Electrostatics is concerned with the field and potential of stationary electrical charges and electric charge distributions. Problems are this type are almost exclusively concerned with mathematics of geometries using the inverse-square law.

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Capacitance of Non-concentric Spheres

We all know how to obtain the capacitance $C=\frac{ab}{b-a}$ (ignoring constants) for two concentric spheres of radii $a,b$. I was just thinking to myself, what would happen to the capacitance for ...
2
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2answers
431 views

Gauss' law giving zero field where field is not zero?

Two plastic sheets with charged densities as shown: I'm trying to find the field at $B$. I obtained the correct answer by adding up the fields created by each charge density. But I realized that ...
5
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3answers
1k views

Can Laplace's equation be solved using Fourier transform instead of Fourier series?

Sorry for the long text, but I am unable to make my question more compact. Any periodic function can be Fourier expanded. Usually, they say in mathematical physics books, if the function is not ...
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1answer
213 views

Can a super-extremal charged black hole be made out of electrons only?

In a previous Question it was argued that it would be impossible to add enough charge to a black hole to make it pass the extremal black hole limit since adding charge would increase the mass of the ...
4
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1answer
484 views

Sparks from van de graff generator

I was at a lecture yesterday and there was a demo of a van de graff generator. He held the smaller metal globe which is attached by a wire, about 4cm from the main globe. This created a spark between ...
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2answers
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How can a conductor be grounded yet there are induced charges on it?

A classic example for the method of images is the following, quoted from Griffiths's Introduction to Electrodynamics, page 121: "Suppose a point charge $q$ is held a distance $d$ above an infinite ...
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2answers
596 views

Charge on Sphere due to Contact with Capacitor

Question: Consider a parallel plate capacitor which is connected to potential difference $V$. Let there be a small spherical conductor, assume that its radius is much smaller than the distance ...
0
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2answers
171 views

Can hair be used as an dielectric?

I was letting my mind freewheel, and it occurred to me that hair, containing keratin, is a polymer. It is also capable of acquiring and maintaining a charge as happens, on occasion, when brushed. So ...
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1answer
2k views

How does a Primary Charge Roller work?

I have been recently trying to get more deeply into the workings of a common laser printer. While the basic concept seems to be fairly simple to understand I have been having trouble finding more ...
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4answers
1k views

Is an electron/proton gun possible?

In the 1944 SF story “Off the Beam” by George O. Smith, an electron gun is constructed along the length of a spaceship. In order to avoid being constrained by a net charge imbalance, it is built to ...
6
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1answer
1k views

What is the penetration length of static electric field into conducting metals?

How large is the penetration length for static electric field into good conductors? I have two versions: (1) few atomic spacings $$a\sim n_{e}^{-1/3},$$ and (2) Debye length computed by Fermi ...
2
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1answer
299 views

Where does the smell of electrostatic charge come from?

Everybody knows you can produce electrostatic charge rubbing two different materials together. But have you ever smelt e.g. at the plastic after charging it? There actually is a distinct ...
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4answers
5k views

What is the electric potential at a point?

1) What does the electric potential at a point exactly mean? My teacher tells me that current flows from higher potential to lower potential but when I ask him the reason, he fails to give me a ...
3
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2answers
626 views

Electrostatics:Basic question on electric current

I've got two questions for you. Electric current is the flow of electrons across a conductor.Why has it always got to do with electrons and not with protons? (I know neutrons are not eligible for ...
3
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1answer
159 views

Capacitance of two cocentric spheres, contradicting results

Suppose we are given two conducting, cocentric spheres of radius $a_1$ and $a_2$ respectively. The inner sphere with charge $q$, the outer sphere with charge $-q$. I can calculate the capacitance of ...
1
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1answer
89 views

Creating the opposite of an optical lattice

Is it possible to create periodic potentials that instead of creating a well for an atom to be trapped in, repulsed by that specific location? If yes, can we use this as a means to make artificial ...
6
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1answer
470 views

Boundary Conditions Invariant Under Conformal Transformations in Electrostatics?

in two dimensional electrostatics it is assumed that the whole physical system is translationally invariant in one direction. Here, the two-dimensional Laplace equation $$\Delta \phi(x,y) = ...
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1answer
1k views

Electric field between two conducting plates of different potential?

not sure if this question's been asked before, though I couldn't see one in my brief search on here... Well, the problem I am trying to solve is that I want to determine the electric field strength ...
3
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4answers
903 views

How beam focusing looks like in electron microscope?

I mean I know there are electrostatic/electromagnetic lenses which does focus the beam, but I am not sure how it is possible to foсus beam down to a few 10nm while emitter might be 1mm thick while ...
2
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2answers
371 views

How does electron gun accelerates electrons?

I know that in electron guns we see in TV's and lots of other places, we have electron emitter (cold/hot W needle in the simplest case) and electrons are accelerated using lattice with high-voltage ...
0
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2answers
1k views

Electric field of not-grounded conducting plate with a given potential?

I have been trying to find an equation (or some solution) of how to calculate the electric field strength (in N/C) of a conducting rectangular (nearly flat) plate which has non-zero potential to it, ...
3
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4answers
4k views

Electric field outside a capacitor

I know that the electric field outside of a capacitor is 0 and I know it is easy to calculate using Gauss's law. We create cylindrical envelope that holds the same amount of charges (of opposite ...
1
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1answer
620 views

capacitance between widely-separated parallel plates

There's a caveat, which is often ignored, to the "easy" equation for parallel plate capacitors C = epsilon * A / d, namely that d must be much smaller than the dimensions of the parallel plate. Is ...
4
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2answers
474 views

Algorithm of Lightning Strikes? [duplicate]

Given an array of charge for a given area (2D or 3D), what algorithm would describe the path that lightning takes? An example algorithm would be from the highest charge of the cloud, find the lowest ...
3
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1answer
647 views

How many electrons are displaced when combing hair?

Feynman talking about electricity: http://www.youtube.com/watch?v=qhh32JYkQPk When brushing your hair, Feynman mentioned that a "few" electrons were transferred to the brush (or vice versa, can't ...
2
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2answers
271 views

Is it meaningful to imagine a sphere uniformly charged with 2e?

If the charge is large, considering charge density is usually meaningful despite the discrete nature of electrical charge. The following sentence is part of a problem in a textbook on ...
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2answers
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Two spheres (A physics olympiad problem)

Browsing an archive of problems of a local physics olympiad, i stumbled upon a problem which seems not a very trivial. Given two identical metal spheres in vacuum, with mass $m$ and radius $R$. One ...
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2answers
13k views

Determine the point at which the electric field is equal to zero?

Two point charges, -2.5 micro coulombs and 6 micro coulombs, are separated by a distance of 1m (with the -2.5 charge on the left and 6 on the right). What is the point where the electric field is ...
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2answers
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Tension in a curved charged wire (electrostatic force) - does wire thickness matter?

Consider a conducting wire bent in a circle (alternatively, a perfectly smooth metal ring) with a positive (or negative) electric charge on it. Technically, this shape constitutes a torus. Assume ...
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6answers
1k views

Laplacian of $1/r^2$ (context: electromagnetism and poisson equation)

We know that a point charge $q$ located at the origin $r=0$ produces a potential $\sim \frac{q}{r}$, and this is consistent with the fact that the Laplacian of $\frac{q}{r}$ is ...
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1answer
426 views

Electric field of a charged spherical surface [closed]

Figure The dielectric shaped as on the figure has dielectric constant $\varepsilon=\varepsilon\left(r\right)$ and free charge density $\rho=\rho\left(r\right)$. What is the electric field and ...
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2answers
5k views

Determine Charge With Electroscope?

You have three separate glass rods, and you know one is positive, one is negative and one is neutral. You also have an electroscope that is positively charged. How can you determine which rod is ...
7
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2answers
537 views

Torque of an electric engine

So I have some follow up questions from this thread: Electric engine transmission Basically, I am looking for a more precise mathematical statement that makes this true. Why is it that the electric ...
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5answers
2k views

Why isn't there a centre of charge?

When determining the gravitational attraction between 2 solid bodies, we can simplify computations by taking their masses to be concentrated at their respective centres of mass. However, had they been ...
4
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1answer
420 views

Balloon rubbing; where do the electrons go?

If you rubbed a balloon with a towel, where would the electrons go: the balloon or the towel? Why? I'm guessing the electrons would go to the object with a larger mass, but it's just a guess. :)
6
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1answer
636 views

In Method of images type problems, why isn't the induced charge taken into account while solving it via Green's functions?

To take the simplest example, $$\Phi(\vec{r}) = \begin{cases} V & r\leq a \\ 0 & r\geq a \end{cases}$$ For a plane conducting surface that extends all the way. Choosing an appropriate ...
2
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2answers
917 views

What is the effect of temperature on electrostatic-gravitational balance?

We have two identical massive metal spheres at the same temperature at rest in free space. Both have an identical charge and the Coulomb force [plus the black-body radiation pressure if the ...
7
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6answers
743 views

What prevents the accumulation of charge in a black hole?

What prevents a static black hole from accumulating more charge than its maximum? Is it just simple Coulomb repulsion? Is the answer the same for rotating black holes? Edit What I understand from ...
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3answers
601 views

Paradoxical interaction between a massive charged sphere and a point charge

Suppose we have a sphere of radius $r$ and mass m and a negatively charged test particle at distance d from its center, $d\gg r$. If the sphere is electrically neutral, the particle will fall toward ...
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4answers
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Resistance between two points on a conducting surface

Suppose we have a cylindrical resistor, with resistance given by $R=\rho\cdot l/(\pi r^2)$ Let $d$ be the distance between two points in the interior of the resistor and let $r\gg d\gg l$. Ie. it is ...
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2answers
3k views

Why two objects get charged by rubbing?

It is always told as a fact without explaining the reason. Why do two objects get charged by rubbing? Why one object get negative charge and other get positive charge?
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1answer
3k views

Electric Field for a hollow sphere with point charge

I think I am over thinking this question: A point charge of $-2\space\mu C$ is located in the center of a hollow sphere. The internal and external radius of the sphere is given by $6.5$ and ...
12
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2answers
5k views

What is the net charge of the Earth?

This question arose in a seminar today about the solar wind... This is my vagueish understanding of the problem - please correct if you see errors! The 'classical' picture of atmospheric electricity ...
6
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4answers
2k views

Method of Images

The method of image charges is a well-known and very useful tool for solving problems in electrostatics. Unfortunately, when I was taught this method, it was presented simply as an algorithm. No real ...
7
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3answers
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Charge density in concentric spheres

Question: If there are two conducting spherical shells and the inner shell is grounded, what will be >the charge density in the inner shell if there is a charge Q placed on the outer shell? ...
12
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2answers
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Virtual photon description of B and E fields

I continue to find it amazing that something as “bulky” and macroscopic as a static magnetic or electric field is actually a manifestation of virtual photons. So putting on your QFT spectacles, look ...
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2answers
222 views

energy field of a newly created particle

The question is: How to calculate the energy of electrostatic field of a newly created particle. The usual formula involves integration 'all over space'. According to GR I believe that 'all over ...
4
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1answer
252 views

Couch shocks everything!

How do I get rid of the static charge I get from my microfiber couches? Every time I get up and touch something it zaps me... I'm mostly worried about my laptop getting fried.
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3answers
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Coulomb force in SI and cgs

Coulomb force in SI is $ F = \frac{Q1*Q2}{4\pi\varepsilon R^{2}} $ while in CGS $ F = \frac{Q1*Q2}{R^{2}} $ why is it? I mean doesn't it any make difference in dimension? since $ \varepsilon $ ...
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10answers
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Why does dust stick to rotating fan propeller?

Why does dust stick to rotating fan propeller? Intuitively, most people (including I) think of the dust will not stick to rotating fan propellers. EDIT 1: Thank you for the great explanations. I am ...