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
3
votes
1answer
51 views

What is the correct interpretation of Electric flux? (beyond a mathematical formula)

From when I first learned flux and till now, I was thinking of flux as a measure of 'flow'. Now, this interpretation breaks down if you consider conductors as I will show below. Here, there is abrupt ...
0
votes
2answers
27 views

Why is it that when calculating the electric field of a cylinder, the linear charge density is used?

I think that the surface charge density is more appropriate as the cylinder, unlike a rod, does have a surface. However if I look at textbooks like Halliday or even stuff on the internet it seems ...
0
votes
1answer
24 views

Charges in a conductor

When a conductor is placed in some external electric field, why can't the free electrons just escape out of it? Is the positive charge distribution on the opposite side(surface) always strong enough ...
0
votes
1answer
41 views

What will be the electric field intensity in the space between the two plates? [closed]

Suppose, we have a parallel plate capacitor and we know the following about it: Area of each plate = $A$ Distance between the two plates = $d$ Charge on each plate after fully charging the capacitor = ...
0
votes
0answers
25 views

Derivation of Gauss' Law of Gravitation [duplicate]

this question is simple, I was looking for a good derivation to Gauss' Law of gravitation $$\int \vec g.d\vec A=-4\pi GM $$ but was unable to find a good enough one online. Hence may I know its ...
0
votes
2answers
67 views

I don't understand the discontinuity in electric field across a surface

In Griffith, it was given that when we cross a surface charge density, a discontinuity in the electric field occurs. The proof was given from Gauss law. $$E_{\rm above}^\perp-E_{\rm below}^\perp=\frac{...
0
votes
0answers
49 views

The Potential and Electric Field of a Cylinder. Apparently a huge inconsistency? [closed]

The problem is as follow: Obtain the potential and the electric field created by a cylinder of radius R and height h with volumetric density $\rho$ constant at a point z of its external axis the ...
10
votes
14answers
696 views

Why is the field inside a conducting shell zero when only external charges are present?

In many introductory books on electrostatics, you can find the statement that the field inside a conducting shell is zero if there are no charges within the shell. For example, if we place an ...
0
votes
2answers
50 views

How to Apply Gauss Law? [duplicate]

Lets say that we have a point charge $q$. Let's draw a Gaussian sphere at a distance $d$ from the charge, as no charge is enclosed inside the sphere the integral $$ \oint_A \vec E \cdot \text d \vec A ...
1
vote
2answers
37 views

How to find integral's bounds - calculating electric field using Gauss's law?

This is the original question: The space between two parallel infinite planes $ x=0 $ and $ x=L $ is filled with charge of the density $ \rho\left(x\right)=ax^{2}\left(L-x\right) $ where $ a $ is a ...
1
vote
2answers
45 views

Calculating surface charge density as a function of time

An infinitely large conducting sheet of thickness $d$ and of conductivity $\eta$ is uncharged. At an instant $t=0$, an external uniform and electric field $E$ is switched on. Due to this, the ...
1
vote
2answers
31 views

Time-domain model of a capacitor when the capacitance is varying with time

The current through a capacitor as a function of time is given by; $$i(t)=C\cdot \frac{d}{dt}U(t)$$ When assuming that the capacitance $C$ does not vary with time. But what if it does? I don't know ...
1
vote
3answers
59 views

Why is electric field inside a conductor non-zero even if there is point charge placed inside it?

If I place a point charge q inside a conductor, The electric field at any point inside it will be non zero (Kq/x²). If we draw a Gaussian surface inside the conductor, the net enclosed charge will be ...
2
votes
3answers
34 views

Argument for electric field inside spherical shell

If I have a conducting spherical shell of outer radius $R$ and inner radius $r$, the electric field inside is $0$. The argument commonly given is: Pick a point $P$ inside the shell (i.e. radius < $...
1
vote
1answer
51 views

Can gauss law for magnetism be used for open surfaces?

Suppose there's a loop of current carrying wire in a plane,then it's stated in my book that magnetic flux through the area of loop will be negative and of equal magnitude as the flux outside the loop ...
0
votes
1answer
28 views

Capacitance with different dielectrics [closed]

I have to calculate the capacitance of a spherical or a cylindrical capacitor (The problem contradicts itself) and the free charge density at any point of the inner conductor. The region between the ...
6
votes
3answers
245 views

Why doesn't finite field propagation speed contradict Gauss's law? [duplicate]

[Edit] Not sure why this was closed. The answers there do not answer my question, and are not even correct... Imagine a charge sitting in space. It causes an electric field everywhere, with magnitude ...
0
votes
2answers
85 views

I have a doubt regarding electric field inside uniformly charged spherical shell

A spherical shell, uniformly charged, exerts no field inside it ; the point being either at centre or off-centre. According to Gauss law if we construct a spherical Gaussian surface all inside the ...
1
vote
0answers
26 views

Net Electric field on a Gaussian surface

While applying Gauss' Law, the electric field at a point on the Gaussian surface has to come from superposition of electric fields of all the charges, whether outside or inside the Gaussian surface. ...
7
votes
1answer
174 views

The shell theorem and the Hairy Ball theorem

To get straight to the question, skip to the 'This is what spherical symmetry really means' paragraph. I recently inquired about the shell theorem but this is a different matter (link), so I hope it ...
1
vote
1answer
45 views

The shell theorem and divergence in Susskind's GR lecture

In the lecture available here, at around 1:36:50, Susskind seems to argue that you can derive the fact that the gravitational field inside a spherical shell (of constant density) is 0 from the ...
0
votes
1answer
46 views

Use divergence theorem to compute acceleration of a sphere [closed]

Suppose we have $\vec{F}$ being the force on a proof mass $m$ in the field of a mass $M$ with mass density $\rho(\vec{r})$ given by $\vec{F}(\vec{r})= m\vec{g}(\vec{r})$ and $\vec{g}(\vec{r}) = \nabla ...
1
vote
2answers
58 views

Finding direction of field when using Gauss law

I have seen this stack question Applying Gauss' Law to find Electric Field but I got confused when I saw the comment and the answer because, clearly the flux is a scalar quantity (due to dot ...
1
vote
2answers
75 views

What is the meaning of $\rho _b$ blowing up at the surface?

In Griffith's it has been said that while deriving the equation $\nabla\cdot D=\rho_f$ where $D\equiv\epsilon_0E+P$ and $\rho_f$ is the free charge, there has been no mention of the surface bound ...
0
votes
1answer
39 views

Do the electric field and magnetic field derived from the Lienard-Wiechert potentials satisfy Gauss's law?

I've already got the electric fields and magnetic fields derived from the Lienard-Wiechert potentials: $${\bf E}=\frac{q}{4\pi\epsilon_0}\frac{R}{(\bf R\cdot u)^3}[(c^2-v^2){\bf u}+\bf R\times(u\...
0
votes
0answers
14 views

Validity of Gauss Law [duplicate]

If the electric field due to a point charge varies as $r^{-2.5}$ instead of $r^{-2}$, then would the Gauss Law still be valid? I infer that the $r^{-2}$ term in the Electric field comes as a result ...
1
vote
1answer
111 views

Doubt regarding grounding of a sphere and charge distribution [closed]

An insulated sphere with dielectric constant $K$ (where  $K>1$) of radius of $R$ is having a total charge $+Q$ uniformly distributed in the volume. It is kept inside a metallic sphere of inner ...
2
votes
2answers
80 views

How can Poisson's equation be true when $\phi$ or $\vec A$ is time dependent?

In electrostatic case, the charge density and potential at a point is related by: $\nabla ^2 \phi = -\frac{\rho}{\epsilon_0}$ The same is true for the Magnetic potential $\vec A$ and current density $\...
0
votes
1answer
49 views

Change of integrals used in Gauss' Law [closed]

I have this question where in which the integrals are made from a volume to the integral only dependent on the radial distance R. While they prove this in part b) of the answer in part a) they somehow ...
1
vote
0answers
20 views

Charge density inside dielectric with conductivity

Consider the figures I and II , they consist of similar circuits with identical batteries. There are two different slabs connected in the circuit, both are geometrically identical and have the same ...
0
votes
2answers
41 views

Charge distribution in a Conductor

I recently read a question which even I am having a doubt in. So here it is Suppose there are two isolated conductors both the condcutors are brought in contact now the charges will flow through the ...
0
votes
2answers
74 views

Charges on conductors [closed]

Suppose two similar conductors which are unequally charged are brought close to each other,then charges from one will flow to another and ultimately both of them will be equally charged and either ...
1
vote
4answers
46 views

Electric Field due to Linear Charge Distribution [closed]

The above image is taken from the book concepts of Physics by Hc verma. I am having a bit of trouble understanding that the direction of electric field will always be perpendicular to the curved part ...
0
votes
0answers
13 views

What is the electric field due to a 1D line of charge on the edges of a pillbox geometry?

The "Introduction to Plasma Physics C17 Lecture Notes", which I'm reading online, set out the following scenario in section 1.1.2: Consider the electric field due to a 1-D line of charge (...
0
votes
1answer
33 views

If an object is enclosed within a metallic spherical shell having surface charge + q C. The object will carry charge - q C.? [closed]

I have doubt in the statement is there any link between surface charge and object enclosed within the shell. I think object in enclosed shell can have any charge +ve or -ve . Or it is due to the fact ...
0
votes
1answer
27 views

Change in Electric Flux on Rotating a Circular Ring

A Circular ring of radius r made of a non conducting is placed with its axis parallel to a uniform electric field. The ring is rotated about a diameter through 180 degrees. Does the Flux increase, ...
0
votes
0answers
47 views

Application of Gauss law to find the field on surface of a metallic spherical shell

Consider a hollow metallic spherical shell given a charge Q. The entire charge must reside on the outer surface of the hollow sphere. Now consider a Gaussian surface on the outer surface of the sphere....
1
vote
1answer
55 views

Deriving the Gauss Constraint in Free Maxwell Theory

In section 6.2 (page 128) of David Tong's Lectures on QFT, Gauss' law is derived for the free Maxwell theory. The result of computing the Hamiltonian of the theory is (eq. 6.17), $$H = \int d^{3} x \...
0
votes
2answers
34 views

Field inside cavity of charged conductor

Can we use gauss law to prove that field in a cavity of charged conductor of any shape is zero?? If so how as the shape may lack symmetry? If not how can we prove the field to be zero? I know that the ...
2
votes
5answers
121 views

Why is $\oint_S \mathbf{E}\text d\mathbf{s}=q_{in}/\epsilon_0$ valid when finding electric field inside charged sphere(charges are inside sphere)? [duplicate]

Let $r < R$, where $r$ is the distance to a point from the center of the sphere where we want to find electric field and $R$ is the radius of the sphere. Why can we use $\oint_S \mathbf{E}\cdot\...
0
votes
3answers
79 views

Why $\vec{E} = \frac{\sigma}{2 {\epsilon}}$ does not has a variable for distance?

Upon solving a question where I had to find the Electric Field $\vec{E}$ due to an infinitely large uniformly charged sheet of charge density ${\sigma}$ , I found that the Electric Field at a point ...
-2
votes
2answers
52 views

Why are there electric field lines outside the conductor but not inside?

The Electric field at point P (for an electric slab) is given by $E_P=\frac{\sigma}{\epsilon_0}$, however, since $E$ inside the metallic slab is zero, the electric field at point P is contributed by ...
1
vote
1answer
26 views

Electric density on the edge of a hollow spherical conductor [closed]

Suppose I have a sphere with radius $R$ and charge $Q$ and another hollow sphere with inner radius $2R$ and outer radius $3R$ with charge $2Q$, both of them are conductive. I want to calculate the ...
0
votes
1answer
35 views

Can Gauss Law for any arbitary closed surface be derived from Coulomb's Law? [duplicate]

As far as I know, Gauss' Law is useful for calculating the electric field where Coulomb's Law doesn't work. For example, it is used for calculating the field produced by a thin sheet of charge and ...
0
votes
0answers
27 views

About importance of electric flux [duplicate]

Why is electric flux defined at all? It seems that without having symmetry in objects, we cannot use it to find something important. Please shed some light on its history also.
0
votes
2answers
42 views

Charge and Electric field inside a sphere

Suppose we are given a sphere with total charge $Q$ and radius $R$. To find the total charge $Q$, we can use the relationship $$\rho = \frac{dQ}{dV}\implies Q=\int_0^R\rho \cdot dVdr$$ where $dV$ is ...
-2
votes
1answer
46 views

Confusion from Griffith's book

In Griffith's Electrodynamics (Third Ed.), on page no. $176$, it is written: It may have appeared to you that I left out the surface bound chrage $\sigma_b$ in deriving Eq. 4.22, and in a sense ...
-1
votes
1answer
54 views

Electric flux due to coaxial, non-conducting, uniformly charged discs

Recently I came across a question which involved two coaxial, non conducting, uniformly charged discs, each having a surface charge density $\sigma$. I was required to find the electric flux through ...
1
vote
1answer
17 views

Gaussian Surface for insulated plates have charge Separation

I was wondering the most suitable Gaussian Surface to choose that would allow me solve the electric field easily. Given 2 insulating infinitely long plates that have charge separation. We need to find ...

1
2 3 4 5
20