A law in Classical Electromagnetism and Newtonian Gravity.

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In Gauss's law, why do we use an infinte long wire or long plane to calculate electric field intensity?

In the NCERT textbook of class 12, in the section on applications of Gauss's law, there are three applications. The first application is to calculate the electric field intensity around an infinitely ...
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53 views

Inverse Square Law and extra space dimensions

Newton's famous Inverse Square Law says that in $n=3$ dimension of space, force is inversely proportional to the square of the distance between a source and a target. I understand that for higher ...
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26 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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223 views

What does it mean that a magnetic field's flux vanishes through any closed surface?

I'm reading the Britannica guide to Electricity and Magnetism, and I came across the following quote: A fundamental property of a magnetic field is that its flux through any closed surface ...
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Displacement vector in parallel plate capactor

This ought to be simple, but I'm running into some questions... Let's say we have a parallel plate cap with some linear homogeneous dielectric media between the plates. The plates are distance $a$ ...
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42 views

What do we mean with magnetic monopole and dipole?

What do we mean with magnetic monopole and dipole? I can not find a way to relate magnetic monopoles and dipoles with electric ones. I do not understand their outcomes. Also,what is their role in ...
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conducting hollow sphere in magnetic monopole

if a hollow copper sphere(or any conducting hollow sphere) is connected to dc at points diametrical and a magnetic monopole is right at the center of the sphere then will there be any movement of the ...
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2answers
70 views

Flux through plane surface in hemisphere [closed]

Suppose a charge is placed at the centre of a hemispherical surface of radius $R$ then what would be the electric flux passing through the planar surface opposite to the charge in the hemisphere? I ...
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A flat ring and electrical field

Question: A flat ring (inner radius $R_0$, outer radius $4R_0$) is uniformly charged. In terms of the total charge $Q$, determine the electric field on the axis at points a) $0.25R_0$ ...
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Electric field of infinite slab

When reading a book about basic electrodynamics (in a section about electrostatics), I came upon the following problem: An infinite plane slab, of thickness $2d$, carries a uniform volume charge ...
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68 views

Gauss's law and superposition for parallel plates

Two large, flat metal plates are separated by a distance that is very small compared to their height and width. The conductors are given equal but opposite uniform surface charge densities +- ...
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122 views

Conceptual question on Gauss's Law

By my understanding, the electric field in the surface integral expression for Gauss's Law represents the total electric field and any point on a closed Gaussian surface. However, when we employ ...
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209 views

Confused about Gauss's Law for parallel plates

I am having trouble understanding Gauss's Law. Suppose we wish to find the electric field strength between two parallel plates with charge density $\sigma$. I know it should be ...
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100 views

Coulomb's law and Gauss' Law

Which of these laws is more fundamental or forms the basis of electrostatics? I started off with Coulomb's law and then I studied Gauss' law. I was wondering which one is more universal? My professor ...
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Electric Flux - Vector Components

How is $vcos(\theta)$ the perpendicular vector? I think I'm missing something fundamental in my trig and vector knowledge...
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Paradox in electrostatics in relation to Gaussian surfaces?

I have encountered something that is very confusing. My problem is this. I am assuming two infinite cubical Gaussian surfaces sharing a common side. One of the cubes contains a charge $q_1$ at a ...
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1answer
64 views

Electric Flux - What is the point?

Electric flux is a defined quantity that is proportional to the no. of field lines passing through a given area element for a given electric field. It is not proportional to the relative density of ...
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Wait… why exactly does farady's ice pail experiment prove Gauss's law?

You'll notice there are no equations in this: that's because this is a question of morale, not of math. But a humble one at that! I come to learn, not to expound. But don't let that limit the form ...
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62 views

Calculating flux of axisymmetric electric field through a sphere [closed]

The following problem and its solution is taken from I. E. Irodov's book basic laws of electromagnetism : I do not understand how the fact that field is axisymmetric leads to the conclusion that ...
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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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Rigorous proof of Gauss' law for an arbitrary charge distribution from Coulomb's law

Most of the books about electromagnetism prove Gauss' law for a point charge in vacuum: $$ \Phi = \int_{\Sigma} \mathbf{E} \centerdot d \mathbf{S} = q/\epsilon_0 $$ and then simply state that for ...
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Divergence of a vector field, going through the math [closed]

The example I'm working on has this given identity: $\bigtriangledown \cdot \mathbf{\bar{r}}=3$. The question is: find the divergence of a vector field $\bar{\mathbf{E}}=\frac{\mathbf{r}}{r^{3}}$. ...
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1answer
63 views

What is the charge density in the proof of Earnshaw's theorem?

I am trying to understand the proof for Earnshaw's theorem. Though the theorem states that a collection of point charges cannot be maintained in a stable stationary equilibrium configuration ...
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Is there a limitation on Gauss' law? [duplicate]

Recently I had a question to find the electric field at a distance $R$ from the origin, where the space is filled with charge of density $\rho$. I did this by assuming a Gaussian surface of radius ...
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1answer
53 views

Why does $E = 0$ inside conducting sphere? [duplicate]

Given this picture, I've understood that giver r>R, E = q/(4πεR^2) but I just can't get why inside the sphere, E equals 0? And the notes don't explain something. I've tried to look it up on the web ...
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Electric flux of a closed surface, $\Psi = Q $ or $\Phi =\int\vec{E}\cdot d\vec{A}$

I have problem with the equation of electric flux. I use one book of fundamental physics and another book of electromagnetic engineering; the two of them give different equations for electric flux. ...
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81 views

Electric Field from charged sphere within another charged sphere does not reinforce?

Lets say I have a positively charged conducting sphere of Q. The electric field outside the sphere is $$E = \frac Q{4\epsilon\pi r^2}$$ Now suppose this sphere is enclosed inside another hollow ...
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Gauss's law not making sense

If we have a point charge and outside of it we have a non-conducting Gaussian sphere, then Gauss's law says that the net flux should be zero. I agree that the total field lines coming in are equal to ...
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Gauss's Law of Electric Field how it actually works? & How Gauss derived it?

I want to know how Gauss derived his equation of Electric Field. Did he derive it from Coulomb's law? I don't think so. Please tell me some details about how this law works? inside a Gaussian ...
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252 views

Electric field around two charged hollow cylinders

There are two hollow cylinders with same lengths "l" as shown in the figure below. The smaller inner cylinder is negatively charged. The outer one is now induced to become positively charged. I am ...
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1answer
497 views

Electric Field of Hollow Cylinder

Let's say we have a hollow cylinder with a charge $q$, radius $r$ and height $h$ as in the figure below. I am trying to find the electric field perpendicular to the surface of the hollow cylinder. I ...
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1answer
96 views

Is it equivalent to derive Gauss's law from discrete and continuous source distributions?

I've seen two derivations for Gauss's law in electrostatics. The first assumes a discrete charge distribution, the second a continuous one: Use superposition $$\vec{E}=\sum_{i=1}^n\vec{E}_i,$$ so ...
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Electric Field Contributions

Figure 1: Two thin parallel wires Figure 2: The cross section of a hollow sphere containing a smaller, hollow sphere The electric fields for both figures are calculated using different principles. ...
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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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Question about electric flux in the corner of a cube [duplicate]

A charge $Q$ is places at the corner of a cube of side $a$. What is the electric flux through all the six faces of the cube? What is the electric flux on each one of it's faces? I am aware of ...
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992 views

Gravitational field intensity inside a hollow sphere

It is quite easy to derive the gravitational field intensity at a point within a hollow sphere. However, the result is quite surprising. The field intensity at any point within a hollow sphere is ...
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1answer
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How does the dieletric displacement change among two dieletric materials?

Here's a question I am working on. "A sphere of linear dielectric material with permittivity $\epsilon_1$ and radius $a$ is surrounded by an infinite region of linear permittivity $\epsilon_2$. In the ...
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Relation between electric field and dipole moment

I want to show the following equality $$\int_{\left|\vec{r}\right|<R}d^3r\vec{E}\left(\vec{r}\right)=-\frac{\vec{p}}{3\epsilon_0}$$ where $\vec{p}$ is the dipole moment of a charge distribution ...
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Can Gauss' and Ampere's Laws be written in terms of the divergence of an energy four-vector?

In the first 20 minutes of this video, Susskind derives the continuity equation for charge conservation: $$\dot{\rho}+\nabla\cdot\vec{J}=0$$ (Where $\vec{J}=\frac{\partial\dot{q}^m}{\partial A^m} ...
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Calculate the flux of a point charge with Gauss's law

I know from my class that to calculate the flux of a point charge with Gauss's law, I have to make a surface that intersects with all of the flux lines resulting from the charge, and then make this ...
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Electric field of Symmetric Parts [closed]

So I'm preparing for a test and one thing that I haven't seen examples of, but know is possible is using Gauss's Law on objects that have symmetric parts. I made up the following question: Find ...
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72 views

Finding charge density from from differential form of gauss law

I didnt get why he didvided and multiplied by r^2.This question is from d j griffith .
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55 views

How is it possible for an infinitely large charged plane to cause the same electric field regardless of distance? [duplicate]

Assume there is an infinitely large plane with a charge density $\sigma$. I understand how to derive, using Gauss' Law, that $E = \frac{\sigma}{2\epsilon_0}$ is the electric field at a distance $r$ ...
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Gauss law in integral form

Scanning through the lecture notes of my professor I came across some confusing definition, that he calls "Gauss law in a global form" which has the following representation ...
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821 views

Zero divergence of Electric field

I'm trying to rigorously derive the integral form of Gauss's law from Coulomb's law and the divergence theorem. Arrive at $$ \oint\limits_{\partial V} E\cdot da = \begin{cases} \frac ...
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1answer
66 views

Help regarding understanding derivation of electrostatic potential in a solution to a problem

I was looking at the solution of finding the energy stored in a charged solid sphere in which the electric field was and then later stated the electrostatic potential is I understand that to ...
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Is there a charge across all space? [duplicate]

We're studying electrostatics in class, and the teacher introduced us to Gauss' Law a few days ago as $$\int \vec{E} \cdot \mathrm{d}\vec{A} = \frac{Q}{\epsilon_0}$$ Now suppose that the entire ...
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Does Gauss' Law apply to real physical solid conductors?

In a conductor there is no electric field because there is no charge. There is no charge inside because any charges present inside would repel each other and be driven to the surface of the conductor. ...
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Electrical field of the coil

Take the case of two coils, first one connected to alternating current supply, and the second one connected to load. First coil creates magnetic field, and electric field is reduced by anti-emf ...
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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 ...