A law in Classical Electromagnetism and Newtonian Gravity.

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Electric potential due to surface charge distribution on a conducting sphere

Let's consider a conducting sphere. If we charge the sphere, it is understood that there will form a surface charge distribution such that the surface of the sphere is an equipotential surface $ 0=\...
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76 views

Proof of integral form of Gauss's Law from Coulomb's law without using differential form of Gauss's Law

The integral form of Gauss's Law is: $$\unicode{x222F}{\vec{E}}\cdot{\vec{dS}}=\dfrac{q}{\epsilon_0}.$$ Is there a direct derivation of it from Coulomb's law without using differential form of Gauss'...
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Surface charge outside conductor

If I have a hollow conductor of arbitrary shape, and have a charge placed inside is cavity, then is there anything I can say for sure about the charge distribution on the outer surface? I know that ...
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55 views

Do any fundamental particles with gravitational or electric dipoles exist?

For magnetism: $$ \oint \vec{B} \cdot \mathrm{d} A = 0 $$ For electricity: $$ \oint \vec{E} \cdot \mathrm{d} A = \frac{Q}{\epsilon_0} $$ For gravity: $$ \oint \vec{g} \cdot \mathrm{d} A = -4\pi G ...
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27 views

Force between the plates of a capacitor

As we know that the electric field between two parallel plates of a capacitor is $$E=\frac{\sigma}{\epsilon_0}$$, so the magnitude of force exerted by one plate on the other should have been $$F=QE$$. ...
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What moves the charges between capacitors?

Suppose I charged two capacitors to charges Q1 and Q2. By charging a capacitor to charge +Q , I mean that one plate acquires a net charge +Q and another plate acquires a net charge -Q.The capacitors ...
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36 views

Determination of the electric field of charged object using Gauss's law

when we determine the electric field of a charged rod of infinite length,we consider a circular cylinder to be the gaussian surface for convenience.In the case of a charged sheet we choose the ...
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1answer
71 views

Does changing a closed surface in the manner outlined contradict Gauss' Law?

As I understand it, Gauss' Law states that the electric flux on any arbitrary closed surface is equivalent to the sum of all charges enclosed within the surface times a constant. Mathematically, this ...
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37 views

Electric field inside an insulator's cavity [closed]

I'm trying to find the electric field inside insulating sphere's cavity, and I don't know how. However, if there was an conductor I'd know that $E=0$ from Gauss's Law.
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173 views

The Zero Electric Potential of the “Earth”

I know its the potential differences that matter and generally we define the zero of the electric potential according to our convenience. I would like you to look at this standard problem: Charge $-...
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Calculating charge density $\rho(r)$ using Gauss law (both forms)

Below is a question given in my assignment. I tried applying Gauss law in both forms, differential and surface integral form. But both there is a difference by a factor of $2$. Is the differential ...
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21 views

Electric field of an infinite plane (with and without an infinite conductor)

Suppose we have an infinite and uniformly charged (of surface charge density $\sigma \gt 0$) plane at $z = 0$. We can find the electric field at any point $(x, y, z)$ by computing an integral all ...
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42 views

Electric Flux in a Cube [closed]

Suppose there are 2 cases: A hollow cube with a point charge $+q$ at the center of one of the faces A hollow cube with a point charge $+q$ at the midpoint of one of the edges. In case 1, the ...
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65 views

How to apply Gauss law at null points?

How do I use law to determine total flux at Gaussian surface at null point? It seems , when I consider a Gaussian surface around null point, two axial electric field lines enter it but they don't ...
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44 views

electrical field in coaxial cable

When getting the electric field between the outer and inner cylinder. why is it that we are only concerned with the field generated by the positive charge distribution on the inner surface and not ...
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32 views

Electric Flux in a Gaussian Surface

Why is electric flux of a charge everywhere inside a Gaussian Surface constant? I want explanation ( not from any equation ).
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What is the relationship between potential energy and electrical potential?

I actually always thought this was trivial, now I am not so sure. For a potential $\phi$ the potential energy is $V=q\phi$ where q is a test charge. Now I am thinking this may work differently in two ...
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While deriving Coulomb's Law from Gauss' Law, the power of 'r' comes out to be exactly 2 while experiment shows that it differs about 10^(-16). Why?

While deriving Coulomb's Law from Gauss' Law, the power of 'r' comes out to be exactly 2 while experiment shows that it differs about 10^(-16). Why is it so? I'm referring to the book 'Physics by ...
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57 views

Calculating the surface integral over a charged box [closed]

In a question that I'm trying to solve, we're told that there is a box with dimensions 20cm long, 4cm high, and 3cm deep. we're given that the electric field on every surface of the box is pointing ...
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1answer
47 views

Gauss law and electrostatic induction. Concentric spheres

Imagine you have hollow concentric spheres A and B with radius a and b (b>a), respectively. If A is a conductor and B has a certain density charge, I´ve been taught that B will induce some net charge ...
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1answer
93 views

Electric Flux is zero

When is the Electric Flux zero through a closed surface? I know that if number of field lines entering is equal to leaving then it is true. Which I think is always true for a closed surface. So can ...
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2answers
46 views

Electric Field Vector on an insulating solid ball

An insulating solid ball with radius $R$ has a uniform charge density $ρ$. Find the electric field vector inside and outside of the ball if it has dielectric constant $K$. Normally, I'd treat this ...
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65 views

Spherical Shell with Electric Field Zero Everywhere Inside It

If an isolated, charged spherical shell has a uniform charge distribution, the electric field everywhere inside it is 0, by Gauss' Law. Is the converse true? That is, given an isolated, charged ...
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1answer
52 views

Surface density charge, divergence of the electric field and gauss law

It´s known that the divergence of the electric field at a certain point is given by this formula: $$\nabla \cdot E=\dfrac{\rho (r)}{\epsilon_{0}}$$ Being $\rho (r)$ the volume charge density at that ...
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59 views

Non-Zero Electric Field Inside A Conducting Shell

Statement: "The electric field is zero everywhere inside the conductor, whether the conductor is solid or hollow." Question: A coaxial cable consists of a long, straight filament surrounded by a long,...
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1answer
43 views

Gauss Law with a hollow asymmetric surface

In this video, Walter Lewin argues that no charge will appear on the inside surface of a hollow conductor in electrostatic equilibrium. He uses a Gaussian surface contained entirely within the ...
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How do we calculate electric field on the axis of a disc using gauss law and the concept of solid angle?

We can easily find the electric field at the axis of the disc by considering a differential ring and then integrating it to form a disc, but I was searching for rather a bit simplified proof using ...
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1answer
41 views

Gauss law in dielectrics

How shall we apply Gauss's law for a space such that the volume enclosed by the Gaussian surface have 2 or more mediums with different dielectric constants, such that equal or more than two ...
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1answer
59 views

Confusion regarding gauss law

Gauss law states that flux due to net electric field on a Gaussian surface is charge enclosed/permittivity. Lets take a spherical Gaussian surface with +q charge at centre. We can simply calculate the ...
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1answer
37 views

Coaxial cable with electric flux

I had a question when I solved some examples of coaxial cables. I want to find the E and D field using $\rho_s = {Q \over {2\pi r L}}$. Here is my question: Why is the inner surface of the cylinder ...
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1answer
58 views

Electric field at surface of a spherical shell

The shell theorem provides a well known result that for a spherical shell with uniformly distributed charge $Q$ and radius $R$, the electric field at a distance of $r$ from the center is: $$\begin{...
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1answer
41 views

Properties of a body with spherical symmetry

I'm studing Gauss law for gravitational field flux for a mass that has spherical symmetry. Maybe it is an obvious question but what are exactly the propreties of a spherical simmetric body? A ...
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1answer
54 views

Gauss's law, electrical flux density [closed]

Q. Given a 60-μC point charge located at origin, find the total electrical flux passing through the plane z = 26 cm. I can understand what the question means, but I can't do anything. Is it using ...
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279 views

Why is Electric field flux through a closed surface in Gauss's law not zero?

I learned that the vector flux through any closed surface is always 0. So if you have a sphere(closed surface) and you put it in an uniform electric field, then the total flux is 0. However, the ...
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Electric field intensity near to a small conducting plate?

I know the electric field intensity near a infinite charged conducting plate. when the plate is very large we assume that there is a symmetry and take the electric field intensity as same as for ...
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46 views

When deriving potential between plates of parallel plate capacitor, why isn't the charge distributed on the top *and* bottom of both plates?

Let's say we have a canonical parallel plate capacitor with area $A$ and separation $d$ where $A>> d^2$. A charge of $+Q$ is placed on the top plate and $-Q$ is placed on the bottom plate. We ...
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39 views

Electric field Intensity , parallel plates

My book says that the electric field due to infinite long plates doesn't depend on 'r', so does it mean that no work is done in moving a point charge towards or away from it? Also considering the ...
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40 views

Electrostatics Of Conductors

My textbook says that no excess charge can reside inside the conductor because electric field inside a conductor is 0. But say i introduce a positive charge inside a conductor, it generates its own ...
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1answer
50 views

Is Gauss law still true in dielectric material?

In vacuum we have $$\nabla \cdot \mathbf{E} = \frac {\rho}{\varepsilon_0}.$$ Can we still use this formula when there's dielectric material in space? Where $\rho$ is total charge density.
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Electric field between 2 parallel plates

The question state that 2 large parallel plates are a distance $d$ apart and the field at $d/2$ is $E$ if the distance between the plates are reduced to $\frac{d}{2}$ what is the field strength ...
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1answer
101 views

Gauss' Law Proof for a cube

Some days back I learnt the proof of Gauss' Law by this method. (Proof) My teacher did it in this way using a sphere. I got to thinking whether it can be proved using a cube instead of a sphere. I ...
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Electric field due to a charged irregularly shaped balloon

There is a question in my textbook that says: A rubber balloon is given a charge $Q$ distributed uniformly over its surface. Is the field inside the balloon zero everywhere if the balloon does not ...
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33 views

Experimental tests of Gauss's law

Can you please tell me what this small article means. Why did the charges flow to the outer suface of the hollow conductor, and how does this relate to gausse's law and the inverse-square law. Thanks ...
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1answer
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Is there an underlying reason why some forces are inversely proportional to the square of the distance? [duplicate]

This is the first time I'm studying those subjects (I'm still in high school) and my teacher couldn't give me an answer. I'm referring specially to Newton's law of gravitation and Coulomb's law of ...
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1answer
112 views

What is the proof for Gauss's law? [duplicate]

What is the proof for Gauss's law? Can you give me some explanation and details with the proof?
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1answer
65 views

Gauss law in gravitation

Is it possible to use Gauss's law of electromagnetism, (The net electric flux through any closed surface is equal to $1⁄\epsilon$ times the net electric charge enclosed within that surface.) to ...
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47 views

Does Gauss flux theorem hold in relativity?

Does the Gauss flux theorem, stated in the classical electrostatics as $\iint{\vec{E}}\cdot{\vec{dS}}=q/\epsilon_0,$ hold in the case of relative motions. For instance if we observe a charged body ...
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1answer
35 views

Simulating the Electric Field inside a Hollow Sphere of Uniform Charge

I've recently been studying Gauss's Law and have come across some results that I want to verify. For one, I am trying to verify that the electric field inside a conductor (in this case it could be ...
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1answer
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Gauss Law - charges outside the gaussian surface

I have just learned Gauss Law and this question is bothering me: Suppose a cubic gaussian surface and a charge next to its right side (image below). According to Gauss Law, the electric flux over ...