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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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Electric field Calculations [on hold]

The electric field due to an infinite line of charge is perpendicular to the line and has magnitude $E=\frac{2}{\lambda r}$. Consider an imaginary cylinder with radius $r= 0.250\ \text{m}$ and length$...
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Can a point charge inside a cavity affect the electric field outside the conductor? [on hold]

A solid conductor has a cavity in its interior. Would the presence of a point charge inside the cavity affect the electric field outside the conductor? Why or why not? Would the presence of a point ...
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1answer
38 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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Proof or derivation of Gauss's law [duplicate]

I know all about the law and how to use it.But I've always had a doubt on it's proof. Wherever I look there's either a derivation from Coloumb's law or from the differential form in Maxwell's ...
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3answers
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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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2answers
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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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1answer
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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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2answers
120 views

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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1answer
45 views

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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1answer
40 views

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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0answers
31 views

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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1answer
39 views

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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1answer
53 views

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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1answer
98 views

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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3answers
152 views

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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0answers
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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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Making sense of bound charge

Given a spherical shell with inner radius $a$ and outer radius $b$ with polarization $\frac{1}{r}\hat{\mathbf{r}}$, the density of the volume charge (inside the shell) is negative the divergence of ...
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1answer
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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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1answer
46 views

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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3answers
44 views

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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1answer
31 views

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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1answer
61 views

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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1answer
30 views

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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2answers
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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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2answers
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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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4answers
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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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3answers
60 views

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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1answer
34 views

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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1answer
37 views

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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2answers
22 views

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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2answers
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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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1answer
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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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2answers
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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 ...
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0answers
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Property of surface Green function in electrostatic field

Let's consider a 2D-square with 4 equal subsquares containing different dielectrics. Inside the square domain, the unknown electric potential function $\Phi$ satisfies the Laplace equation: $$\nabla^...
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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
78 views

Electric Field between two parallel plans of opposite charge density

So considering two infinite parallel plans of opposite charge density let's say +σ for the left plan and -σ for the right plan Why is the electric field calculated this way : $$ E = σ/2εo + σ/2εo ...
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Why the integral of Berry curvature over a closed surface is not zero?

I read [1,2] that for a spin-1/2 particle under magnetic field, the Berry curvature is a monopole, $$ \mathbf F_{\pm} = \mp\frac{\mathbf B}{2B^3}, $$ of which the integral over a closed surface is $2\...
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1answer
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Confusion in deriving Gauss law for magnetism

I am deriving Gauss law for magnetism from Coulomb's law of magnetic poles. I have a cubical magnet as shown below and the Gaussian surface is inside the magnet: The magnet can be considered as a ...
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2answers
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Gauss Law For Electrostatics [duplicate]

In Gauss Law for Electrostatics, Electric flux term contains Electric field due to charges that are both inside and outside the Gaussian surface. If we use Gauss Law to calculate electric field at a ...
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Two dimensional hyperbolic potential has no charge density but a surface charge density?

I am learning about electric potential, and I am confused about what exactly is going on in the following situation: Say we have a potential $V =- V_0 \frac{xy}{a^2}$ This means that $\nabla^2V=0$. ...
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1answer
48 views

Electric potential everywhere around an infinite slab

The problem: Consider an infinite slab with uniform charge density $\rho$ between two planes $z=\frac{d}{2}$ and $z=-\frac{d}{2}$. Find the electric potential $V$ in the entire space and plot $V$ ...
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1answer
77 views

I'm confused about electric flux?

In a previous physics class, I learned that the electric flux was $\vec{E}\cdot\vec{A}$ (dot product), and hence the unit is $Nm^2/C$. But in my electromagnetics book, it says the unit is Coulomb, and ...
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0answers
72 views

Flux through a cube of side length $l$

Let's say I have a cube sitting in the first octant with one corner at the origin and of side length $l=0.1$meters. The question from the text is as follows, "The electric field is uniform, has ...
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0answers
33 views

How to calculate the Electric field of an cylinder with length of infinity and given charge density of the surfac? [closed]

I know how to calculate the Electric field of this example if the given variable would be the charge density of the volume but since only the charge density of the area is given, I'm very confused ...
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4answers
434 views

Does a point charge inside a conducting shell cause redistribution of charge in the shell?

A point charge Q is placed inside a conducting spherical shell at a random place (non-centre). I have read that there is no force on Q from the shell no matter where Q is inside the shell ('there ...
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3answers
147 views

Electric field of an infinite sheet of charge [closed]

I am trying to derive the formula for E due to an infinite sheet of charge with a charge density of $ \rho C/m^2$. I assumed the sheet is on $yz$-plane. I used Coulomb's law to get an equation and ...
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0answers
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Space charge density of bound charges

This is a question from Irodov's Problems in General Physics. I can understand the physics but I think I am doing something wrong in the calculus. The problem is : Extraneous charges are uniformly ...
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2answers
114 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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1answer
56 views

Cavendish's experiment on concentric conducting shells

In a paper were there was a section addressing Cavendish's experiment on concentric conducting shells which was basically the following : Two conducting spherical shells were put together (like the ...