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 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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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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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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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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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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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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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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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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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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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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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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Gravity in 2+1D spacetime and inverse linear law
In our 3+1D universe, gravity obeys the inverse square law. In a 4+1D universe, gravity would be expected to obey the inverse cube law et cetera.
In a 2+1D universe, one would similarly expect gravity ...
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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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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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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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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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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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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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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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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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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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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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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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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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Why is the electric field zero inside a hollow conducting sphere? [duplicate]
If you have a conducting hollow sphere with a uniform charge on its surface, then will the electric field at every point inside the shell be 0.
The reason the electric field is 0 at the center is ...
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"Find the net force the southern hemisphere of a uniformly charged sphere exerts on the northern hemisphere"
This is Griffiths, Introduction to Electrodynamics, 2.43, if you have the book.
The problem states Find the net force that the southern hemisphere of a uniformly charged sphere exerts on the northern ...
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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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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 d\vec{A} = \frac{Q_{enc}}{\epsilon_{0}} $
However, in the lecture, it ...
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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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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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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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Deriving Coulomb's Law from Gauss's Law
I've been thinking about this for the past couple of days. I apologize if my explanation isn't very clear.
I have already seen derivations of this, but I'm still not satisfied.
In the derivations of ...
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Proof of Coulomb's law in two and higher dimensions
I have found that the Coulomb force in two dimension varies with $\frac 1 r$:
\begin{equation}\tag{2}F=\frac{1}{2\pi\epsilon}\cdot\frac{q_1q_2}{r}\end{equation}
But I was not able to prove it. I think ...
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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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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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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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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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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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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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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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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'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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Electric field inside conductor with a cavity
Suppose I have a neutral spherical conductor with a cavity inside. Suppose there's a $+q$ point charge inside the cavity.
I know that the electric field $\vec{E}$ is zero within the conductor, also ...
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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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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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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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Charge inside a charged spherical shell
If I were to put a negative charge inside a negatively charged spherical shell, will it move to the center?
Electric field inside the shell due to the shell is zero (Gauss's Law), would that mean the ...
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Charge outside Gaussian Surface doesn't contribute to Flux?
I roughly understand the explanation for this: any electric field line that enters the surface, must leave it, since field lines can't terminate abruptly in space. My question is, what if you have a ...
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