Questions tagged [gauss-law]

A law in classical electromagnetism and Newtonian gravity which relates (charge) density to the divergence of a field, or alternatively the charge in a volume to the flux through the bounding surface.

Filter by
Sorted by
Tagged with
-2 votes
0 answers
31 views

Unphysical solution to radial flow in a compressible fluid for Gaussian initial condition

Here's the problem I want to solve: a density of some fluid is moving radially outwards at constant velocity starting from a Gaussian initial condition, so the flux will be $\vec{j} = |V|\hat{r}$ and ...
user avatar
0 votes
0 answers
22 views

How is the time evolution of a Newtonian universe of infinite size that starts with constant mass density?

So, if we start with the description in the title, what happens in such universe (no internal stress, it is a continuum dust)? At first analysis, it seems it will remain that way, because symmetry ...
user avatar
5 votes
3 answers
345 views

How to solve the Gauss' law?

Imagine we have the first Maxwell Equation: $$ \nabla \cdot \mathbf E = \frac{\rho}{\varepsilon_0} \\ \mathbf E = -\nabla \phi \\ \nabla \cdot (-\nabla\phi) = \frac{\rho}{\varepsilon_0} \\\nabla^2 \...
user avatar
1 vote
1 answer
43 views

If Electrical flux is no. of field lines passing through the area then why the formula is $E$ dot $A$ (Area)?

I have been taught that flux is no. of field lines passing through the surface. But my question how does the formula for calculating electric flux is matching with the above statements? The formula ...
user avatar
1 vote
1 answer
34 views

Why is the net flux the same for both spheres?

There are 2 spheres both of radius "r" and "R" respectively. Using Gauss' law to find the net flux from the surface, we use: $$𝝓 = \frac{Q(charge \ enclosed)}{\epsilon_0} = E × ∮...
user avatar
  • 13
0 votes
0 answers
50 views

On the impossibility of stable equilibrium of a charge in an electric field

I had read from my textbook that a positive charge cannot be in stable equilibrium as if we take a gaussian surface surrounding the charge then assuming that the charge is in equilibrium then using ...
user avatar
0 votes
1 answer
31 views

What's the net flux from sphere?

I have a sphere of radius "r" , the sphere has a total charge "q" distributed equally around the surface. A point "P" is at a distance "R" from the centre of ...
user avatar
  • 13
2 votes
4 answers
407 views

Electric potential generated by spherical symmetric charge density

I know this question is pretty basic but I found a supposedly wrong formula in my notes and I'm trying to understand where this is coming from. Suppose we have a spherically symmetric charge density $\...
user avatar
1 vote
1 answer
17 views

Charge density by Gauss divergence theorem when the electric field is dincontinuous

Let's say the electric field across a surface is discontinuous. Now if I want to find the surface charge density which electric field should I use in Gauss divergence theorem?
user avatar
  • 157
1 vote
1 answer
29 views

Why doesn't electric flux depend on a charge outside the surface? [duplicate]

Let us assume a gaussian sphere with zero charges inside it, then the flux will also be zero in accordance to Gauss' law. But if we have a charge or many charges outside the sphere such that the ...
user avatar
0 votes
2 answers
67 views

Can we derive Ampere's Circuital Law from Gauss's Law or vice versa?

I was curious if it is possible to derive Ampere's Circuital Law from Gauss's Law as they are very similar and both can be applied for highly symmetrical problems $(Infinite\space wires,Rings..etc)$ ...
user avatar
3 votes
3 answers
657 views

What is the difference between Dirac delta vs removing point from space approach?

Let us take for instance E&M, in it when we deal with the failure of divergence theorem to give us the right expression when evaluating the volume integral of divergence of electric field over ...
user avatar
0 votes
0 answers
14 views

Does the electric field due to Faraday's law have zero divergence? [duplicate]

How do we know that the electric field that is produced due to Faraday's law of induction does have zero divergence since when proving Maxwell's equation of gauss law, where the divergence of electric ...
user avatar
0 votes
1 answer
40 views

The second uniqueness theorem in electrostatics

Does the second uniqueness theorem just say that if there is an electric field that satisfies Gauss's law for a surface surrounding each conductor + a surface of elnclosing all the conductor, it is ...
user avatar
0 votes
4 answers
78 views

Gauss' Law in differential form applied to charged sphere [closed]

I need to use the differential form of Gauss' Law $$\nabla · \vec E = \rho / \epsilon $$ applied to a charged sphere to obtain that the exterior field is given by $$\vec E = \frac{Q}{4 \pi \epsilon r^...
user avatar
  • 11
1 vote
1 answer
86 views

Flux through faces of cube if charge is placed at an edge-center

The charge at edgecenter will be shared by 4 cubes so each cube will get $q/4\epsilon$ . The adjacent faces of the edge ( where the charge is located ) will have $0$ flux through them as no Electric-...
user avatar
1 vote
1 answer
31 views

Why do we consider external electric field in Gaussian equation of electric flux?

We know in the Gaussian equation that the net flux through a closed surface is equal to the flux of the charge inside the surface. Mathematically we see that the left hand integral consists of the ...
user avatar
3 votes
2 answers
79 views

Why is the gravitational potential inside a hollow sphere same as that of the gravitational potential on the surface of the hollow sphere? [duplicate]

Gravitational potential inside a hollow sphere is given by $$V(r)=\frac{-Gm}{R}$$ Why is it the same as the gravitational potential on the surface of the hollow sphere, which is given by $\frac{-Gm}{R}...
user avatar
  • 33
2 votes
1 answer
82 views

Gauss' law in the presence of surface charges [duplicate]

Assume $V$ is a volume such that $\rho=0$ in $V$ where $\rho$ is the charge density. Assume further that we have a surface charge density $\sigma$ on the surface $S$ enclosing $V$ such that the total ...
user avatar
  • 149
0 votes
3 answers
173 views

Is it possible to introduce magnetic monopoles without breaking $∇ · B = 0$?

In another word, the net magnetic charge is always zero everywhere, which means magnetic field is still strictly source free. On the other hand, the net magnetic current jm can be nonzero, which means ...
user avatar
  • 365
0 votes
1 answer
49 views

Integrate continuity equation in QM

From Shankar's QM book pg. 166: The continuity equation for probability density in QM is $$\frac{\partial P(\vec{r},t)}{\partial t}=-\nabla \cdot \vec{j}(\vec{r},t),$$ where $P=\psi^*\psi$ is the ...
user avatar
  • 3,905
0 votes
1 answer
93 views

How should the singularity of the Coulomb's law be understood? [duplicate]

The electric field at the point $\vec r$ due to a point charge $q$ at the origin $$\vec E=\frac{q}{4\pi\epsilon_0}\frac{1}{r^2}\hat{r}$$ blows up at the origin. In other words, the force between two ...
user avatar
1 vote
8 answers
179 views

Why can't electric field by a single charge be at an angle?

I am having a very difficult time understanding this basic concept of why the direction of the electric field by a single isolated charge is radially outward or inward but not at an angle. I have been ...
user avatar
  • 757
2 votes
0 answers
11 views

Determination of the electric and magnetic field of a beam of protons as functions of the distance $r$ to the beam with the help of Ampere and Gauss

I want to calculate the fields $\vec{E},\vec{B}$ as a function of $r$. I know that the current implied by the beam is $I=env_{p},v_p=\frac{c}{3}$ and the charge density is $\rho=en$. On top of that, ...
user avatar
  • 21
1 vote
1 answer
29 views

No net charge in conductor or no charge at all? Electrostatics

I understand that there can be no net charge in a conductor because any moving free electrons would induce a countering electric field that would then cause the net E field inside a conductor to be ...
user avatar
0 votes
1 answer
46 views

Why does electric flux only consider normal components of electric fields?

According to the definition of electric flux, only the normal components of field lines passing through a surface are considered. I am unable to understand why it's so? What would be different or ...
user avatar
0 votes
1 answer
53 views

Why does a charge distribution with cylindrical symmetry have to be infinitely long?

Why does a charge distribution with cylindrical symmetry have to be infinitely long when applying Gauss's law? It seems unnecessary especially since the electric field emits radially.
user avatar
  • 45
0 votes
1 answer
83 views

Electric Flux Through a Circular Disc due to a Point Charge

I am having trouble understanding the proposed method for finding the electric flux through a disc of radius $a$ given by a point charge at distance $z_0$. $$ \int \vec{E} \cdot \hat{n}da = \int_0^{...
user avatar
0 votes
0 answers
34 views

Is the commonly derived Gauss' law for a parallel plate (insulator/conductor) often derived wrong? [duplicate]

I am very confused about plates (conductors/insulators) and applying Gauss law. It seems like gauss law for the isolator is very often derived wrongly. In short: if you have an infinite plate (...
user avatar
  • 1,015
1 vote
2 answers
93 views

Charge kept inside a conducting sphere not at its center

Assume a conducting sphere has a charge which is placed at its center like in the figure given below. In this setup charge is only induced in the walls of the sphere, right? Why cannot the charge be ...
user avatar
  • 167
1 vote
1 answer
46 views

Electric displacement at the boundary of a dielectric and vaccum

At the boundary of an infinite linear dielectric with constant $\kappa$ and a vacuum, a charge q is placed. In order to calculate the electric displacement$(\mathbf{D})$ we can use Gauss's law for ...
user avatar
  • 195
0 votes
1 answer
25 views

Charge inside a surface with a "non-gaussian" field?

I read in a book that gauss law is just a statement for the inverse square law. ( As the $r^2$ terms would cancel with the area $4 \pi r^2$.) Suppose I take a hypothetical field of $$ E= \frac{1-e^{-...
user avatar
  • 113
0 votes
1 answer
39 views

Electrostatic request about forces of dielectric

So this question pertains to few different topics. How to find the electrostatic potential due to the point charge placed outside of a dielectric? (- to understand the difference between $\textbf{D}$ ...
user avatar
  • 143
0 votes
0 answers
11 views

What are the surfaces that contain an interior volume (space separating) called? Are they related to orientability?

I know that a "closed" surface is defined as a compact surface with no boundary. I don't have it clear if they have something to do with having an interior volume (completely enclosed volume)...
user avatar
1 vote
1 answer
54 views

Non-zero total charge in a hollow conductor

Given a closed, hollow conductor (as understood in electrostatics), denote by $V$ its cavity. Let $$Q_V = \int_V \rho(x) \text{d}^3 x$$ be the total charge within the cavity. Is it always the case ...
user avatar
  • 149
1 vote
1 answer
116 views

Unique solutions to divergence equation?

A very common problem in physics is to search for a function $f:\mathbb{R}^n \rightarrow \mathbb{R}^n$ such that $$ \nabla \cdot f = g $$ for some given source density $g: \mathbb{R}^n \rightarrow \...
user avatar
  • 936
0 votes
1 answer
62 views

What can the solution to Laplace's equation tell us?

If $V$ satisfies ${\nabla}^2V=0$ given the boundary conditions associated to the boundaries of some volume $\tau$ in space, then what can $V$ tell us? Does it tell us the potential in all of space? Or ...
user avatar
  • 37
1 vote
1 answer
49 views

When to use Gauss's Law

What is the use of this equation and Gauss's Law As an example, for this problem I was able to to use the equation to have the exact same result without the use of Gauss's law as in the answer. ...
user avatar
0 votes
1 answer
22 views

Why does Gauss's law for magnetism hold even when there are two bar magnets?

I'm struggling to understand Gauss's law for magnetism, which states that the net magnetic flux through any closed surface is always zero. I understand why it holds true if you have a single magnet ...
user avatar
0 votes
1 answer
23 views

Question regrading the meaning behind flux of Electric Field

Consider a small area $dA$ ,now the normal vector to the area $dA$ is $\hat{n}$ ,now $E .\hat{n}$ gives us the flux along the direction of our area ,now my question is why multiply with dA ,(since dA ...
user avatar
0 votes
1 answer
75 views

Difference between $D$ and $E$ electric fields and how to prove their relation

My original question was how I could get from [$\Phi = \int \textbf{D} \cdot d\textbf{S}$] $\to$ [$\textbf{D} = \epsilon \textbf{E}$] using Gauss' Law ($\iint_{A} \textbf{E} \cdot d\textbf{A} = \Phi_{...
user avatar
0 votes
1 answer
56 views

If no net charge is in a Gaussian surface, is the electric field zero?

Gauss’ Law states that that the electric flux of a Gaussian surface with no charge enclosed is zero $$\oint {\bf E} \cdot d{\bf A} = \frac{q_e}{\epsilon_{0}}.$$ If you do some algebra you can ...
user avatar
0 votes
2 answers
66 views

Electric charge in compact space

Why in a compact space in the presence of an electric charge there must be the same charge with the opposite sign?
user avatar
  • 65
1 vote
0 answers
33 views

Volumetric charge density of a Gaussian surface $\rho$

If I have a long cylinder (infinite length) and has a radius R=4cm , A cross section of it has length $L=15m$ and charge $q=3\mu C$ , The cylinder is surrounded by a thin shell (Thickness$\approx0$) ...
user avatar
0 votes
1 answer
79 views

Direction of electric field of a cylinder

In this example of Griffiths, we see a cylinder with the given volume charge density. It turns out that the electric field only goes outward in the direction perpendicular to the curved surface, so in ...
user avatar
  • 137
1 vote
1 answer
62 views

Concentric sphere and a spherical shell [closed]

I have the following system: A non-conducting sphere with radius $R$ is placed inside a spherical non-conducting shell with inner radius $2R$ and outer radius $3R$. The shell and the sphere are ...
user avatar
  • 131
0 votes
1 answer
63 views

Using square loops to calculate electric field of infinite plane of charge

Electric field of infinite plane of charge is given by: $$E=\frac{\sigma}{2\varepsilon_0}$$ This can be derived using Gauss's Law or integrating the contribution by circular loops of charge enclosing ...
user avatar
  • 113
-1 votes
1 answer
40 views

In Gauss' Law, how is the choice of $\epsilon_0$ practical for graphically illustrating field lines?

In Gauss' Law the constant $ \epsilon_0 $ was chosen as the proportionality factor between line density and field intensity. In a theoretical sense, this is considered a wise choice because it leads ...
user avatar
  • 1
0 votes
0 answers
68 views

Gravitational Field Inside a Body with General Relativity

Is there possible to describe the gravitational field inside a body, in a similar way you do with Gauss Law of gravity, but with General Relativity? $$ \oint_{\mathcal S} \vec{g} \cdot \vec{\mathrm d ...
user avatar
0 votes
0 answers
23 views

How to prove Poisson's equation for gravity? [duplicate]

When deriving, by integration from the Newton's law, the gravitational acceleration field inside a sphere we get: $$\mathbf a = \frac{4}{3}\pi G \rho (\mathbf {r_c-r_p})$$ where $\mathbf {r_p}$ is a ...
user avatar

1
2 3 4 5
27