A law in Classical Electromagnetism and Newtonian Gravity.

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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
127 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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1answer
362 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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1answer
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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2answers
149 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
526 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
451 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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2answers
386 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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2answers
164 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
101 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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1answer
754 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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3answers
65 views

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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1answer
148 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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1answer
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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1answer
73 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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3answers
393 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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5answers
163 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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1answer
159 views

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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1answer
92 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
100 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
525 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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3answers
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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
167 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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3answers
135 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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4answers
1k views

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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1answer
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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0answers
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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58 views

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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2answers
265 views

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
232 views

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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1answer
537 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 ...
2
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1answer
346 views

Method of image charges [closed]

In an attempt to understand the Method of image charges, I'll try to calculate the total charge on grounded conducting plane - with electric dipole & point charge. Given: Point charge $Q$, ...
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2answers
227 views

Gauss' Law and area vector

Recently I've been doing some physics exercises on electric and magnetic fields and read up somewhere that the vector area of a closed surface is equal to zero. That made me wonder why, when using ...
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246 views

Gauss law for gravitational field

Gauss's law is fundamental law of electrostatics. But Can we apply Gauss's law for Gravitational field also?
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Sphere of electric charge revisited

I am thinking about a sphere of homogeneous charge distribution (see Electric field due to a solid sphere of charge, for example). Here we use a Gaussian surface (blue area) to find the electric ...
2
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1answer
272 views

How to approximate trajectories and movement of two oppositely charged particles?

Imagine a single, stationary charged atomic ion, say a Lithium anion or cation (Li+ or Li-). Now imagine another a single free, oppositely charged particle--perhaps an electron or Hydrogen ion (H+)--...
2
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1answer
49 views

Would a non-conducting body ever acquire a uniform static charge throughout it's volume?

I'm studying electromagnetism and optics in first year and solving a lot of problems involving conveniently symmetrical conducting and non-conducting bodies having various uniformly distributed ...
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2answers
134 views

Question about Gauss' law and dipoles

I've got a question about dipoles and Gauss' law: Consider an electric dipole $p=ql$ in free space, centred at the origin of a Cartesian reference frame. Using Gauss’s Law, discuss if the electric ...
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1answer
171 views

Gauss's law and charge on surface

Consider a cone (not necessarily right cone), with a charge $q$ at its apex. Fix its base, and let the vertex be movable. Now suppose we intend to find the flux through the base. Since the flux ...
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1answer
63 views

Are $Q1$ and $Q2$ attracted or repelled to the sphere shown in the figure below? [closed]

Can you tell from the image below if Q1 and Q2 are attracted or repelled. Will Q2 only be attracted to the sphere if Q2 is enough bigger than Q1? Will the positive charge inside the shell attract ...
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2answers
97 views

Potential difference inside charge distributions

Always when I think about potential difference inside a symmetrical charge distribution, I think of it being equal to zero because it's dependent on the field and I imagine the directions of each of ...
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4answers
383 views

Electric field on the surface of a charged sphere

We know that the electric field for a point charge is $$ E = \frac{KQ}{R^2}. $$ If $R$, i.e. distance from the electric field producer to the point where we want to find the electric field becomes ...
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95 views

Shell theorem using Gauss Law

Let me present you my problem: Two spherical shells with radius $R_1$ and $R_2$ ($R_1 < R_2$) and masses $M_1$, $M_2$ are concentric. Calculate the gravitational force $\vec{F_g}$ applied ...
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1answer
37 views

where does the term half in the formula of electrostatic potential energy comes from?(system of point charges)

Electrostatic potential energy stored in a system of point charges (from wikipedia) The electrostatic potential energy $U_E$ stored in a system of N charges q1, q2, ..., qN at positions r1, r2, ...,...