A law in Classical Electromagnetism and Newtonian Gravity.

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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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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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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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91 views

Two capacitor plates with equal positive charges $q$

I read in a book that if both the plates of a parallel plate capacitor are given equal positive charges $q$, then the charges on the facing surfaces will be zero and the charge on the outer surfaces ...
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64 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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19 views

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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41 views

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
42 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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1answer
86 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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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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280 views

Charge outside Gaussian Surface doesn't contribute to Flux?

I roughly understand the explanation for this: any electric field line that enters the surface, must leave it, since field lines can't terminate abruptly in space. My question is, what if you have a ...
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48 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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1answer
86 views

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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29 views

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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182 views

Is it really to solve problem below by using, in the main, Gauss law?

There is an infinite cylinder surface which uniformly charged along and has a surface charge density, which can be represented as $$ \sigma = \sigma_{0}cos(\varphi ), $$ where $\varphi$ - polar angle ...
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1answer
55 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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Gauss's Theorem in electricity and its gravitational counter part [duplicate]

We all know the Coulomb's law is the electrostatic counter part of the Newton's law of gravity.So by considering a gravitational potential,is there a gravitational counter part for Gauss's theorem in ...
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1answer
51 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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351 views

Why is the electric field inside a conductor zero in equilibrium?

My textbook says the field inside a conductor must be zero in order for the system to be equilibrium and therefore there must be no excess charge inside. Their proof: 1) Place a gaussian surface ...
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1answer
307 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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1answer
51 views

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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47 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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69 views

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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1answer
51 views

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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133 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
105 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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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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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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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, extendind just barely over the ...
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1answer
57 views

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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1answer
353 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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803 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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269 views

Why the electric field $\vec{E}$ is constant (=position independent) for an infinite 2D sheet of constant charge?

So I'm reading a text on electricity and it talks about using the integral to compute the total charge of a collection of points, which I mostly understand. But then we get to finding the electric ...
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1answer
18 views

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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2answers
63 views

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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1answer
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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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82 views

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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1answer
52 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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1answer
541 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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2answers
45 views

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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1answer
60 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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1answer
4k views

Electric field due to a solid sphere of charge

I have been trying to understand the last step of this derivation. Consider a sphere made up of charge $+q$. Let $R$ be the radius of the sphere and $O$, its center. A point $P$ lies inside the ...
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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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79 views

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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1answer
627 views

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 ...
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56 views

Confusion about Gauss's law for Electrostatics

I just learning about Gauss's law in integral and differential form. There's something I'm a bit confused about: Let $\vec{r}$ be the location of your test charge with respect to the origin, and ...