A law in Classical Electromagnetism and Newtonian Gravity.

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Why does the density of electric field lines make sense, if there is a field line through every point?

When we're dealing with problems in electrostatics (especially when we use Gauss' law) we often refer to the density of electric field lines, which is inversely proportional to the radius in the case ...
2
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0answers
56 views

Gauss' Law and Electric Field Close to a Ball

So I've learned about Gauss' law and I have something in my head. Why does electric field that is very close to a ball is not close to infinity. Take a look at this image: As we can see, if we make ...
6
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0answers
394 views

Modified Coulomb potential [on hold]

I'm working through Byron and Fuller's "Mathematics of Classical and Quantum Physics" and came across this problem: If the electric potential of a point charge were $\phi(r) = \frac{q}{r^{1-\...
3
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1answer
53 views

Removing an electron from a conductor

I'm trying to understand how to think of and visualize a conductor where charge is added. As I understand, conductor are defined as materials (where the nucleus is stationary) that permit electrons ...
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3answers
64 views

Intuitive explanation for uniform electric field between capacitor plates

Could anyone explain why the intensity of the electric field between plates of a charged capacitor is constant? Moreover, the varying the distance between plates doesn't change the electric field ...
5
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2answers
54 views

Significance of electrical fields of infinite objects

I've noticed a pattern with the electric fields of charged objects of infinite dimensions. A point charge, which can be considered a charge of 0 dimensions, has an electric field that goes as $r^{-2}$...
1
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0answers
31 views

Discontinuity of electric field formula [on hold]

I'm trying to understand where the formula for the discontinuity of an electric field when you cross a uniformly charged surface comes from: $$\vec{E}_{\textrm{above}} - \vec{E}_{\textrm{below}} = \...
0
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1answer
165 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 ...
0
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1answer
190 views

Electric field inside coaxial cable

I have a very long coaxial cable with a cylindrical core of radius $a$ that has negative charge density $\rho = -k/r$ where $r$ is the distance from the axis of the cylinder, and an outer shell of ...
2
votes
3answers
113 views

How did the constant $\pi$ creep into Einstein's field equation? [duplicate]

The ratio of a circle to its diameter in Euclidean space appears in places that sometimes appear to be mysterious. I am wondering if in Einstein's field equations he is using Poisson's formulation of ...
1
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2answers
34 views

Trouble understanding Electric flux and gauss law

Well, i know that the electric flux is the number of field lines passing a certain area, but (1)what does that mean? I can't the concept itself. I know it have many applications, gauss law one of them,...
1
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1answer
43 views

Floating in a Dyson Sphere

Consider your typical Dyson Sphere scenario. You are standing on the inner side of the sphere. You look up and see the shining sun far away. My question (or thought experiment rather) is: ...
2
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4answers
260 views

Why do magnetic field lines converge where the strength is strongest?

In most of the sites, they just say that "to determine the strength of the magnetic field, one must look at how many lines are present at a particular location." But my question is why? Why is this ...
3
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3answers
123 views

What does the Dirac delta function physically do while deriving Gauss Law form Coulomb's law?

While doing this derivation, the the source coordinates are mentioned as "$s$" and the coordinate of the point at which field is to be calculated is mentioned as "$r$". Kindly follow this Wikipedia ...
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1answer
12 views

Potential and Field for a sphere with a central core of differing density [closed]

A spherically symmetric planet of radius $a$ consists of a central core of radius $b(<a)$ of uniform density $\rho_1$ surrounded by an outer region of uniform density $\rho_2$. Obtain an expression ...
5
votes
3answers
182 views

How to show mathematically that the electric field inside a conductor is zero?

The electric field is characterized by the equations $$\nabla\cdot \mathbf{E} = \dfrac{\rho}{\epsilon_0}$$ $$\nabla \times \mathbf{E} = 0$$ Or equivalently, $\nabla^2 V = -\rho/\epsilon_0$ and then ...
1
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1answer
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? ...
2
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1answer
121 views

Electric field in a hollow object

I am currently visiting a course about electrodynamics. In my last lecture it was said that if a hollow sphere is inside of a bigger sphere, but only in the bigger sphere there are spherically ...
3
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3answers
308 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{...
0
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1answer
158 views

How can electric field representation be obtained from Enge representation using Maxwell's equations?

Suppose we have a long electric capacitor. Let $L$ be its length ($z$ coordinate), $W$ its width ($y$ coordinate), and $D$ its full height (full aperture; $x$ coordinate). Let $L\gg W\gg D$. The ...
1
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1answer
116 views

How to calculate Electric Field near a charged conducting surface without Gauss' law?

I have two problems : In every textbook I find the use of Gauss' law in calculation of Electric Field near a charged conducting surface. Can it be calculated without Gauss' law? Suppose while using ...
4
votes
4answers
203 views

Electric field dependence on distance

How can it be proved that for a point charge, $E$ is proportional to $$1/r^2$$ using the concept of Electric field lines (or lines of force)? I tried to show that if field lines are close, then ...
0
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1answer
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 ...
3
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1answer
78 views

Gaussian surface question: arbitrary wire in a plane

I have a question about the setup in the image below. For the wire with $Q+$, if I draw a Gaussian Cylinder that just encloses the wire (as shown), where $s_1$ is the top surface of the cylinder and $...
2
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1answer
126 views

What is the significance of the Inverse-square law? [duplicate]

Considering its occurrences in various fields like Electrostatics, Gravitation, Acoustics etc. how does the law bind these topics together?
4
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1answer
80 views

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 ...
2
votes
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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0answers
55 views

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=\...
4
votes
2answers
96 views

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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1answer
37 views

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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2answers
31 views

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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2answers
135 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 ...
4
votes
1answer
62 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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1answer
47 views

Derivation Poisson's gravity equation by divergence theorem [closed]

I'm trying deduce the poisson's equation $\nabla^2\Phi (x)=-4\pi G\sigma(x)$ by divergence theorem Let $D:x^2+y^2+z^2\leq 1$ and $\sigma:D\to \mathbb{R}$ be the mass density function of $D$ (suppose ...
0
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1answer
104 views

Why Poisson's equation is important?

The Poisson equation can be deduced by Newton's mechanics: $$\Delta \Phi =-4\pi G\sigma$$ Einstein tried to give a "Poisson's equation" that works with his theory. This equation seems to be ...
0
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4answers
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Gauss Theorem:Electric field of an uniformly charged non-conducting spherical shell

I want to know the electric field of an uniformly charged non-conducting spherical shell. I know that in case of conductors(metals),the sphere can be shell or it can be solid,but in both the cases ,...
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5answers
221 views

Charge inside a charged spherical shell

If I were to put a negative charge inside a negatively charged spherical shell, will it move to the center? Electric field inside the shell due to the shell is zero (Gauss's Law), would that mean the ...
2
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2answers
154 views

Is there something similar to Gauss's Law For Gravity in General Relativity?

In Newtonian Physics there is an equation that for the Gravitational Flux of an object known as Gauss's Law For Gravity. Gauss's Law for Gravity describes the number of Gravitational Field Lines ...
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1answer
37 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 $$F=QE$$. ...
0
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2answers
118 views

Electric flux density between the 2 plates of a capacitor

I am reading a solved exercise about a parallel plate capacitor in which states that the electric flux density between the 2 plates is: $$D=p_{s}$$ where $p_{s}$ is the surface current density of ...
0
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2answers
40 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 ...
2
votes
1answer
77 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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2answers
193 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 $-...
0
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1answer
42 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.
0
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2answers
51 views

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 ...
0
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3answers
786 views

How to find the distribution of charge on two spheres connected by a conducting wire?

A solid metal sphere of radius $R$ has charge $+2Q$. A hollow spherical shell of radius $3R$, concentric with the first sphere, has net charge $-Q$. What would be the final distribution of the charge ...
0
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0answers
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 ...
0
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1answer
51 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 ...
0
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3answers
68 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 ...
0
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2answers
71 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 ...