Questions tagged [electric-fields]

For questions that utilize the concept of electric fields (commonly denoted by the letter E), or for questions whose answers likely involve electric fields. More specific than the [electricity] tag, as questions about the phenomenon & theory of electricity do not necessarily involve the discussion of fields.

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9 views

How to apply Gauss's law when dielectric constant in a capacitor varies continuously?

Let's say the problem is to compute the capacitance of a cylindrical capacitor with a dielectric material between the plates. The capacitor is considered to be long enough to ignore end effects. The ...
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1answer
25 views

Electric flux density and electric field displacement vector are the same quantity?

I was told by my professor that electric flux density and electric displacement vector are the same quantity. But Electric Flux Density is the no of flux per unit area that is given be $\frac{Q}{4 \pi ...
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1answer
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Charge a conductor dome indefinitely frome the inside

Suppose we have a hollow conducting dome with a small hole from which you can touch the inner surface with, let say, a conducting rod. I make sure that the dome is completely uncharged: it has the ...
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1answer
46 views

Number of Electric Lines of force for 1 Coulomb

I read a statement about the lines of forces of an electric field: Total number of lines of force emanating from a charge body is equal to the charge of the body measured in Coulombs. The statement ...
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1answer
48 views

Divergence of electric field of point dipole

Am I correct to say that since the divergence of the following E field $$ \mathbf{E} = \frac{1}{4\pi\epsilon_0}\left[ \frac{3(\mathbf{p_0}\cdot\hat{r})\hat{r}-\mathbf{p_0}}{r^3} \right] - \frac{1}{3\...
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Electrostatic potential in a semiconductor

I was thinking about a very simple question. Imagine we have a semiconductor "embedded by vacuum". Regarding this situation, I was thinking what is the potential felt by the electron ...
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2answers
39 views

Why do we conclude that an electric field is null if the flux is null?

Gauss's Law states that the flux is equal to the charge inside divided by a constant. and is also equal to the surface integral of the electric field. So, if there is no charge inside the closed ...
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1answer
21 views

Why does a charge placed on the same plane as the face of the hemishphere NOT affect the electric flux from the point charge at the centre?

Why doesn't an external charge placed at A or C as in this image not contribute to any change to the already existing electric flux of the hemisphere due to q?
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Why is electric flux due to a point charge placed at the face of a hemishpere, cone and cube the same?

In all these 3 cases, the net electric flux is found to be $q/2ε_0$. I think this has something to do with the integral of $\left(\mathbf{E}\boldsymbol{\cdot}\mathrm d\mathbf{S}\right)$ which appears ...
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21 views

Evaluating the net force that the southern hemisphere of a uniformly charged sphere exerts on the northern hemisphere

Find the net force that the southern hemisphere of a uniformly charged sphere exerts on the northern hemisphere. I am perfectly aware that this question has been asked many times (here), but I am ...
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Electric field's intensity point vs region

I was looking through electric fields when I got confused, I searched about it on the web but I couldn't quite make a conclusion. So imagine you have an electric field, can you have a point in some ...
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1answer
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Electric field on test charge due to dipole

In worked example 4.1 of Intermolecular and Surface Forces by Jacob Israelachvili, he is calculating the electric field on a test charge due to the dipole shown in the picture. He assumes $r\gg l$ and:...
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2answers
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Relationship between Electric Fields, Potential Difference and Resistance in Circuits

The battery in a closed circuit creates a uniform electric field in the wire, which pushes the electrons from the negative to the positive terminal. The electrons clearly have more potential to do ...
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Why is Gauss' Law for Electric Fields still applicable when $\vec{E}=kr^3\hat{r}$?

Problem 2.9 from Griffith's "Introduction to Electrodynamics" Suppose the electric field in some region is found to be $\vec{E}=kr^5\hat{r}$, in spherical coordinates ($k$ is some constant). ...
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1answer
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How is dielectric constant both $E_{net}/E_o$ and $ε/ε_o$?

The questions asks that, given the (surface) charge density (σ) on the plates of a parallel plate capacitor and dielectric constant (k), what would be the magnitude of induced charge density on the ...
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Electric field of electric dipole and gradient properties

I am trying to work out whether there is a way to calculate the electric field of a dipole from the following formula: $$\phi(\vec{r}) = -\vec{p} \cdot\vec{\nabla}\phi_0$$ Where $\phi_0$ is the ...
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27 views

Electric field intensity due to a finite line charge distribution [closed]

I'm trying to evaluate to evaluate the electric field at a point P due to a line charge of finite length from A$(0,0,z_1)$ to B$(0,0,z_2)$ with charge distribution given by $\lambda$. Note: I'm not ...
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1answer
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What is the intuition behind why $\vec{E} = \int \mathrm{d}\vec{E}$ works for summing up infinitesimal contributions of electric field?

Say you want to find the electric field, $\vec{E}$, at some point in space, $P$, which is induced by some uniformly charged rod, $Q$, of known length, $L$. What you would do is break this charged rod ...
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1answer
22 views

Electric field inside uniformly distributed charges

One of the problems I was solving states that "By Gauss’ law the electric field inside a sphere of uniformly distributed charges is 0". I don't understand how that is possible. I thought ...
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0answers
15 views

Potential felt by an electron at the interface with a semiconductor

I was thinking about a very simple question. Imagine we have a semiconductor "embedded by vacuum". Regarding this situation, I was thinking what is the potential felt by the electron ...
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1answer
32 views

Two protons moving in opposite directions. Special relativity and electromagnetism

Imagine two protons moving in the opposite directions with a velocity $v$ or $\beta c$, where $\beta = v/c$. At $t = 0$, they are a distance $r$ apart one along the same line (see the picture). I am ...
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1answer
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Polarization of a material

Can someone explain where this minus comes from? Aren't $a_R$ and $a_n$ parallel so the dot product should be 1. The radius increases outwards aswell as the surface $a_n$, right?
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1answer
47 views

Would this be divergenceless?

If I were to put two charges of opposing polarity next to each other (a finite distance away but not superimposed on each oter) and would then take the divergence of the whole $E$-field, would that be ...
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0answers
31 views

What is the electric field at point P? [closed]

A total amount of charge Q is distributed evenly along a thin, straight plastic bar of length l. (a) Find the electric field at point P, at a distance x from one end of the rod (Figure). (b) Find the ...
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0answers
11 views

Electric field and voltage given number of electrons and distance? [closed]

What would be the electric field and voltage at a distance 0.35m away from an object with an excess of 6.1 x 10^6 electrons? I calculated the charge, q, using q = Ne to be -9.76 x 10^-13 C, but I'm ...
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1answer
21 views

Interpretation of potential difference of a capacitor

Suppose I have 2 charges of arbitrary charge separated by a distance of 2a. The potential at a point, say A, finite distance from the two charges is the sum of the potentials at that point because of ...
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1answer
76 views

Equation of Continuity statements I dont understand

There are two statements about Equation of Continuity in my professors notes that I don't understand. $$ \nabla \cdot \textbf{J} = - \frac{\partial\rho}{\partial t} $$ The Equation of Continuity can ...
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2answers
112 views

Laplace's Equation and Boundary Condition Problem

Calculate the potential and the electric field at point $P(r,θ,\phi)$, where $|r|> l/2$, due to a thin nonconducting rod of length $l$ that carries a total charge $Q$ that its uniformly distributed ...
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2answers
36 views

Energy density of Induced Electric Field

For electrostatic fields, we write the energy density using $$u = \frac12\epsilon_o E^2$$ is this formula also valid for a non-conservative electric field produced by changing magnetic field? Or, can ...
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1answer
30 views

Voltage gained by expelling electrons from a metal

Suppose I have a metal ring and it loses 100 electrons (by some method, for example through an electron gun), how can I calculate the positive voltage that this ring acquires? or how can I calculate ...
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0answers
18 views

Flux through conducting surfaces

I had a doubt regarding electric flux.Can electrix flux be defined through conducting surfaces as no electric fields lines pass through the conductor ?. Or is it that we only consider electric field ...
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0answers
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How to compute the energy of a ball with charge $Q$ [closed]

The total charge and size of the ball is a given, it is also known that the charge is distributed equally. I can’t remember the integral that solves this, what is it?
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1answer
34 views

What is the difference between static electricity and electricity from a battery/power plant?

Static electricity An object holding a static charge has an electric potential. If it touches an object with different electric potential a current will pass until the potentials are equalized. One ...
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1answer
44 views

Why is the speed of light ignored in this formula?

I'm trying to follow this worked example from my lecturer. Here's the question: and here's the answer to part 1: When I was attempting this without looking at the answer, I did correctly identify ...
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0answers
61 views

How to calculate the total charge separated by the Hall effect?

If a plate is undergoing the Hall Effect, how can we calculate the total charge $Q$ present on either side of the plate at the equilibrium state? And how can we calculate the force that such a charge ...
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3answers
39 views

Electric field inside conductor is zero though we are getting $E$ inside Solid Sphere

I know that the electric field inside a perfect conductor is zero as all the charges resides on its surface to minimize its energy but if it's true then why we are still getting the electric field ...
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4answers
284 views

Why do we get a reflected electromagnetic wave when it hits a perfect conductor?

We've an EM wave $\vec{E_i}=\vec{E_0}e^{i(\omega t-kz)}$ As it reaches on the surface of the perfect conductor we know the electric field must be zero, so we deduce that another electric field must ...
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1answer
34 views

Potential difference relation with Electric field intensity

An equipotential surface has the same potential at all points and thus zero potential difference between any two points. Consider the situation 2 as in the figure, If I use $E=-ΔV/Δr$ to find ...
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1answer
37 views

Faraday's Law (General form) and the Change in flux

For the Introductory E&M class, I am taking this year I was working on some problems involving the general Faraday's Law $$\oint{E.dS}=-\frac{d\phi_B}{dt}$$ I was confused regarding, How we ...
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1answer
16 views

Electric field in a shell in asymmetric situation

Suppose there is a metallic shell having a uniform charge Q spread over it uniformly. Now we bring a charge Q1 near it. What is the field at the centre of the shell and in general anywhere in the ...
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1answer
39 views

Electric field computation with two point-charges and an infinite conducting sheet [closed]

Coordinates in this question are in metres: An infinitely large conducting metal sheet is located at z=0 (covers the xy plane). Point charge of 20 μC is at (0, 0, 1) and of -10 μC is at (2, 0, 1). ...
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2answers
50 views

Direction of asymptote to electric field line

For two positive point charges in space separated by some finite distance, the electric field lines we observe look like this: (for point $P$ being the neutral point, the line shown in red is ...
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1answer
53 views

What is causing the acceleration of charges in an ideal TEM transmission line?

As I understand, in an ideal TEM transmission line we can set up the telegrapher equations and solve to show that the line propagates voltage and current waves. My confusion arises when we recognize ...
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0answers
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Electric field lines of conductors through complex variables

The Feynman Lectures on Physics Volume 2, Chapter 7, Section 7-2 discusses the shape of two dimensional electric field lines near conductors through the method of finding two dimensional solutions for ...
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0answers
13 views

Visualizing the dielectric profile between a conductor and an dielectric during wave equation derivation

I was deriving the wave equation for a conductor and a dielectric medium. While solving it considered the dielectric constant with negligible variation over distances on the order of one optical ...
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1answer
77 views

Proving Maxwell's equation, divergence of $E$

For a sourceless medium perturbed as shown below, how can I prove that divergence of $\vec E$ and $\vec H$ equal to zero? $$\vec D = \varepsilon \vec E -j \xi \vec B$$ $$\vec H = \dfrac{1}{\mu} \vec B ...
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0answers
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If we connect the two terminals of a semiconductor diode with a simple wire, then will the current flow? [duplicate]

We know that inside a semiconductor diode, there is an internal electric field from the N side to the P side. This implies that the N side is at a higher potential than the P side of a semiconductor ...
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1answer
34 views

What is the electric field inside this shell? [duplicate]

A problem from Griffiths asks us to find the electric potential inside and outside a spherical shell. The potential on the shell is specified to be $V(R, \theta) = k \cos(3\theta)$. There is no charge ...
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0answers
49 views

Are there two groups of charges associated in an alternating current half wave?

Edit: to better express the problem: As alternating current passes along a wire: Individual current charges produce a magnetic field after zig zagging rapidly locally with a small resultant vector. ...
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1answer
121 views

Brewster's angle reflected wave- is it part of the refracted or incident ray?

I am trying to figure out what is happening to the charged particles in the reflective surface in the case of Brewster's angle. When this angle is different than zero or Brewster's angle, then the ...

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