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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Can such a field line exist between two positive charges? [duplicate]
I am aware of the usual diagram of field lines between two positive charges.
My question is that is such a field line wrong, if so why?
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Parallel plates uniformness
All questions are highly related, so I preferred to ask them together.
Q1: Why is the electric field uniform between parallel plates and is it only uniform between? and not outside?
Q2: Why uniform? ...
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ELECTRIC FLUX CALCULATION [closed]
A point charge +q is placed on centre of face CBEH of cube ABCDGHEF
Find a) net electric flux due to +q charge through the cube
b) electric flux through each individual face of the cube
For part a of ...
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$E$-Field within uniformly charged cylinder surface
Say I have an infinitely long hollow cylinder, and on its surface I have a uniformly distributed surface charge. Now, I want to calculate the electric field of that cylinder both inside and outside. ...
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Can we use superposition of electric fields to conclude that between plates of capacitor the field is $2\frac{\sigma}{\epsilon_0}$? [duplicate]
Consider a parallel plate capacitor. This is a setup of two very large parallel plates, each a conductor and each with area $A$, and one having positive charge $Q$ and the other negative charge $-Q$.
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Unknown integral identity in derivation of first Maxwell equation
Reference: "Theoretische Physik" (2015) by Bartelsmann and others, page 391, equation (11.23).
While deriving the first Maxwell equation based on Coulomb's law, the authors are using the ...
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Electrostatics, using Gauss law to find electric flux through continuous body distributions
While calculating electric flux through an uncharged ring kept near a charge, we tend to draw a spherical Gaussian surface that covers the ring by edges but while using the gauss law, we tend to take ...
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Symmetry which shows that the magnitude of electric field due to infinitely large sheet doesn't depend on perpendicular distance from the sheet
The magnitude of electric field due to a uniformly charged, infinitely large sheet is
$$E = \frac{\sigma}{2\epsilon_0}$$
($\sigma$ is surface charge density)
It is a constant for all points in space, ...
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Why is the electric flux due to a point charge on a ring the same as of a disc?
flux means amount of ef lines passing perpendicular to a surface. but the ring is hollow so the efls would go through some part of the ringand else will just pass from its hollow part.in case of a ...
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Force between charged hemispheres
The question has been asked before, but most of the questions I found were for solid spheres. I'm asking about a hollow sphere/shell. Also, I'm not looking for a calculation. I have a conceptual ...
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Electric Field Due to Large Sheet
In a recent lecture, our physics professor was going over the Gauss's law derivation for the electric field due to a large (flat) sheet using
$$\oint\vec{E}\cdot d\vec{A}=\frac{q_{in}}{\epsilon_0}$$
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Electric Field for Non-Symmetric Charge Distributions
In real-world situations where charge distributions are asymmetric and continuous, how is the electric field calculated? Gauss's Law in integral form can't be practically applied for asymmetric ...
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Does Gauss's law (Maxwell 1st eq) have to change when the conductivity of the material is non-zero?
Studying Lorentz-Drude model on any book (e.g. Optical proerties of solids by Wooten, Fisica II by Mencucini-Silvestrini et c.) one finds the following equation relating the relative dielectric ...
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If flux is number of electric field lines passing through a surface or 3D figure, that means it is a number so why it is not dimensionless? [duplicate]
My teacher said that electrostatic flux is the number of electric field lines passing through a surface or a 3-dimensional figure, and explained its mathematical expression as $Φ = ES\cosθ$. However,I ...
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If a Gaussian surface is assumed in a non-uniform electric field and charge enclosed is zero, is the net electric flux coming out still zero?
Assume a Gaussian surface in a non-uniform electric field that is directed along X-axis. Say the field is getting weaker as we go along positive X direction and it's constant along Y and Z directions. ...
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Where can I include the distance between the plates in the capacitor equation? [duplicate]
E (volts per meter) = Q (coulomb) / εo (8.85e-12) x Area (m2)
E* vacuum = 1e18 volts per meter
https://study.com/skill/learn/how-to-use-gauss-law-to-find-the-electric-field-inside-a-parallel-plate-...
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How is Electric Field inside a Conducting Spherical Shell containing a Charge inside is zero?
I know that this may be a duplicate question but wait, I want to analyse the phenomenon from a different perspective.
For a conducting plane sheet of charge
There should be positive charge at both ...
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Charges inside a cube (given field at the surfaces) [closed]
I recently solved a question which asked me to find the charge inside a cube of length $a$ placed in an electric field $\vec{E} = C x \hat{i}$.
Using Gauss law, I found the answer to be $C \epsilon_0 ...
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If the electric field inside an infinitely long charged cylinder is non-zero except origin, how can be the inward flux zero?
If the electric field inside an infinitely long charged cylinder is non-zero except origin, how can be the inward flux zero?
https://www.youtube.com/watch?v=BF3wEV4tWq8
If we look at this video, we ...
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3 dimensional diode $E$ field profile
While deriving the electric field profile of a diode, 1D Gauss's Law is typically used:
$$\frac{dE}{dx}= \frac{\rho}{\varepsilon_0}.$$
However, the diode is at least 2-dimentional and, in real world, ...
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Is there a generalization of Gauss's Law for enclosed dipoles, quadrupoles, etc
Given the electrostatic field $\mathbf E$, its integral over a closed surface $\mathcal A$ is the total charge enclosed by it: $$\epsilon_0\oint_{\mathcal A} \mathbf E \cdot d \mathbf A = Q_{\mathcal ...
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Why can we write $\iint_S \vec{E}\cdot d\vec{a}=\frac{Q_{enc}}{\epsilon_0}=0$ when we are considering a Gaussian surface within a spherical shell?
Gauss' Law tells us that for a point charge q at the origin and a spherical surface of radius r centered at the origin, we have
$$\iint_S \vec{E}\cdot d\vec{a}=\frac{q}{\epsilon_0}\tag{1}$$
If we have ...
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Boundary condition of gravitational potential
I solve a system of coupled equations numerically. One of the most important, is equation of the gravitational potential,
$$\nabla^2 \phi = 4\pi G m \rho(r)$$
But I have physical problem with boundary ...
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Can you create a coil gun with asymmetric forces?
One of the problems in making a coil gun shoot high-velocity projectiles is that after the projectile passes the mid-point of the coil, it experiences suck-back: a force that slows the projectile and ...
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Parallel plate capacitors when one plate is a mesh
The capacitance per unit area of a parallel-plate capacitor is $\frac{\epsilon_0}{d}$.
But what if one of the plates is a mesh, but the distance $d$ is much much greater than the size of the holes in ...
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Why is the divergence of a point charge zero? [duplicate]
I have already calculated the divergence of the electric field, i.e.
$$\vec{\nabla} \cdot \vec{E}(\vec{r})=\left( \begin{array}{rrr}
\frac{\partial}{\partial x} \\
\frac{\partial}{\partial y} \\
\...
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Gauss law and its application on irregular figures
According to the Gauss’s law the flux due to external charge always remains zero. Also the total flux is given by the charge enclosed/ epsilon. So consider this surface,what is the fate of the flux ...
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Gauss' law not considering excess charge
I am trying to understand Gauss' law but do not understand this part -- does Gauss' law not consider excess charge (outside the Gaussian surface)?
In a system where we are using a Gaussian surface, ...
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Gravitational potential and Bessel functions
In electromagnetism, we can solve Laplace and Poisson equation using Bessel functions. But my question is why don't we use Bessel functions to solve these equations for gravitational potential?
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How does the divergence of the Coulomb field "blow up" at origin?
Many sources (DJ Griffiths, other answers on stack exchange) claim that the divergence of the vector field $\vec E=\frac{\hat r}{r^2}$, $\vec \nabla \cdot \vec E$ "blows up" at $\vec r=0$. ...
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Can we call this to be total charge of infinite planar sheet?
Im following Ncert textbook for physics and I was learning about Charge due to infinitely planar sheet. In this they say that the electric field due to the infinitely long planar sheet to be the same ...
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How is the electric field of an infinitely charged plane sheet the same for any point in the gaussian surface?
How is the electric field same at any point from the planar sheet with uniform charge density which is enclosed by a gaussian surface as shown below
Now I can understand the formula derivation by ...
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Calculating the Electrostatic Energy of a Charged Sphere
I'm trying to solve this problem :
Given a distribution of volumetric charge density in space:
where $r$, is the distance from the beginning of the axes: $$\rho(r)=\left\{
\begin{array}{cc}
\frac{A}{...
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Uniqueness theorem in presence of dielectrics
Let us consider a sphere made of a linear, homogeneous and isotrope dielectric with constant $\epsilon_r$ which is inserted in a vacuum where a uniform electric field $\underline{E}_0$ was applied (...
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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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Having a problem understanding the density charge per unit area in a coaxial cable (capacitor)
Given the following scenario, why is the charge per unit area not the same with opposite sign? I am finding it difficult to understand, since the charge per unit area for two parallel plates in a ...
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Cylindrical capacitor and charge density per unit area [closed]
I am dealing with the following problem:
Assume that a charge has been placed on the inner cylinder, and that the entire charge is distributed on the outer surface of the inner cylinder as shown in ...
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Newton's approximation of 2+1D gravity
I learnt that the curvature tensor in 2+1D spacetime is zero in vacuum. How is it possible to come from there to the Newton's theory in 2D + time, where I guess, the gravitational force law is still ...
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1D application of the differential form of Gauss' Law for the electric field from a point charge
(This might be somewhat related to a previous question I posted here, however it seemed different enough to warrant a separate post.)
I'm trying to see how, for a point charge at the origin, I might ...
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Uniformly charged sphere inside a dielectric [closed]
Consider a metal sphere of radius $b$ with uniform surface charge inside an insulating material with permittivity $\epsilon$. I want to calculate $E$ and $D$ in the dielectric region. I set up a a ...
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Is it possible to have a non-uniform electric field such that $\nabla\cdot\vec{E}=0$?
If the electric field on a closed region is uniform then by Gauss's law you have $0=\nabla\cdot\vec{E}=\rho/\epsilon_0$, so $\rho$ would be zero.
Is the converse necessarily true? Could we conclude ...
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General solution to the Laplace equation in spherical coordinates
I'm currently going through Jackson chapters 3 and 4 and don't understand what exactly "$l$" or its physical meaning is when looking at the general solution to the Laplace equation in ...
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Where do I fail, trying to adapt Gauss law in 2D? [duplicate]
So I went through the Khan Academy tutorial on divergence and flux calculations for an area C encircled by a parametric function $s(t)$.
Here $C$ will be a circle with a radius $r$, centered by a ...
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Electric flux, is q/absolute permitivity, but is also cross product of electric field and area vector, then why doesnt it increase with radius? [closed]
A charge q is enclosed by a gaussian spherical surface of radius R if the radius is doubled the outward flux will remain the same. How is that possible if flux is also defined as the cross product of ...
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Are irregular surfaces of equal electric field magnitude special?
When we use Gauss' law to derive expressions for the electric field, we usually exploit certain symmetries to ensure that the $E$ term is constant and pulls out of the electric flux integral. For ...
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Faraday's law: How to interpret flux on a time/voltage graph?
Background
This is related to a homework assignment, but my question is more on the conceptual side. I will therefore only paraphrase the problem.
Problem
The question begins with the idea of dropping ...
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What is the general solution to Poisson's equation when source extends to infinity?
If the distribution of the source charges does not go to zero at infinity (as in the case of an infinite line charge), can we still write the most general solution of Poisson's equation $$\nabla^2\phi(...
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If the magnitude of the Electric Field at any point on a surface is 0, then is the net charge enclosed guaranteed to be zero?
I got this question on a recent Physics exam. The answer was Yes.
I understand the basic logic using Gauss's Law:
$$\phi=\frac{Q_\text{enclosed}}{\varepsilon_0}=\iint_S\vec{E}.d\vec{A}$$
So if there ...
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Magnetic flux in a loop from a circular coil
Problem
At the center of a circular coil with length $L$, radius $b$ and $N$ windings is there a small circular ring with radius $a << b$. The ring is coaxial with the axis of the circular coil....
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Is magnetic flux through a closed surface still zero if you just have the North pole of a magnet inside the surface
Before I ask the question, I want to be clear that I am NOT talking about magnetic mono-poles.
Gauss Law of Magnetism says that magnetic flux inside a closed surface is always zero, the reason being (...
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