A law in Classical Electromagnetism and Newtonian Gravity.

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The origin of Gauss' law for magnetism [closed]

What is the physical axiom leading us to the Gauss' law for magnetism?
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108 views

Sphere of uniform charge density with a cavity problem

Suppose we have a sphere of radius $R$ with a uniform charge density $\rho$ that has a cavity of radius $R/2$, the surface of which touches the outer surface of the sphere. The question was to ...
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62 views

Gauss law for a cylinder shielded by a grounded conductor?

So I am trying to solve the following problem: My approach: Applying Gauss's law on the two regions yields the following $$\mathbf{E}=\left\{\begin{matrix} \frac{\rho _0 \rho ^3}{4\...
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339 views

Charge per unit length and charge per unit area

In the Halliday and Resnick book, I am asked the find the linear charge density of the inner wall of a shell. This confuses me because the inner wall of a shell is an area, not a one dimensional line. ...
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109 views

Gauss' Law and enclosed charge

In Halliday and Resnick, I am asked to find the charge on a drum (a cylinder) given the electric field very close to the drum. In the solutions manual, the author appears to enclose the drum with a ...
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86 views

Determining Electric Field Inside Long Cylinder (Using Gauss' Law)?

I'm working on a problem with an (infinitely) long cylinder with a charge density, and I'm trying to find the electric field. Using the charge density, I found the enclosed charge of a proportional, ...
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253 views

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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241 views

Gauss Law - Infinite line charge

I came across a sentence which made no sense to me as I was studying the electric field of an infinite line charge: The flux through the FLAT ENDS of our cylindrical Gaussian surface is zero ...
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133 views

Gauss law example - Electric field and dA [duplicate]

I am still very confused and lost. I still dont understand why E1 is pointing down , E3 and 2 pointing up. while dA is point the left and dA2 and dA3 are in the same direction of the E3 and E2. I ...
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36 views

Gauss law question with regard to this example

I am really confused in Gauss law. Why do E3 and E2 pointing up? and also E1 pointing down? The lecture note said infer from symmetry and you will get the following but I dont really understand. ...
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Gauss Law Question [duplicate]

Why is ${\rm d}\vec{A}_1$ pointing up and ${\rm d}\vec{A}_2$ pointing down? Electric field ${\rm d}\vec{E}_1$ is pointing up so isn't it supposed to be perpendicular to the surface?
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Gauss Law Question. Could anyone explain to me why does S3 is 0 in this lecture note example?

Why does S3 equal to 0 ? for E3 dot dA = 0? Could I also know why does dA1 and dA2 point up and down? while dA3 point to the right?
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Newton's shell theorem in 2d [closed]

I was wondering how to prove the analog of Newton's shell theorem for 2 dimensions, in which gravity obeys an inverse-linear law. Meaning: that an anywhere inside a circle, the gravitational field ...
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307 views

Difference between $E$ field configuration, sheet of charge: infinite sheet of charge, conducting vs. non-conducting

This is a very easy question, but I often confused myself. Perhaps someone could explain this concept again: A non-conducting infinite sheet of charge has the electric field configuration \begin{...
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2answers
130 views

How is the differential form of Gauss Law used?

How is the differential form of Gauss's Law $\mathbf{\nabla}\cdot{\bf E} = \dfrac{ρ}{ɛ}$ used? What I mean is, where am I measuring $E$ and what is $ρ$ in this context?
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379 views

Flux through a sphere due to a charge outside of it [duplicate]

A point charge of $\rm+5.00 μC$ is located on the $x$-axis at $x=\rm5.00m$ , next to a spherical surface of radius $x=\rm4.00m$ centered at the origin. According to Gauss's law, the net flux through ...
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33 views

Potential on a uniform

My doubt is in the part where he sets $V=V_s - \int{E dr}$. My idea is that he is summing two potentials, from the surface, and the one he's trying to calculate with the integral. Is that right? If so:...
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152 views

Flux of electric field through a closed surface with no charge inside? [duplicate]

I'm reading the Feynman lectures on electromagnetism and in Vol II, Chapter 1.4 Vol. II, Chapter 1-4 he talks about the flux of the electric field and says that flux of $E$ through and closed surface ...
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2answers
555 views

Gauss' law in differential form for a point charge

I'm trying to understand how the integral form is derived from the differential form of Gauss' law. I have several issues: 1) The law states that $ \nabla\cdot E=\frac{1}{\epsilon 0}\rho$, but when ...
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1answer
56 views

Effect of introducing an external charge beside a Gaussian surface

As far as I know, Gaussian surface's are surfaces that enclose a net charge and are shaped in such a way that the electric field vector's magnitude is the same over the entirety of the surface. My ...
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2answers
472 views

What is Gauss's Law in two dimensions?

I am trying to figure out how the equation for the field if a Gaussian surface was applied to a 2D plane. I did see another question already asked on the subject, but I didn't get a particular ...
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415 views

When I take a Gaussian surface inside an insulating solid sphere, why does the outer volume have no effect on the electric field?

Say I try to find the magnitude of the electric field at any point within an insulating solid sphere. I know that in the case of a conductor, the electric field within it is 0. However, I have not ...
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171 views

What is the divergence of a uniform field?

I was recently studying Maxwell's equations. Got a bit confused about divergence. Would someone please tell me if the divergence of a uniform electric field = $0$, & why it is so?
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1answer
105 views

Help me understand Gauss law

Suppose I have the following, the gaussian surface is the drawing in the middle. So charge enclosed is zero, and then eletric field must be zero since the area of the gaussian surface is not zero. But,...
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37 views

Eletric field on a slab, uniform volume charge density

These are the question and the solution in solutions manual. However, I don't understand the step in which he goes from $\rho V/A$ to $\rho \Delta x$.
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788 views

Is there no electric field inside a hollow cylinder?

This is from question 4 here: http://oyc.yale.edu/sites/default/files/ps02_1.pdf http://oyc.yale.edu/sites/default/files/ps02_solutions_1.pdf The question discusses a hollow conducting cylinder ...
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Contradictory surface charge density relations

I've seen in many places the relation $$\sigma = - \epsilon_0 \frac{\partial V}{\partial n}$$ Where $\sigma$ is the surface charge density, $V$ is the electric potential, and $n$ is the direction ...
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160 views

Charge distribution on a Gaussian surface

In the text, it is said that the skewed distribution of positive charge on the inner wall cannot produce an eletric field in the shell to affect the distribution of charge on the outer wall. Why? ...
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73 views

Do relativistic electrons have more charge?

Gauss's law tells us that the total electric flux out of a closed surface is equal to the charge enclosed divided by the permittivity. When a charged particle is moving close to the speed of light it'...
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74 views

Is it possible for a conductor initially, not to have a charge?

Well I'm confused. The thing that was implanted to me is that when I hear about conductors, some charge is present and it can move freely. Now what I want to know is that is it possible for a ...
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1answer
64 views

Simple question regarding Gauss's electric law

I just read that electric flux=enclosed charge/permittivity. Considering the charge in an enclosed surface is always 0, what is the point in even having this equation? Or is the equation actually ...
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407 views

Flux through closed surface

My class teacher says charge kept outside a closed surface will not hold any flux because number of field lines entering are same as number of field lines exiting. But when I imagine sufficiently big ...
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175 views

Flux of $E$ through the shaded side

A charge $q$ sits at the back corner of a cube, as shown in Figure. What is the flux of $E$ through the shaded side? One of the solution stated that. Looking at the figure, we notice two things: ...
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Surface bound charge in the electric displacement

In Griffiths, the electric displacement is written with just volume charge density, and that is because, he says, 'we cannot apply gauss law precisely at the surface of a dielectric, for here volume ...
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95 views

Will two touching, neutral conductors in an electric field separate?

If you put two square, neutral conductors in the middle of a uniform electric field such that they are touching, will they separate? I thought yes. When they are touching, as shown in the picture, ...
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1answer
104 views

Electric field between capacitors [closed]

A parallel-plate capacitor consists of two parallel, conducting plates of area $A$, separated by a distance $d$. Each carries a charge of magnitude $Q$; positive on one, negative on the other. Using ...
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4answers
544 views

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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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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1answer
172 views

What would happen if the Earth were hollow? [duplicate]

This is a question of my exam. What would a person experienced if he were put in any point inside the Earth that is hollow (all its mass is concentrated in the surface). Finding the gravitational ...
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137 views

Is the electric field at a single point inside a charged sphere zero?

Many physics textbooks say, Gauss' law shows that the electric field inside a sphere with uniform charge distribution on the surface equals zero. What I want to know is, do they mean total, i....
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Why, when and where is Gauss's law applicable?

Why is it said that Gauss's Law is mainly applicable for symmetric surfaces/bodies? Why not for asymmetric surfaces? I want a logical explanation! BTW my teacher said that Gauss's law is ...
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1answer
107 views

Electric field of a plate with homogenous charge density

As an example for Gauß Law's application, one can find the calculation of an electric field of a plate with homogenous charge density in nearly every textbook: $$E = \frac{\sigma}{2\epsilon_0}$$ I do ...
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136 views

question about Gauss law

If I have an infinite plate with the surface charge of sigma. I know that my electric field is constant $2\pi\sigma$ (using Gauss's law). If I build the Gaussian surface above the plate the charge ...
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1answer
147 views

How do you know when you need to use distributions to represent charge densities? [closed]

I tried to solve a problem using Gauss' law in the following way. Let's assume we have a spherical shell of radius $R$ with a charge $Q$ being homogenously distributed on its surface. I am trying to ...
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42 views

Dirac delta function equation intuition and proof [duplicate]

What is the intuition and where should I find proof of this equation (do not know what its name is). It is used to derive Gauss law from Newton equation. $${\nabla \cdot \Bigg ( \frac{\vec{s}}{|\vec{s}...
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Electric field from time varying charge density

Inside a cylinder of infinite length in $z$ axis, there is charge density $ ρ = cos(βz -ωt)$. I want to find the electric field and as far as i can understand we will get a radial component of $E$. ...
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How would a closed conductor with only 1 layer of (atoms/molecules) behave if a charge is placed inside it?

I have quite a few questions actually related to this . Is it possible to have such a situation practically? If theoretically possible, how would the system behave?
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What is meant by “unique direction” in most of the arguments in application of Gauss' Law?

This term is really bothering me a lot. While explaining the radial direction of electric field of a uniformly charged sphere, my book writes: Notice the use of argument of symmetry. There is no ...
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1answer
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Gauss' law and external electric flux through a cube: net flux is not zero while the interior charge is 0. What have I done wrong?

Consider a cube with side length $L$ and with its sides parallel to the basis vectors $\vec{i}$, $\vec{j}$ and $\vec{k}$. The $X$ axis goes right through the center of two of its faces. The closest ...
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566 views

Capacitance of three plates

I'm sorry if this has been asked before, but here it goes. Consider three parallel plane conducting plates (they can be infinite) and suppose the middle plate has some thickness $\delta$ and the other ...