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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 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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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. ...
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44 views

Why does charge 'stick' to the Gaussian surface?

I'm currently studying Gauss's Law and interaction of the charge with different Gaussian surfaces etc. But here's something that I couldn't understand. Why does a charge 'stick' to a Gaussian surface? ...
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Deriving the electric displacement field ($D$ field)

I am trying to derive the $D$ field (or electric displacement field): $$D=\varepsilon _{0}E+P$$ I am using the following relationships: $$\rho=\rho_{f} + \rho_{b}$$ $$ \rho_{b} =-\nabla \cdot P$$ ...
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Electric field of infinite sheet

I have a question regarding the electric field of an infinite sheet in the $x-y$-plane at $z=0$ with a constant sheet charge density $\sigma$. There are many ways to obtain the result $$\boldsymbol E=\...
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Electrostatic force per unit area on a hemisphere due to its other half

From Griffiths, intro to electrodyanmics: Now, I approach the problem a different way then he does, and I miss the answer by a factor of half The way I do it is that I find the electric field ...
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Why is $ \nabla \cdot \vec{E} \neq 4 \pi\ k$ times the charge density?

For a line charge with density $\lambda$, we wish to compute the divergence at a point on line charge. We start from definition of divergence: $ \nabla \cdot \vec{E}=\dfrac{d \iint \vec{E} \cdot d\...
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Is it possible to have a spherically symmetric constant Electric Field $\vec{E} = E_0 \hat{r}$?

I've been studying the Laplace equation for zero charge distribution: $$\nabla^2 V = 0$$ and I know that this is the general solution to the Laplace equation for an azimuthally symmetric ...
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How is the $E$-field getting canceled between outer and inner surface of a neutral conducting spherical shell?

I am reading Purcell's E&M book and in one of the example questions, it shows that there is no E field between outer and inner surface after a a point charge is located at an arbitrary position ...
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Why Gauss divergence theorem isn't working? [duplicate]

$\vec{E}$ is electric field $r$ is distance between source and field points $\hat{r}$ is a unit vector from source point to field point $x,y,z$ are Cartesian coordinates of field point ...
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Will the flux through an arbitrary closed surface be finite or infinite when a plane charge intersects the Gaussian surface?

Let's consider a closed Gaussian surface (in red). The white line and the white shaded part lies inside the Gaussian surface and the black line and the portion above it lies outside the Gaussian ...
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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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What is the mathematical reasoning behind the inverse square law of two charges?

The Hon. Henry Cavendish performed an experiment with two spheres, by which he proved that no electric force is produced inside a hollow charged sphere. In other words, proving that no electric field ...
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Electric field due to uniformly charged infinite plane sheet

For getting the electric field in this case we use the Gauss's law. we get the equation $$ 2EA = pA/\epsilon_0 $$ here $E$ is electric field, $A$ is the cross sectional area, $p$ is the uniform ...
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An alternative version to solve a electrostatic problem without definition of flux

I have this problem: The figure shows the electric field lines around a system of three charges $q_1$, $q_2$ and $q_3$. The central charge have a value of $q_2=-10.0\,\mu\mathrm C$. Find the value of ...
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Charge inside spherical cavity [duplicate]

Suppose we have a sphere and a cavity inside which is displaced at a distance $d$ from the center. If a charge $q$ is placed in the center of that cavity, a surface charge $-q$ is induced in the ...
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How shall we compute the flux in this case?

I have a finite surface charge (in yellow) which cuts a Gaussian surface (in green). Red points are the points of singularity on the Gaussian surface (i.e. where $\vec{E}$ is undefined). Does this ...
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How is the third case obeying integral form of Maxwell's second equation?

Let $m$ denote pole strength. In the diagrams: (1) Sky blue: Closed Gaussian surface (2) Red: North pole of magnet (3) Green: South pole of magnet (4) Yellow: Part of magnet cutting Gaussian surface ...
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What actual difference does it make whether electric or magnetic field lines are open or closed?

If both electric and magnetic fields attenuate with distance by the inverse square law, what difference does it make that the latter's field lines are 'closed'? And if a magnetically-induced electric ...
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Confusion concerning the application of Gauss's law using symmetry arguments

Suppose we want to prove Coulomb's law from Gauss's law. The thing to do is to invoke a spherical Gaussian surface centered at a point charge, notice that there's symmetry and use that to calculate $\...
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Is there a higher-level reason why $\nabla\cdot(\hat{\bf r}/r^2) = 0$ in three dimensions but not two? [duplicate]

I am working through Griffiths, Introduction to Electrodynamics, and finding the divergence of the electric field generated by a single charge sitting at the origin. $$\mathbf{E}(\mathbf{r}) = \frac{\...
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Gauss' Law to Find Electric Field Inside a Uniform Insulating Ball

My question is more about how Gauss' Law can be used to find the strength of the electric field inside an insulator when the Gaussian surface used only contains a portion of the total charge. From my ...
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How does Gauss's Law work with this charge density setup?

My friend and I are self-studying electrodynamics. In Griffiths, Introduction to Electrodynamics (1999), the concept of divergence is introduced mathematically and the following vector field is drawn. ...
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Why is the divergence of electric field equal to $\rho \over \epsilon_0$ in electrodynamics?

These two equations are true in electrostatics/magnetostatics: $$\nabla \cdot \vec{E}= {\rho \over \epsilon_0},$$ $$\nabla \cdot \vec{B}=0.$$ I have learned that they are also true in electrodynamics....
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Why is the electric field between two parallel plates uniform? [duplicate]

According to sources online (eg HyperPhysics) the electric field strength around a point charge is $$E=k\frac{Q}{r^2}$$ This must means that the further you get away, the electric field should ...
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Gauss law with two infinite planes

The electric field of an infinite plane above its surface is $E=\frac{\rho}{2\epsilon_0}$, where $\rho$ is the surface charge density and $\epsilon$ is the permittivity of free space. If we have two ...
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Electric flux of a cube with charge at the center [closed]

I've known gauss' law that any closed surface with some net charge inside, the electric flux would be q/ε0 , but some professor told us that a cube cannot be a gaussian surface and that the electric ...
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Electric field due to an infinite plane slab

So the solution says that in the x z plane, E = 0 by symmetry that is my problem, how is E = 0, maybe I can't visualize it correctly, however if I assume that that's really the case, I can continue ...
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Electrostatics: Charge Distribution and Energy - Confusion

Consider the following situation: Between two metallic plates, are two dielectrics of dielectric constants $K$1 and $K$2. The surface charge density on the upper metallic plate is $\sigma$, and that ...
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Can $E=\frac{q}{4\pi\epsilon_0 r^2}$ be directly derived from differential form of Maxwell equations?

The electric field of a point charge $q$ is well known to be $$\mathbf E=\frac{q}{4\pi\epsilon_0 |\mathbf r|^3}\hat{\mathbf r}$$ This can be derived easily from integral form of Gauss’s law. Taking $...
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Notion of flux and field lines

I am curious about the origin of electric flux and field lines. -Flux- I am aware of the fact that flux is a mathematical concept, but how did it find its way into physics? Was it just introduced ...
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Closed field lines in case of a Bar magnet

Field lines in case of charges go from +ve to -ve but incase of magnet, they dont start or stop anywhere. They form closed loops. Is this consequence of the fact that single poles dont exist or ...