A law in Classical Electromagnetism and Newtonian Gravity.

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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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Field between the plates of a parallel plate capacitor using Gauss's Law

Consider the following parallel plate capacitor made of two plates with equal area $A$ and equal surface charge density $\sigma$: The electric field due to the positive plate is ...
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655 views

What is the electric field between and outside infinite parallel plates?

I know that Gauss's law says $$\oint_S {\vec{E} \cdot d\vec{A} = \frac{q_{enc}}{{\epsilon _0 }}}$$ and that because $\vec{E}$ is always parallel to $d\vec{A}$ in this case, and $\vec{E}$ is a ...
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61 views

Electric field in a cylinder

We have electric charge density $\rho(r) = kr$ in a cylinder of infinite height and radius $a$. I'm asked to find the electric field. I'm doing it using two methods and I don't undesrtand why then ...
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197 views

Maxwells' equations and Coulomb's law

Coulomb's law and Maxwell's equations should be consistant as one can be derived from the other. Say we have a point charge with such a charge that $-kq=1$, meaning that at any point the electric ...
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How to choose Gaussian surfaces while solving problems?

I have a doubt regarding this problem: Two large identical flat metal plates are placed parallel to one another, seperated by a small distance compared to their linear size. One plate is given a ...
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219 views

Flux through a conduting cylinder?

A point charge of magnitude $Q$ is placed inside a conducting cylinder of length $L$ and radius $R$ at its centre. What is the flux through the cylinder? I know that I have to use Gauss Law here ...
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392 views

Electric flux for a rectangular surface? [closed]

I have the following homework problem: A line of charge $\lambda$ is located on the z-axis. Determine the electric flux for a rectangular surface with corners at coordinates: $(0, R, 0)$, ...
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377 views

Charges lying on a Gaussian Surface

Let's say you have a spherical charge distribution of radius R. This distribution has some charge density as a function of radius. I know that I can determine the electric field outside of the charge ...
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702 views

Finding Electric Field outside a Charged Cylinder

I'm trying to solve a problem that involves finding the electric field due to a uniformly cylinder of radius $r$, length $L$ and total charge $Q$. Well, my thought was: if I am to use Gauss' Law, I'll ...
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Find the quantity of charge - given potential function

A potential function is given by $V(r)=\frac{Ae^{-\lambda r}}{r}$ Find charge density and hence charge. I first took the gradient of potential to get $\vec{E}(r)=\frac{Ae^{-\lambda ...
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Gaussian surface question

There is an infinite slab of charge, and a (Gaussian surface) cylinder whose ends are both outside of the slab. $\phi_A$ is the flux through this cylinder, by symmetry the component of the flux ...
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Conducting surface inside conducting surface

Let's say there's a closed conducting surface. Then by Gauss's Law the E field bound by the surface must equal the charge inside. There's no charge inside, so the E field cancels. This is a Faraday ...
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598 views

Solving by using Gauss law [closed]

Task: find the vector $ \mathbf E $ in the center of the sphere with radius $R$, which has charge volume distribution $\rho$ , $$\rho = \mathbf a \cdot \mathbf r ,\qquad \mathbf a = ...
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375 views

What is discontinuity in Vector Fields

I am reading David J. Griffiths and have a problem understanding the concept of discontinuity for E-field. The E-field has apparently to components. (How does he decompose the vector field into the ...
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56 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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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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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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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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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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How to calculate the electrostatic force applied on an object that is along the axis of a charged tube's surface?

Let's say there is a charged tube(a cylinder with no top and bottom) with radius r and length l, charge q1 which also made out of insulating material. And also if there is an object with charge q2 ...
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42 views

How to calculate the electrostatic force applied on an object that is along the axis of a charged tube?

Let's say there is a charged tube(a cylinder with no top and bottom) with radius r and length l, charge q1 which also made out of insulating material. And also if there is an object with charge q2 ...
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Gauss's Law problem [closed]

I've been thinking about this for a while, but I'm not sure how to proceed. I understand uniform charge-density problems, but the added non-uniform deal makes me uneasy: find the e. field inside a ...
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Electric Field: distributed uniformly in one infinity tape of length [closed]

One charge density surface is distributed uniformly in one infinity tape of length with $2a$ width from distance $d$. Determine the Electric Field in the point perpendicular from the distance $d$ ...
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How to prove Gauss's law div(E) = rho/epsilon from Coulomb's law? [duplicate]

As we know from coulomb's law that: $$\vec{E} = \frac{q}{4\pi\epsilon R^2} \hat{R}$$ using the above equation, how can I verify that: $$\vec{\nabla}\cdot \vec{E}=\frac{q}{\epsilon}$$ I have tried to ...
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Do these steps demonstrate that acceleration of charged particle is proportional to current?

One formulation of Maxwell's Gauss Law for electric field is: $$\bigtriangledown E = 4 \pi k \rho $$ This can be worked into the Divergence Theorem as follows: $$\int\int_{A} F_\perp \:dA= 4\pi k ...
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Is Gauss' law useful to determine the electric field strength of a charge distribution? [closed]

Under what conditions is useful Gauss' law to determine the electric field strength of a charge distribution? Can someone help me with this question?
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Electric lines of force

Why cant electric lines of force pass through the charged sphere? Well, basically that's how a Faraday cage works, but how can it be so?
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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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Newton's Law of Gravitation, Gauss Law and GR

From One of My Unpublished Papers $$\frac{d^2 x^{\alpha}}{d\tau^2}=-\Gamma^{\alpha}_{\beta \gamma}\frac{dx^{\beta}}{d\tau}\frac{dx^{\gamma}}{d\tau} \tag{1}$$ For radial motion in Schwarzschild’s ...
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581 views

Electric Flux Density - Ring Charge

A ring placed along $y^{2}$ + $z^{2}$ = 4, x = 0 carries a uniform charge of 5 $\mu$C/m. Find D at P(3,0,0) Should I be using Gauss's Law to solve this problem? I was considering using a spherical ...
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Is Newtonian gravity consistent with an infinite universe? [duplicate]

Let us assume that we have have an infinite Newtonian space-time and the universe is uniformly filled with matter of constant density (no fluctuations whatsoever), all of it at rest. By symmetry, the ...
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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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Gauss's Law vs Newton's Law

This is thought experiment. I couldn't get a good answer because I keep getting negative mass. Gauss's Law say that eletric field is proportional to charge, how much charged is enclosed. Newton's ...
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578 views

Electric fields in/around conductors

So according to my notes, the field inside a conductor is zero. But what, exactly, is meant by inside? I think we are in electrostatics for the purpose of this question. The reason it is zero is ...
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Gauss Law for Electric Fields

What is the integral form for the Gauss Law for Electric Fields? or ?
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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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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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A little question about Gauss' Law

So I've just learned Gauss' Law a few days ago. I also worked out some applications of Gauss' Law. But I have a little confusion. In a couple of books that I referred, I found a statement that I don't ...
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In electrostatics total flux linked from the closed surface enclosing the charge is equal to $Q/\varepsilon_0$. This is according to Gauss Law

In electrostatics total flux linked from the closed surface enclosing the charge is equal to $Q/\varepsilon_0$. This is according to Gauss Law. Is this the experimental value or defined value. If ...
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Gauss's Law - Electric Field outside a Shell?

I'm somewhat confused as to why the electric field outside a spherical shell is $\frac{Q}{4\pi r^{2}\epsilon_{0}}$ Going through the work: $$ Q = 4 \pi r^{2} \sigma ; \frac{4\pi ...
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Why doesn't a gaussian surface pass through discrete charges?

I have read that Gaussian surface cannot pass through discrete charges. Why is it so? I have even seen in application of Gauss' Law when we imagine a Gaussian Surface passing through a charge ...
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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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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 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 and ions?

My text book says that with we have a singly ionized sodium atom net charge +e and if we choose a spherical surface centered on the ion and large enough to contain it all we do not need to know the ...
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Gauss's Law for a Uniformly Charged Solid Sphere [duplicate]

We want to calculate $\vec{E}$ at a distance $r$ from the center $O$ of a spherical polar coordinate system. Let the point on the Gaussian surface at which we want to calculate $\vec{E}$ is ...
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Gaussian surfaces and Gauss law

Does Gauss law holds for any closed surface or it only holds for only Gaussian surface. Are every closed surface a Gaussian surface?
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Weird consequence of Gauss's law

According to Gauss's Law, the electric field at a surface is the function of only the charge enclosed inside it. But that doesn't make sense. I mean, if I put the surface in an electric field, won't ...
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What is meant by “net charge”?

Lets consider a system of two opposite charges separated by a certain distance (dipole), if we ask what is the net charge for this system? the answer would be zero. The net charge (what I have come ...