A law in Classical Electromagnetism and Newtonian Gravity.

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Why is the flux 0? I don't understand this concept

! Why does it say that the flux due to q_2 and q_3 through S is 0? Doesn't it contain a nonzero charge q_1? Does anyone also know the difference between "no charge" vs "net charge is 0"? My book ...
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40 views

Electric field between capacitors [closed]

A parallel-plate capacitor consists of two parallel, conducting plates of area $A$, separated by a distance $d$. Each carries a charge of magnitude $Q$; positive on one, negative on the other. ...
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59 views

Is the electric field at a single point inside a charged sphere zero?

Many physics textbooks say, Gauss' law shows that the electric field inside a sphere with uniform charge distribution on the surface equals zero. What I want to know is, do they mean total, ...
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question about Gauss law

If I have an infinite plate with the surface charge of sigma. I know that my electric field is constant $2\pi\sigma$ (using Gauss's law). If I build the Gaussian surface above the plate the charge ...
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24 views

where does the term half in the formula of electrostatic potential energy comes from?(system of point charges)

Electrostatic potential energy stored in a system of point charges (from wikipedia) The electrostatic potential energy $U_E$ stored in a system of N charges q1, q2, ..., qN at positions r1, r2, ...
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120 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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126 views

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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379 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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70 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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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 ...
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49 views

Is the charge of an ion evenly distributed?

This question relates to: Gauss' law and ions? Is the charge distribution in an ion spherically symmetric due to quantum mechanical effects or do we assume it when using Gauss's law, as in the ...
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Gauss’s Law inside the hollow of charged spherical shell

Use Gauss’s Law to prove that the electric field anywhere inside the hollow of a charged spherical shell must be zero. My attempt: $$\int \mathbf{E}\cdot \mathbf{dA} = \frac{q_{net}}{e}$$ $$\int E ...
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Gauss' Law for Magnetism Derivative Form: With or without volume integral?

I've been reading through FLP Vol. II, and he has proven that as the flux through a closed surface is: $\ \int_{surface} \mathbf{F} \space \mathrm{d}\mathbf{a} $, according to the divergence theorem, ...
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1 charge at the center and many uniformly distributed on the surface of a perfect ideal conducting solid sphere

Suppose there is a perfect ideal conducting solid sphere. Suppose somehow a charge of $+Q$ is kept exactly at the center of the sphere and its surface is also given a $+Q$ charge uniformly distributed ...
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If we change the radius of spherical surface does electric field or flux change?

Suppose a point charge is located at the center of a spherical surface. The electric field at the surface of the sphere and the total flux through the sphere are determined. 1).What happens ...
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Electric field around charged cylinder

This is a homework question, so please don't give me the answer outright. I just need help conceptually. "A cylindrical shell of length 190 m and radius 4 cm carries a uniform surface charge density ...
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433 views

Proof that flux through a surface is independent of the inner objects' arrangement

$$\Phi=\iint_{\partial V}\mathbf{g} \cdot d \mathbf{A}=-4 \pi G M$$ Essentially, why is $\Phi$ independent of the distribution of mass inside the surface $\partial V$, and the shape of surface ...
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359 views

Finding the electric field on a point (x,y,z) using Coulomb's Law

Using Gauss' Law, the answer is $$\frac{Q}{4 \pi \epsilon R^2}.$$ However if I were to do the integration using Coulomb's Law, I get $$ \int_0^{2\pi} \int_{0}^{\pi}\int_r^a \frac{\rho \sin\theta dR ...
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703 views

Gravity force strength in 1D, 2D, 3D and higher spatial dimensions

Let's say that we want to measure the gravity force in 1D, 2D, 3D and higher spatial dimensions. Will we get the same force strength in the first 3 dimensions and then it will go up? How about if ...
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98 views

Method of image charges [closed]

In an attempt to understand the Method of image charges, I'll try to calculate the total charge on grounded conducting plane - with electric dipole & point charge. Given: Point charge $Q$, ...
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1answer
76 views

How to calculate charge on an internal and external surface of a conductor, due to an internal charge

Having a bit of trouble with a question our first year lecturer has given us to think about. Say we're given a hollow cylinder (the hollow region is central and spherical), made of a conducting ...
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321 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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317 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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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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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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221 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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280 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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462 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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442 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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796 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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1k views

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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302 views

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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99 views

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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669 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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447 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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47 views

Ampere's Law and Gauss's Law for EXACT CENTER of Finite Wire: Mathematical Justification [closed]

I have always seen it explained that: Ampere's Law (in integral form) works whenever B is constant around a path, so that you can pull it out of the integral. Similarly, if you can draw a ...
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Divergence Theorem, mathematical approach to Gauss's Law?

Let $D$ be a compact region in $\mathbb{R}^3$ with a smooth boundary $S$. Assume $0 \in \text{Int}(D)$. If an electric charge of magnitude $q$ is placed at $0$, the resulting force field is ...
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49 views

How to calculate Electric Field near a charged conducting surface without Gauss' law?

I have two problems : In every textbook I find the use of Gauss' law in calculation of Electric Field near a charged conducting surface. Can it be calculated without Gauss' law? Suppose while using ...
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40 views

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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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
278 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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169 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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40 views

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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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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46 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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55 views

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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45 views

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 $d$ ...