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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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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
53 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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0answers
17 views

Electric field for uniformly charged axisymmetric surface

I am considering an axisymmetric surface, in cylindrical polar co-ordinates (r, θ, z), defined by r= r(z) between say z_1 and z_2. Can Gauss's law (or any other method) be used to calculate the ...
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1answer
20 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 ...
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0answers
32 views

How to derive Gauss' Law without divergence theorem or surface integral?

This is for a presentation I'm doing. So we know from Coulomb's Law, you can get $$E = \frac{Q}{4\pi r^2\epsilon_0}$$ We also know that $\Phi = E\Delta A\cos\theta$ where $\theta$ is the angle ...
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1answer
62 views

Generalization of the Gauss' Law to a lorentz-covariant law in Paper of Kobe: Is it “guessed”?

In the Paper Generalization of Coulomb's law to Maxwell's equations using special relativity by Donald H. Kobe, he tries to derive Maxwell's equations by trying to find covariant laws between tensor ...
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4answers
2k views

Can Newton’s law of gravitation be derived from Coulomb’s law? [duplicate]

I’m casually learning physics and have noticed that Newton’s law of gravitation and the electrostatic force formulas look similar. I’ve asked this question before but would really appreciate another ...
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1answer
88 views

Why is the constant of proportionality in Gauss's law exactly $1/\epsilon_0$

$\epsilon_0$ is epsilon naught, or permittivity of free space. Let me preface this by saying that I've just started to learn about electromagnetism. When I first saw Coulomb's law, I was incredibly ...
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2answers
35 views

Buoyancy: integrating over a region where the fluid isn't?

On both ProofWiki and Wikipedia, the article's respective authors manage to arrive at Archimedes' principle by applying the Gauss theorem to the surface integral of the fluid's stress tensor $\sigma$: ...
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1answer
51 views

Why there is a distance dependence in Coulomb's law if photons can travel to infinity?

Why there is a distance dependence in coulombs law if photons can travel to infinity? Why there is distance dependence at all?
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1answer
43 views

Flux is not coming zero, although charge inside it is zero!

In the figure, there are two capacitors connected in series. So, they have same charge on them. Since, the plates have same area, therefore they have same charge densities σ. Also, one capacitor have ...
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1answer
41 views

What happens if I place a charge inside a hollow conductor and fix it? [duplicate]

So I know that when you put some charge inside a counter, it resides uniformly on the surface of the conductor in order to make the electric field zero everywhere inside the conductor.. But what if I ...
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0answers
11 views

Electric field in a spherical shell [duplicate]

Question mentioned like this find out the electric field inside and outside a spherical shell of radius r which carries a uniform surface charge density sigma. In the above question it is not ...
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2answers
33 views

Electric field generated by an infinite plane paradoxon

Every element of the distribution generates weaker electric field at a larger distancce. Although other arguments involving gauss' law or taking the limit of the field result it's constancy. How could ...
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1answer
30 views

Field inside a hollow sphere uniformly charged [duplicate]

How to prove that field inside a hollow sphere is zero anywhere inside that sphere using solid angle concept?
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1answer
586 views

Problem verifying Gauss's law

I am trying to verify Gauss's law, differential form, SI units, non-special relativity regime, ignoring time retardation, by performing the differentiation on the left-side of the equations to see if ...
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1answer
58 views

How gaussian surface and continous charge distribution overlap in 2D?

It is well known that Gauss's Law & Coulomb's Law are inter-dependent. Any violation of Gauss's Law will indicate departure from inverse square law and vice versa. Then how gaussian surface and ...
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2answers
51 views

Is the gravitational potential a measurable physical quantity or an artifact of warped measures?

The Euler-Lagrange conditions for stationary points of $$L=m/2 v(\mathbf{\dot{x}})^2-U(\mathbf{x})$$ ($m$ is mass, $v()$ is velocity, $U()$ is the scalar potential, and the boldfaced arguments of ...
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0answers
21 views

Electrostatic force between half cylinder and dielectric plate

The problem is as follows: A half cylinder of radius $R$ and length $L>>R$ is formed by cutting a cylindrical pipe made of an insulating material along a plane containing its axis. The ...
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1answer
107 views

Factor of 4 (or 2) in the gravitoelectromagnetic (GEM) Lorentz-force law. Which is correct? Why is it there?

I realize that the Gravitoelectromagnetic equations (GEM) are derived from the Einstein field equation (EFE) in the degenerate case of reasonably flat spacetime, which is the case for the propagation ...
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0answers
14 views

Applying Gauss's Law on a Non-Uniform Conductor [duplicate]

I've seen tons of examples of Gauss's Law applied to solve for electric field. However, the only shape its ever really applied to is a cylindrical or spherical Gaussian surface. I'm looking at a ...
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1answer
64 views

Why do we assume that Gauss' law of gravitation to remain same even when there are extra spatial dimensions?

Every kid knows that the magnitude of the gravitational force between two point masses is inversely proportional to the square of the distance $r$ between them i.e., $F\sim r^{-2}$. But experimentally,...
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0answers
39 views

Gauss's law on a stator winding (conductor)

I'm trying to perform Gauss's Law on a stator winding. Previously performing it on a circular conductor, is fairly simple. The goal for the circular conductor was to determine the electric field at a ...
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0answers
51 views

Charge distribution on Spherical conducting shells

For example we have very thin conducting spherical shells of radius R and 2R. Initially the smaller shell has Q and other shell has q charge of their own, now there will be charge induction in them ...
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1answer
76 views

How to derive Gauss's law for magnetism, $\nabla \cdot \vec{B}=0,$ if charge density is discontinuous?

I want to derive Gauss's law for magnetism,$$ \nabla \cdot \vec{B} = 0 \,.$$ The derivation in Griffiths Introduction to elecrodynamics uses$$ \nabla \cdot\vec{B} ~=~\frac{\mu_0}{4\pi} \int {\nabla \...
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1answer
32 views

Is Gauss law applicable to image charges in electrostatics?

Take for instance the standard example with a charge in front (distance $d$ from middle) of a grounded conducting sphere of radius $a$. It is not hard to show that the relevant image charge will be $-...
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1answer
58 views

Newton's “Shell theorem” in higher dimensions

In Newtons's shell theorem, the net gravitational force is zero inside a hollow sphere, if the gravitational force is proporional to $1/r^2$. In 2D, the net force is zero inside if the force is ...
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1answer
136 views

Why does $\frac{1}{4\pi}$ appear in many formulas? [duplicate]

Why do most of the physical equations have $\frac{1}{4\pi}$ as constants? I have seen that many equations have $\frac{1}{4\pi}$ as constants like Coulomb, pendulum problems, etc. Can anyone tell me ...
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1answer
46 views

Gauss law in non-uniform electric field

I am trying to figure out how gauss law would hold in an electric field configuration that varies with space. For simplicity, let us assume the classic XYZ coordinate system. Consider an electric ...
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2answers
72 views

Confusion regarding Gauss law and capacitors

In book (Halliday Resnick Krane, 2nd Part, fifth edition), it's written that when you you put some charge in an isolated conductor, then within around $10^{-9}$ seconds the charges all go to the ...
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0answers
27 views

Boundary condition for electric field with addition of polarization

Comparing the boundary conditions for $E$ field and $D$ field, why does one of them E changes to D and the other E stays E? I am looking for physical intuitions, does it have to do with the direction ...
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1answer
31 views

Capacitors electic field

If we have the electric field on the surface of a conductor being $E=\sigma / \epsilon_0$ where $\sigma$ is the charge per unit area then why is the combined $E$ field from two parallel plates not 2x ...
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1answer
42 views

Charge Distribution on Conductor - Uniform or Not?

Consider a hollow conducting spherical shell S1 inside an irregularly shaped conducting wall S2 (in the figure). The sphere S1 is somehow given a charge +Q. Will the charge distribution on S1 be ...
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1answer
85 views

Gauss' Law and Symmetry

While reading my lecture notes about Gauss' Law, here's what I found: Gauss' Law is obeyed by a wider range of fields, than those represented by the electrostatic field. In particular, a field that ...
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0answers
47 views

Laplacian of electric potential in inhomogeneous media

I am confused about a problem on capacitance of a lossless inhomogeneous dielectric sandwiched between conductors. The permittivity of the medium is expressed as $\epsilon = \epsilon_0(1 + sin\theta)$...
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1answer
123 views

Electric flux through finite width/ infinitely long plane due to a point charge

The question is as follows: Consider a point charge Q placed at $(0,h,0)$ (Cartesian coordinates). Find the flux in an area formed by $y=0$, $z\leq0$, $x\geq l$ and $x\leq a$ $( l\leq x\leq a )$. I ...
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1answer
36 views

Finding the electric field when the sphere has multiple charges

In this case, in part (d), why is the charge -Q on the surface of the sphere not taken into account?
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1answer
65 views

Field at the center of a cube with positively and negatively charged faces [duplicate]

I'd like to share an interesting physics problem with the Physics SE community, one I found in a Russian Physics Olympiad Paper (without solution) An insulating hollow cube of edge length $L$ has ...
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1answer
46 views

Why does the graph of the electric potential of a conducting sphere look like this?

The graph of the electric potential of a conducting sphere with radius $R$ is curved when $r > R.$ Since the electric potential outside the sphere is $k\frac{Q}{r},$ shouldn't the graph be linear ...
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1answer
50 views

Explanation of the negative integral

As referred to this question Why can't charge be in a stable equilibrium in electrostatic field?, it is given that Fig. 5–1.If $P_0$ were a position of stable equilibrium for a positive charge, ...
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1answer
55 views

Gauss Theorem for Electrostatics : Why is $D_r$ considered constant?

Gauss Law states that $\int \vec D. d\vec s = Q_{enclosed}$ Consider the spherical case with $\rho_v = cst$ -- for the sake of not doing an integral on other side. Now the proof I was reading says ...
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2answers
53 views

Electric field outside and inside of a sphere

An insulating sphere of radius a carries a total charge $q$ which is uniformly distributed over the volume of the sphere. I'm trying to find the electric field distribution both inside and outside ...
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0answers
44 views

Using Gauss's Law to find the volume charge density above Earth

I am trying to better understand Gauss's Law with the following exercise provided by my lecturer: $9)$ The atmospheric electric field at the surface of the earth is typically 200 V/m, directed ...
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1answer
20 views

What does it mean to say that the electric potential of a system of point charges is, say 5V?

For example, what does it mean to say that the electric potential of an electrically charged plate (not an infinitely large plate) is 5V without any mention of which point on the plane we're ...
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1answer
37 views

How do I prove the charge on the outer part of the last plate is half the total charge in a system of parallel metal plates?

or in other words, if I have $n$ large parallel metal plates with charges $q_1$, $q_2$, ... $q_n$, how do I prove the charge on the outer part of the last plate $\displaystyle \frac{q_1+q_2+..q_n}{2}$ ...
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0answers
43 views

Why do i always get resultant electric field by differential form of Gauss law?

The electric field in differential form of gauss law is the resultant electric field due to a continuous charge distribution. and the law states that the divergence of electric field at any point is ...
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1answer
87 views

Why is a cylindrical Gaussian surface more desirable to derive the electric field at some point from a plane of charge than a rectangular prism?

I'm told that, like in videos such as this one, a cylinder is the Gaussian surface to use when trying to find the electric field at some point away from a plane of charge. I don't see what's wrong ...
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1answer
71 views

How should Gauss's law deal with surface charges? [closed]

If a charge is kept on the surface of a body then do we consider it enclosed and account it in Gauss's theorem? Take for example a charge $q$ kept on top of a hemispherical shell. Finding the flux ...
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3answers
46 views

Why is $\vec E$ constant for a uniform sphere?

I know that a sphere is a desirable Gaussian surface because we can take $\vec E$ out of the integral of Gauss's Law. However, it isn't apparent to me as to why $\vec E$ is constant for a sphere. If $...
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0answers
18 views

Scepticism regarding the exponent of -2 in Coulombs law? [duplicate]

So lately I was speculating why nature choose the number 2 in Coulomb's law like why not 2.$10^{100}$ trailing zeros and then 1 or anything else. I find 2 a bit arbitrary the given explanation being ...