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4answers
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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 ...
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5answers
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Period of oscillation through a hole in the earth

Special mention to the QI episode that kicked this off: Anyway, the host points out that a tunnel that connects a pair of points on the earth's surface can be thought of as a gravity train - where ...
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1answer
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Why we cannot use Gauss's Law to find the Electric Field of a finite-length charged wire?

One of my physics books has a nice example on how to use Gauss's Law to find the electric field of a long (infinite) charged wire. However, at the very end of the example, the author ends by saying ...
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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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Why is the electric field inside a conductor zero in equilibrium?

My textbook says the field inside a conductor must be zero in order for the system to be equilibrium and therefore there must be no excess charge inside. Their proof: 1) Place a gaussian surface ...
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2answers
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Does the induced charge on a conductor stay at the surface?

My textbook says that when a conductor is placed in an electric field, the electrons in it realign so that the net electric field inside the conductor is zero. There isn't a proof for this. It merely ...
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4answers
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Infinitely charged wire and Differential form of Gauss' Law

I have tried calculating the potential of a charged wire the direct way. If lambda is the charge density of the wire, then I get $$\phi(r) = \frac{\lambda}{4 \pi \epsilon_0 r} \int_{-\infty}^\infty \...
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4answers
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Electric Flux - What is the point?

Electric flux is a defined quantity that is proportional to the no. of field lines passing through a given area element for a given electric field. It is not proportional to the relative density of ...
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2answers
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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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1answer
448 views

Gauss's law not making sense

If we have a point charge and outside of it we have a non-conducting Gaussian sphere, then Gauss's law says that the net flux should be zero. I agree that the total field lines coming in are equal to ...
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4answers
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Why can charges outside be ignored in Gauss's Law?

In MIT's 8.02 course, it is shown in lecture 3 that we can derive Gauss's Law from Coulomb's to get $ \phi = \oint \vec{E} \cdot \vec{dA} = \frac{Q_{enc}}{\epsilon_{0}} $ However, in the lecture, it ...
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Is Gauss's law wrong, or is it possible that $\int_s{\vec E} \cdot d\vec{s}=0$ does not imply $\vec E = 0$?

This is a question from David J Griffith's Introduction to Electrodynamics. A specified charge density $\sigma(\theta)=k\cos(\theta) $ is glued over the surface of a spherical shell of radius $R$. ...
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4answers
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Why is electric field of an infinite plate constant at all points?

I know from Gauss law, it is $\vec{E}=\dfrac{\sigma}{2 \epsilon_0}(\hat{n})$ at all points. But it doesn't make sense because of the inverse square nature of electric field which suggests if you move ...
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2answers
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Electric field inside a conductor and induced charges

My textbook says two different things and I'm not sure how to reconcile these two: electric field inside a conductor is always 0. for a conductor with a cavity with a charge q inside it, the field ...
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1answer
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Formal Connection Between Symmetry and Gauss's Law

In the standard undergraduate treatment of E&M, Gauss's Law is loosely stated as "the electric flux through a closed surface is proportional to the enclosed charge". Equivalently, in differential ...
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3answers
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Electric flux due to external charge

Why is electric flux due to external charge i.e a charge outside a closed surface equal to 0? P.S:Moreover I found this statement confusing:- Electric field appearing in the Gauss' law is the ...
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2answers
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Why $1/r^2$ and not another power of $r$ in Newton's law of gravitation?

My book introduces the force of gravitation as a non-contact force between two bodies of mass $M_1$ and $M_2$ separated by a distance $r$ . Then it says it is directly proportional to the product of ...
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1answer
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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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14answers
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Why is the field inside a conducting shell zero when only external charges are present?

In many introductory books on electrostatics, you can find the statement that the field inside a conducting shell is zero if there are no charges within the shell. For example, if we place an ...
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3answers
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Coulomb's law and Gauss' Law

Which of these laws is more fundamental or forms the basis of electrostatics? I started off with Coulomb's law and then I studied Gauss' law. I was wondering which one is more universal? My professor ...
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2answers
393 views

Calculating the potential on a surface from the potential on another surface

The question is short: If a charge (or mass) distribution $\rho$ is enclosed by surface $S_1$, I can calculate the electrostatic (or gravitational) potential on that surface by integrating $\rho(r') \ ...
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2answers
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Gauss' law in differential form and electric fields

I know Gauss' divergence theorem, according to which $$\iiint_D\nabla\cdot\boldsymbol{F}\text{d}x\text{d}y\text{d}z=\iint_{\partial D}\boldsymbol{F}\cdot\boldsymbol{N}_e\text{d}\sigma$$ where $D$ is a ...
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1answer
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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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The discontinuity of Electric Field

''electric field always undergoes a discontinuity when you cross a surface charge $\sigma$'' GRIFFITHS In the derivation; Suppose we draw a wafer-thin Gaussian Pillbox, extended just barely over the ...
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1answer
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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 ...
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4answers
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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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2answers
901 views

Proving electric field constant between two charged infinite parallel plates

It is known that the electric field intensity between two infinitely long charged parallel plates is constant. I had read that one explanation is that if a test charge is placed between the plates, ...
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4answers
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Electric field line density : Theory vs Reality

I've already went through this post. Yet, I still can't understand the meaning of "density" of electric field lines whose number is, in reality, infinite. One of the answers , for instance, states ...
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4answers
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Divergence of a field and its interpretation

The divergence of an electric field due to a point charge (according to Coulomb's law) is zero. In literature the divergence of a field indicates presence/absence of a sink/source for the field. ...
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4answers
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Using Gauss's law when point charges lie exactly on the Gaussian surface

Suppose you place a point charge $+Q$ at the corner of an imaginary cube. Since electric field lines are radial, there is no flux through the three adjacent (adjacent to the charge) sides of the cube....
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4answers
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Is there a limitation on Gauss' law? [duplicate]

Recently I had a question to find the electric field at a distance $R$ from the origin, where the space is filled with charge of density $\rho$. I did this by assuming a Gaussian surface of radius $R$....
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5answers
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Is Gauss' law valid for time-dependent electric fields?

The Maxwell's equation $\boldsymbol{\nabla}\cdot \textbf{E}(\textbf{r})=\frac{\rho(\textbf{r})}{\epsilon_0}$ is derived from the Gauss law in electrostatics (which is in turn derived from Coulomb's ...
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3answers
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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). ...