A law in Classical Electromagnetism and Newtonian Gravity.

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Flux through a face of a cube for an arbitrary position of a charge

Consider an imaginary cube with edge length a in space. A charge q is placed at the centre of one of the faces of the cube. So, what is the electric flux through the face opposite to the charge? ...
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2answers
409 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 ...
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648 views

Apply Gauss' law to find electric field around nonconducting plastic sheets

The question: Two very large, nonconducting plastic sheets, each 10.0 cm thick, carry uniform charge densities $\sigma_1$,$\sigma_2$,$\sigma_3$ and $\sigma_4$ on their surfaces, as shown in the ...
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2answers
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How does a point charge interact with a Gaussian surface?

A spherical Gaussian surface encloses a point charge $q$. The point charge is moved to to a point away from the center of the sphere. Does the electric field at a point on the surface change? ...
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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 ...
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Gauss law-electric field through the spherical surface of a sphere [closed]

FIND THE WORK DONE IN MOVING A POINT CHARGE Q=10 MICROCOULOUMBS FROM THE ORIGIN TO A POINT(4,pie/4,pie/2)SPHERICAL COORDINATES IN THE FIELD E=5e^(-r/4)+10/(rsinx)
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1answer
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Parallel plates with differing charges

I'm given a problem involving two parallel conducting plates a small distance apart. One has charge Q, the other is neutral. I'm asked to find the surface charges on all faces. I began by ...
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Symmetry arguments and plane sheet of charge [duplicate]

The electric field due to a infinite plane sheet of charge is given by $\sigma/\epsilon_o$. Now could we have deduced by symmetry that the electric field's magnitude won't depend on distance?
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Charge outside a Sphere given charge density

If a sphere has a charge density of $\rho =\alpha r^2$, I want to calculate the Electric field outside of the sphere. Starting with Maxwell's equation $\bigtriangledown\cdot E=\frac{\rho }{\epsilon ...
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What is the electric field in a parallel plate capacitor?

When we find the electric field between the plates of a parallel plate capacitor we assume that the electric field from both plates is $${\bf E}=\frac{\sigma}{2\epsilon_0}\hat{n.}$$ The factor of two ...
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Couple of questions about Gravitational field of an infinite plane

Is it possible to find the gravitationaal field without using infinite integrals or Gauss's law? I would like to know if so because I haven't learnt doing infinite integrals or using Gauss's law yet. ...
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4answers
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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 ...
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1answer
137 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 ...
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1answer
233 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
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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 ...
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1answer
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How is the divergence of electric field related to the electric flux? [closed]

From the explanation of Maxwell's equations, I found, the flux of an electric field is mathematically represented by the by the divergence of the electric field.Then, how is the divergence of electric ...
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2answers
469 views

Where is the flaw in deriving Gauss's law in its differential form?

From the divergence theorem for any vector field E, $\displaystyle\oint E\cdot da=\int (\nabla\cdot E) ~d\tau$ and from Gauss's law $\displaystyle\oint E\cdot ...
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1answer
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Does Gauss's law not hold when there are charges outside of the Gaussian surface?

For example, if I have a gaussian surface and a negative charge somewhere outside that gaussian surface, there's going to be a non-zero electric flux. However, According to gauss's law, electric ...
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Proof of the Gauss's law for gravity without divergence [duplicate]

The proof of the Gauss's law for gravity provided by Wikipedia takes use of the divergence theorem. Is it possible to arrive at the integral form of the Gauss's law in a way which doesn't require ...
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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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Electric Field “at” the surface of a conductor

It has been pointed out to me that the Electric field exactly on the surface of the conductor is conventionally taken to be $E=\frac{\sigma}{2\epsilon_0}$; does this come from taking the midpoint of ...
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How is Gauss' Law (integral form) arrived at from Coulomb's Law, and how is the differential form arrived at from that?

On a similar note: when using Gauss' Law, do you even begin with Coulomb's law, or does one take it as given that flux is the surface integral of the Electric field in the direction of the normal to ...
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Solved Gauss' Law for $\vec{E}$ without boundary conditions?

Why can I solve for the electric field of a point charge Q at the origin without boundary conditions? $\nabla\cdot\vec{E}=\rho/\varepsilon_0 = \delta(\vec{r})/\varepsilon_0$ is a 1st order ...
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Divergence theorem and discontinuous vector fields in electrostatics

Wikipedia defines Gauss Divergence Theorem for a continuously differentiable vector field; but in many idealized physical situations, we use it for non-differentiable fields. For example, the electric ...
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Gauss's law giving incorrect answer

Let's consider two concentric spherical shells, one of radius $R$ and one of radius $R - \Delta R$. The outer shell is negatively charged and the inner shell positively, but both the shells have net ...
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Flux through side of a cube

I am looking at Griffiths introduction to Electrodynamics 3rd ED. Problem 2.10 asks for the flux of $E$ through the right face of the cube, when a charge $q$ is in the back left corner of the cube. ...
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1answer
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Why is it true that Laplace's equation does not hold within the sphere in this case?

Find the average potential over a spherical surface of radius $R$ due to a point charge $q$ located inside. (In this case Laplace's equation does not hold within the sphere) This is a question ...
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1answer
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Regarding the proof of Gauss's law

I know that this question has already been asked multiple times but I´m still not getting on the mathematical details behind the answers... So I hope that this question doesn´t get closed. First I ...
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1answer
129 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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1answer
45 views

Electric flux density for a hollow cylinder using Gauss's law [closed]

In the textbook of "Engineering Electromagnetics": I understood it except the part highlighted with yellow(i.e. how did he find the charge distribution of the outer cylinder? What are the ...
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What are the reasons for accepting Coulomb's law? [duplicate]

I read the Coulomb's first memoir on Electricity and Magnetism (Louis L. Bucciarelli english translated version), and found it to contain only three trials (as complained by many) to reach the ...
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1answer
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Why is electric flux zero if my point charge is outside of a sphere? [duplicate]

I am currently studying Gauss Law and Electric flux , during one of my exercises they ask me to find the electric flux of a sphere with radius 5 cm and my point charge is 10 cm to the left of the ...
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Electric field of a Uniformly charged sphere with a cavity [closed]

I have the following question: Consider a sphere of radius $R$, uniformly charged with a volume density $\rho$. The sphere has a spherical hole of radius $R/4$ at a distance $R/2$ from the ...
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In Newton's gravity, is the inverse square law related to the fact that our Universe has (apparently) 3 dimensions? [duplicate]

I read, long ago, a book, whose title I can't remember but I think the author was Carl Sagan. In the book was saying that gravity follows the inverse square law because of our Universe was 3 ...
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4answers
307 views

Electric field in a conductor

Is it always true that the electric field in a conductor is zero? What would happen if I put a very big charge inside an ungrounded hollow conducting sphere like this image? The charges inside the ...
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4answers
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The discontinuity of Electric Field

''electric field always undergoes a discontinuity when you cross a surface charge $\sigma$'' GRIFFITHS In the derivation; Suppose we draw a wafer-thin Gaussian Pillbox, extended just barely over the ...
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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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What is the difference between electric charge and electric flux?

What is the difference between electric charge and electric flux? According to my knowledge electric flux is nothing but electric charge enclosed by the closed surface.
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Paradox with Gauss' law when space is uniformly charged everywhere

Consider that space is uniformly charged everywhere, i.e., filled with a uniform charge distribution, $\rho$, everywhere. By symmetry, the electric field is zero everywhere. (If I take any point in ...
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Why can center of mass be used in calculating gravity?

Why can gravitational forces be based on the center of mass. Due to the fact that gravity is related to the square of the distance should not the gravitational sum of every particle exceed the force ...
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328 views

Gauss's law… if the integral defining $\boldsymbol{E}$ diverges?

I have been told (here) that, under particular conditions, the electric field produced by a charge present in space $D$, defined by ...
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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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Why can we replace a cavity inside a sphere by a negative density?

I have a sphere with radius $R$ and inside this sphere there is a smaller sphere with radius $\frac{R}{3}$. This small cavity has its center at $\frac{R}{2}$, it doesn't matter in which direction. If ...
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Charged infinite surface's created electric field calculation via Gauss's theorem's differential form

I'm wondering how to calculate the electric field of an charged infinite surface with σ surface density via Gauss's theorem's differential form, not integral. We know that divE = 4*Π*ρ We also ...
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1answer
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Is Gauss electric flux law valid in all coordinate systems?

The derivation of Gauss electric flux is as follows : $$\iint{\vec{E}}\cdot{\vec{dS}}=\iint E \, dS \cos\theta \, .$$ The projection of infinitesimal area on the surface $\vec{dS}$ on the radial ...
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1answer
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Can the surface charge density be negative somewhere on the inner surface of a spherical conductor shell?

A positive charge $q$ is located off-centre inside a conducting spherical shell. We know that the total charge on the inner surface of the shell is $-q$. Is the surface charge density negative over ...
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Find Electric Field at certain radii for a sphere

If radius of non-conducting sphere is R=4cm, find Electric field at r1=3 cm (for inner Gaussian surface) and r2=6cm(for outer Gaussian surface) Volume charge density is given as: ρ = c r^2 where c ...
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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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Gauss's law for induced electric and magnetic field

Let us consider an accelerating charge, $Q$. As it is accelerating it would radiate energy in the form of EM waves, as per the classical postulates of EM theory. As such there would be induced ...
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