A law in Classical Electromagnetism and Newtonian Gravity.

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Proving charge on outer surface of parallel plate capacitor must be zero

If we have two conducting plates, with charge $Q$ and $-Q$, why is the charge on the outer surfaces of each conductor zero? I've been trying to wrap my head around the problem. Firstly, don't excess ...
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0answers
13 views

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
52 views

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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0answers
47 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 ...
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1answer
37 views

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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22 views

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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1answer
33 views

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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1answer
43 views

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
62 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 ...
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1answer
57 views

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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1answer
52 views

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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3answers
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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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1answer
56 views

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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1answer
38 views

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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0answers
41 views

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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0answers
50 views

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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0answers
52 views

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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1answer
68 views

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
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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0answers
56 views

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
49 views

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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0answers
62 views

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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0answers
52 views

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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57 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
65 views

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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2answers
41 views

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
62 views

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
42 views

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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1answer
13 views

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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2answers
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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1answer
43 views

The origin of Gauss' law for magnetism [closed]

What is the physical axiom leading us to the Gauss' law for magnetism?
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60 views

Sphere of uniform charge density with a cavity problem

Suppose we have a sphere of radius $R$ with a uniform charge density $\rho$ that has a cavity of radius $R/2$, the surface of which touches the outer surface of the sphere. The question was to ...
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41 views

Gauss law for a cylinder shielded by a grounded conductor?

So I am trying to solve the following problem: My approach: Applying Gauss's law on the two regions yields the following $$\mathbf{E}=\left\{\begin{matrix} \frac{\rho _0 \rho ...
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0answers
214 views

Charge per unit length and charge per unit area

In the Halliday and Resnick book, I am asked the find the linear charge density of the inner wall of a shell. This confuses me because the inner wall of a shell is an area, not a one dimensional line. ...
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1answer
70 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 ...
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1answer
75 views

Determining Electric Field Inside Long Cylinder (Using Gauss' Law)?

I'm working on a problem with an (infinitely) long cylinder with a charge density, and I'm trying to find the electric field. Using the charge density, I found the enclosed charge of a proportional, ...
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2answers
192 views

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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180 views

Gauss Law - Infinite line charge

I came across a sentence which made no sense to me as I was studying the electric field of an infinite line charge: The flux through the FLAT ENDS of our cylindrical Gaussian surface is zero ...
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1answer
86 views

Gauss law example - Electric field and dA [duplicate]

I am still very confused and lost. I still dont understand why E1 is pointing down , E3 and 2 pointing up. while dA is point the left and dA2 and dA3 are in the same direction of the E3 and E2. I ...
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1answer
32 views

Gauss law question with regard to this example

I am really confused in Gauss law. Why do E3 and E2 pointing up? and also E1 pointing down? The lecture note said infer from symmetry and you will get the following but I dont really understand. ...
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1answer
26 views

Gauss Law Question [duplicate]

Why is dA pointing up and dA2 pointing down? Electric field(E1) is pointing up so isnt it suppose to be perpendicular to the surface?
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2answers
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Gauss Law Question. Could anyone explain to me why does S3 is 0 in this lecture note example?

Why does S3 equal to 0 ? for E3 dot dA = 0? Could I also know why does dA1 and dA2 point up and down? while dA3 point to the right?
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1answer
140 views

Newton's shell theorem in 2d [closed]

I was wondering how to prove the analog of Newton's shell theorem for 2 dimensions, in which gravity obeys an inverse-linear law. Meaning: that an anywhere inside a circle, the gravitational field ...
3
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2answers
178 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 ...
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2answers
105 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
169 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? ...
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2answers
111 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 ...