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2answers
34 views

Electric Flux; Number of lines passing through a unit surface?

Most of the definitions on flux and flux density, show a plot consisting of a positive charge emanating a field, and describe that as the number of field lines decrease, the field strength decreases. ...
0
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1answer
32 views

Electric field between capacitor plates

When we try to find the electric field between the capacitor plates, what is the right way to do it? This is one of the ways I've seen and I don't understand why: Using a Gaussian cylinder on the ...
1
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2answers
49 views

Applying Gauss's law on a disc

Shouldn't the electric flux through a circular disc due to a point charge kept at some finite distance from it be zero as all field lines which enter it exit it also and hence the net would be zero?
0
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1answer
20 views

Electric field from the intersection of two spheres with different charges

This question is repeated a lot, but I for two spheres with different charge densities, sphere one with radius a centered at the origin and charge density $\rho_1$, and sphere two with radius centered ...
0
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0answers
44 views

Electric field inside a spherical shell [closed]

Suppose the electric field fell off as $1/r^3$, why the electric field will not be zero inside (except at the center)? I am talking about the uniformly charged spherical shell.
1
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1answer
36 views

Gauss's Law on Parallel Conducting Plates

I have a question regarding the application of Gauss's law to find the E-fields produced by two parallel conducting plates. My textbook (Halliday and Resnick 9e) states that there is no E-field above ...
2
votes
1answer
72 views

Contradictions in electric field of infinite uniform charge distribution [duplicate]

This question stems from the exercise 2.50 of Griffith's Introduction to Electrodynamics, which I am rereading. In the problem, he asks to find the charge density of a volume when the electric field ...
0
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1answer
25 views

$E$ in a solid uniformly charged conductor: Is my reasoning here correct?

Suppose we take spherical conductor which is having both positive and negative charges but as a whole is electrically uncharged and is not under the influence of any external Electric field, We can ...
0
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1answer
28 views

Value of E on a point inside a solid uniformly charged sphere due to the part of the solid sphere on the outside of the point

Suppose there is a uniformly charged solid sphere of radius $R$ and we choose a gaussian surface of radius $r$ centered about the center of the solid uniformly charged sphere where $R>r$. Then is ...
1
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2answers
53 views

The value of $E$ in the LHS of Gauss law equation

Suppose there are multiple point charges in a region and I only take the Gaussian surface which encloses only one of the charges $q$. I have read that the $E$ term on the LHS of the Gauss law equation ...
4
votes
4answers
210 views

Is anything lost by simply saying that a charge is nothing but the divergence of a field?

If we propose that 1) there are fields and 2) that some fields can have places where they converge (that is to say, places where del dot the field is not zero) then we have the definition of such a ...
4
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4answers
149 views

Divergence of $\frac{ \hat {\bf r}}{r^2}$ , what is the 'paradox'?

I just started in Griffith's Introduction to electrodynamics and I stumbled upon the divergence of $\frac{ \hat r}{r^2}$ , now from the book, Griffiths says: Now what is the paradox, exactly? ...
2
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3answers
684 views

Why do we use a cylinder as a Gaussian surface for infinitely long charged wire?

Why do we use a cylinder as a Gaussian surface for infinitely long charged wire and not some other shape like cube?
1
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0answers
91 views

Why is the $\vec E$ field inside a sphere = 0? [on hold]

I was taught Electric Field inside a sphere is 0, because of Gauss Law. But inside a uniformly charged sphere, if I go at a distance of $r$ from the centre, I will be closer to the +ve charge and ...
2
votes
1answer
49 views

$\nabla. \vec E =\frac{\rho}{\epsilon}$ for a non conservative field

$$\nabla\cdot \vec E =\frac{\rho}{\epsilon}$$ In this formula, suppose I have a non conservative $\vec E$ field, and I put this formula into this expression I will get a corresponding value of $\rho$....
0
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2answers
36 views

Electric field inside infinite charged hollow cylinder

Gauss's Law says that electric field inside an infinite hollow cylinder is zero. My question however is that an infinite hollow cylinder can be constructed by taking rings as element and the field ...
0
votes
1answer
53 views

Why charges should go to the surface of conductor? [duplicate]

How can we show that charges should go to the surface of a conductor, assuming that system should minimize its energy? (With no additional assumptions and maybe using variation method!)
1
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2answers
38 views

Electric field inside and outside a hollow spherical shell

If a charge(+q) is placed at distance away from a hollow spherical conducting shell , would the net electric field inside the hollow portion remain zero? If the +q charge was placed anywhere inside ...
0
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0answers
22 views

What is the electric field between two coaxial conducting cylinders when a charged sphere is placed within the inner cylinder?

A long cylindrical capacitor of length $l$ consists of an outer conductor of radius $a$ and an inner conductor of radius $b$, where $l>>a$. The outer conductor is earthed, and the inner ...
0
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2answers
92 views

Why doesn't shell theorem work here?

I think I have a misunderstanding about the shell theorem regarding electrostatics here. Since we have a conducting spherical shell, and we are looking for the $E$ field, shouldn't it be 0 within ...
0
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1answer
35 views

Gauss’s law two concentric cylinders

In the answer key, for part b, they take the charge enclosed to be $Q_{enc} = +\frac{Qh}{L}$ where $h$ is the height of the Gaussian cylinder, $L$ is the length of the cylinder with radius $R_1$, and $...
-1
votes
2answers
49 views

About the electric flux at various part of the cube [closed]

A point charge +q is placed at the centre of a cube of side l. What will the electric flux at one of its sides be? How will the flux change if the charge is put on a corner?
0
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1answer
16 views

Electric field in capacitor arrangement with different dielectric media

Please consider the following arrangement of infinitely extended charged plates. In z-direction the system also extends to infinity. The charged plate in the middle of the figure is 2x negatively ...
0
votes
1answer
27 views

Can we use Gaussian pillbox method to determine electric field at a point just near the surface of a surface charge distribution?

I know we can use Gaussian pillbox method to find the discontinuity at the surface of a surface charge distribution. But can we use Gaussian pillbox method to determine electric field at a point just ...
2
votes
3answers
138 views

Why do my books introduce the equation $\nabla \cdot \mathbf{E}=\frac{\rho}{\epsilon_0}$ without showing partial derivatives of $\mathbf{E}$ exist?

In electromagnetism (electrostatics), we often come across the equation $\nabla \cdot \mathbf{E}=\frac{\rho}{\epsilon_0}$. In order for this equation to be meaningful, $\mathbf{E}$ must be a ...
0
votes
1answer
71 views

Why does the electric flux through the surface of a cube with a point charge inside it remain unchanged when the point charge is moved? [closed]

Why does the electric flux inside a cube remain unchanged when the charge is moved within the cube (not on vertices/faces/edges) but just in volume?
0
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0answers
32 views

What is the physical significance of the complex solutions for the function of electric field inside and outside the solid non-conducting sphere?

Please consider this graph of electric field due to solid non conducting sphere inside and outside the sphere. If we consider the function by its graphical analysis then it is a surjective or many ...
1
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2answers
65 views

When to use Poisson's equation in electrostatics

When does when elect to use Laplace's equation when dealing with charge distributions. For example, if I had a metallic sphere of radius $R$ and charge $Q$, then $$\mathbf E = \begin{cases} 0, & ...
0
votes
0answers
76 views

Why can't Gauss surface be a cube?

For calculating field outside a charged plane conductor, a gaussian surface of Cylinder is considered. I have been said that we consider cylinder because the circle in its upper end is in equal ...
0
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2answers
33 views

Volume charge density equation - dimensions not tallying

Write an expression for the volume charge density $\rho(\mathbf{r})$ of a point charge $q$ at $\mathbf{r}'$ in terms of the Dirac delta function. My attempt: Let $\mathbf{r}-\mathbf{r'}=\mathbf{R}$. ...
0
votes
1answer
45 views

Gauss law electric field inside a conductor [closed]

Can you mathematically prove that if there is a cavity in a conductor and no charge is placed in it, the field at all points in the cavity will be zero?
0
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0answers
20 views

On the Electric Field of conductor under Electrostatic Conditions

Let us take a hollow conductor which has a charge Q uniformly distributed on its surface. Now, we know that the Electric field inside the conductor must be ZERO. But what happens when I bring ...
0
votes
0answers
53 views

What is electric field on the surface of a surface charge?

Electric field just near the surface of a surface charge is $\dfrac{\sigma}{2 \epsilon_0} (\hat{n})$ on one side and $-\dfrac{\sigma}{2 \epsilon_0} (\hat{n})$ on the other side. What would be the ...
0
votes
2answers
97 views

Why Electric field inside the spherical shell is zero? [duplicate]

electric field in and out of the spherical shell Why the field inside the conducting spherical shell is zero? Professor Lewin said and I quote," there is NO charge inside the conductor because any ...
0
votes
1answer
117 views

Point charge inside a hollow conductor, does the exterior field changes when the charge moves?

Suppose that I have a hollow conductor with no specific format. I know that if I put a charge inside it, it will induce charge in the inner surface and on the outer surface a charge with a opposite ...
2
votes
1answer
65 views

Electrostatic in 2D: dimensional analysis

After reading this very interesting post about the electric field and the electric potential of a point charge in 2D and 1D, I've understood that, for the $2D-$case, the following formulas hold: $$ \...
1
vote
1answer
268 views

What is the electric flux through the flat and curved surfaces? [closed]

My question is from Physics For Scientists And Engineers 7th: A particle with charge Q is located immediately above the center of the flat face of a hemisphere of radius R, as shown in the figure. ...
0
votes
3answers
168 views

Electric field in center of non-conducting sphere with non-uniform charge distribution from Gauss's law

I'm currently reviewing electricity for the AP Physics C exam, and came across a problem or general topic I don't really understand that has to do with Gauss's law. The general form of Gauss's law we ...
1
vote
1answer
59 views

Earnshaw's Theorem in Chemical Bonds

Earnshaw's theorem says that: A collection of point charges cannot be maintained in a stable stationary equilibrium configuration solely by the electrostatic interaction of the charges. I also know ...
1
vote
1answer
44 views

Finding electric displacement $\mathbf D$ for a parallel-plate capacitor filled with two slabs of linear dielectric material

This problem refers to Griffiths Problem 4.18: According to my solutions, my lecturer wrote: Only free charge is on plates. $$\mathbf D = -\sigma \hat z \ \text{between the plates and $0$ ...
7
votes
3answers
519 views

Flux received by a negative charge

Consider two charges $+q$ and $-Q$ placed at a distance, note- charge q and Q are different In terms of magnitude. My question: is number of flux lines received by $-Q$ proportional to its own charge,...
5
votes
4answers
863 views

Why is electric field inside a cavity of a non-conducting sphere not zero? [closed]

Consider a charged non conducting solid sphere of uniform charge density, and it as hole of some radius at the centre. Now suppose I apply Gauss law. As there is no charge inside the cavity, no ...
0
votes
1answer
34 views

Calculating flux through a spherical Gaussian sir surface

Three uniformly charged wires with linear charge density $\lambda$ are placed along $x,y$ and $z$. What is the flux of the electric field through Gaussian surface given by $$x^2 + y^2 + z^2 = 1;\, x&...
0
votes
0answers
25 views

Relationship between polarization charge density and free charge density

I have concluded that in a uniform dielectric, volume free charge density $\rho_0$ and volume polarization charge density $\rho'$ satisfy $$ \rho' = \frac{-(\epsilon - \epsilon_0)}{\epsilon}\rho_0 $$ ...
0
votes
1answer
48 views

Principle of superposition in spherical shells

If I have a spherical shell with a uniform positive charge desnity on its surface is near a positive point charge q (sitting in quadrant II area) In consideration of the electric field strength and ...
0
votes
2answers
76 views

Gauss divergence theorem (GDT) in physics

Some of the statements for $GDT$ which I find in modern textbooks (both electromagnetism and multivariable calculus textbooks) are: (1) Calculus: Several variables Adams Let $D$ be a regular, ...
1
vote
2answers
24 views

element of surface area versus vector element of surface area

In the context of calculating electric flux, is there a difference between element of surface area versus vector element of surface area? Thanks
1
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2answers
90 views

Physical example of line charge

Electric field due to an infinite line charge, sheet of charge, point charge, etc are popular problems solved in most text on Gauss's law of electromagnetism. My question: does an (exact or ...
5
votes
3answers
145 views

Why are the two outer charge densities on a system of parallel charged plates identical?

One of the ways examiners torture students is by asking them to calculate charge distributions and potentials for systems of charged parallel plates like this: the ellipsis is meant to indicate any ...
0
votes
1answer
61 views

What is the difference between Closed and Bounded surface?

When I was going through "The Feynman's Lecture on physics" Volume-2 , I found the line "It is useful to speak of the flux not only through a completely closed surface, but through any bounded ...