A law in Classical Electromagnetism and Newtonian Gravity.

learn more… | top users | synonyms

1
vote
1answer
309 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 ...
1
vote
1answer
139 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 ...
1
vote
2answers
1k 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 ...
1
vote
1answer
96 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 $r$ ...
1
vote
1answer
73 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 ...
1
vote
2answers
104 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 ...
1
vote
1answer
59 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 ...
1
vote
2answers
3k views

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 ...
1
vote
2answers
509 views

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, ...
1
vote
2answers
114 views

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 ...
1
vote
2answers
9k views

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 ...
1
vote
1answer
2k views

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 ...
1
vote
2answers
514 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 ...
1
vote
1answer
463 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 ...
1
vote
1answer
913 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 ...
1
vote
1answer
335 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 ...
1
vote
1answer
75 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 ...
1
vote
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 ...
1
vote
1answer
48 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. ...
1
vote
4answers
115 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 ...
1
vote
1answer
82 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 ...
1
vote
2answers
83 views

Sphere of uniform charge density with a cavity problem

Suppose we have a sphere of radius $R$ with a uniform charge density $\rho$ that has a cavity of radius $R/2$, the surface of which touches the outer surface of the sphere. The question was to ...
1
vote
1answer
319 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 $Q$, ...
1
vote
1answer
128 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 ...
1
vote
1answer
724 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 ...
1
vote
1answer
516 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 ...
1
vote
4answers
6k views

Potential difference between point on surface and point on axis of uniformly charged cylinder

Question: Charge is uniformly distributed with charge density $ρ$ inside a very long cylinder of radius $R$. Find the potential difference between the surface and the axis of the cylinder. Express ...
1
vote
1answer
5k 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 ...
1
vote
1answer
257 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 ...
1
vote
1answer
346 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 ...
1
vote
3answers
620 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: $(0, R, 0)$, ...
1
vote
1answer
597 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 ...
1
vote
2answers
1k 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 ...
1
vote
2answers
2k 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 ...
1
vote
1answer
104 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 ...
1
vote
1answer
789 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 = ...
1
vote
1answer
588 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 ...
1
vote
1answer
28 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 ...
1
vote
0answers
27 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? ...
1
vote
0answers
60 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 ...
1
vote
0answers
90 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 ...
1
vote
0answers
58 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 ...
1
vote
0answers
293 views

Charge per unit length and charge per unit area

In the Halliday and Resnick book, I am asked the find the linear charge density of the inner wall of a shell. This confuses me because the inner wall of a shell is an area, not a one dimensional line. ...
1
vote
1answer
138 views

Charge distribution on a Gaussian surface

In the text, it is said that the skewed distribution of positive charge on the inner wall cannot produce an eletric field in the shell to affect the distribution of charge on the outer wall. Why? ...
1
vote
0answers
42 views

Dirac delta function equation intuition and proof [duplicate]

What is the intuition and where should I find proof of this equation (do not know what its name is). It is used to derive Gauss law from Newton equation. $${\nabla \cdot \Bigg ( ...
1
vote
1answer
98 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 ...
1
vote
1answer
92 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 ...
1
vote
1answer
86 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 $a$ ...
1
vote
0answers
34 views

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 ...
1
vote
2answers
638 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 ...