A law in Classical Electromagnetism and Newtonian Gravity.

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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 ...
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0answers
49 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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2answers
46 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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2answers
53 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
54 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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2answers
107 views

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
112 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 ...
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 ...
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0answers
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
54 views

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
146 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
66 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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0answers
48 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
39 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
27 views

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 ...
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1answer
468 views

Electric Field within the cavity of a conducting sphere?

So the hypothetical situation that I am confused about is below: The situation consists of a point charge, +q, contained within the cavity of a spherical conductor of neutral charge. I understand ...
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1answer
53 views

How to determine the cylindrical gaussian surfaces position while finding the electric field?

Today I encountered a question that had the solution: electric field outside of a charged nonconductor is $$ E=\frac{\sigma}{2\epsilon_0} $$ which had the diagram below: Fig. 1 and for the ...
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2answers
111 views

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
45 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
125 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
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 ...
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1answer
70 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 creating a ...
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0answers
25 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
41 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
54 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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5answers
232 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 ...
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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 ...
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1answer
63 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
78 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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2answers
123 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 ...
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 ...
3
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2answers
118 views

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 ...
3
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1answer
66 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
53 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 from ...
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0answers
81 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
126 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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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 ...
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0answers
63 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
79 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
110 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
61 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
120 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 ...
2
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1answer
149 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 ...
2
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0answers
53 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 ...
2
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2answers
156 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
191 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 ...
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1answer
72 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
56 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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0answers
25 views

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 ...
2
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1answer
76 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 ...