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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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 ...
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194 views

Density of repulsive particles on a disk?

NB: the external circle (where particle or water is in it) is fixed ! It's a 2D theoretical problem (just for understand something in particular). Here, no gravity, no temperature. I put in a disk a ...
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233 views

Is it true that $\vec{E}\neq 0$ inside a 1- or 2-dimensional conductor?

It is known that when a conductor is placed in an electric field, the charges redistribute themselves such that $E=0$ inside the conductor. I was also told that the same is NOT true for the 2D and 1D ...
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Infinitely charged wire and Differential form of Gauss' Law

I have tried calculating the potential of a charged wire the direct way. If lambda is the charge density of the wire, then I get $$\phi(r) = \frac{\lambda}{4 \pi \epsilon_0 r} \int_{-\infty}^\infty ...
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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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Charge distribution on conductors?

You have seen that the excess charge on an isolated conductor moves entirely to the conductor’s surface. However, unless the conductor is spherical, the charge does not distribute itself uniformly. ...
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2k views

Electric field and electric potential of a point charge in 2D and 1D

in 3D, electric field of a piont charge is inversely proportional to the square of distance while the potential is inversely proportional to distance. We can derive it from Coulomb's law. however, I ...
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928 views

Is the electric field at the edge of a uniformly charged disk infinite?

Consider a disk with a radius $R$ (I'll use $R=1$ at various points here) that has a constant surface charge density $\sigma$. Unlike the similar problem of the field in the vicinity of a infinitely ...
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78 views

How to find the equillibrium points using Jacobian and Hessian?

Given that I have Jacobian and Hessian matrices of three particles interacting with each other in a harmonic trap through Coulomb's law in a 2D plane, how do I find the equilibrium points of them (I ...
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1answer
270 views

Two electron beams exert different forces on each other depending on frame of reference?

I am sure there is a simple explanation for my confusion, but I am a little puzzled: We are dealing with two parallel electron cannons that each produces a straight beam of electrons. They are placed ...
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4answers
977 views

How does positive charge spread out in conductors?

I know that when there are excess positive charges in a conductor, for example, a metal sphere, the positive charges will spread out over its surface. However, I am confused about how this excess ...
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Dirichlet and Neumann Boundary condition: physical example

Can anybody tell me some practical/physical example where we use Dirichlet and Neumann Boundary condition. Is it possible to use both conditions together at the same region? If we have a cylindrical ...
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How does instant charging of one plate affect the potential of the other plate of a floating capacitor?

If I have an uncharged floating capacitor and I instantaneously connect one plate to some potential, then that plate will acquire some charge. In practice, the other floating plate will ...
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184 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 ...
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351 views

electric field inside a conductor?

We have studied so far that electric field inside a conductor if no charge is placed inside is zero. But we know that every conductor has only a limited number of electrons. What happens when ALL the ...
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1answer
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What defines the maximum charge a capacitor can store?

The formula for a capacitor discharging is $Q=Q_0e^{-\frac{t}{RC}}$ Where $Q_0$ is the maximum charge. But what property defines the maximum charge a capacitor can store? If it depends on ...
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1answer
96 views

How do aspherical gravitational monopoles look like?

I was recently pointed by laboussoleestmonpays to a beautiful paper from some time ago, Aspherical gravitational monopoles. Alain Connes, Thibault Damour and Pierre Fayet. Nucl. Phys. B 490 no. ...
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How does rubbing cause the transfer of electrons from one object to the other? [duplicate]

I have just learnt about electrostatics. Why would there be a transfer of electrons? Is it because of the difference of the materials (i.e. triboelectric series)? So in the case of two different ...
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Why a glass rod when rubbed with silk cloth aquire positive charge and not negative charge?

I have read many times in the topic of induction that a glass rod when rubbed against a silk cloth acquires a positive charge. Why does it acquire positive charge only, why not negative charge? It ...
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How can I prevent being zapped by static electricity every time I touch a doorknob or handle in the office?

I don't know what it is about this office, but it seems everything I touch (doorknob, bathroom faucet, edge of kitchen sink in the break room), I get zapped by static electricity. It's getting old. ...
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1answer
74 views

Are the axial electric field lines of a dipole the only ones that extend to infinity?

Consider an electric dipole and its electric field lines. There will be many field lines that do not extend to or originate from infinity, but rather begin at the positive charge and loop back ...
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1answer
197 views

Why does Hauksbee's electrostatic machine produce light?

I'm reading on the history of the discovery of electricity and the electron, and I've went from reading about Rutherford's gold leaf experiment all the way back to Francis Hauksbee's spinning glass ...
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1answer
687 views

What are the limits of applicability of Coulomb's Law?

Coulomb's law is formally parallel to Newton's Law of Universal Gravitation, which is known to give way to General Relativity for very large masses. Does Coulomb's Law have any similar limits of ...
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133 views

Electric Field One-Form

I know for instance that we can interpret the electric field as the one-form that given a vector gives the change in potential in the direction of the vector, however I'm very unsure about how to ...
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2answers
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When I connect in series two floating capacitors, one charged and the other not charged, does current flow?

Suppose I energize one capacitor by connecting it across a battery, allowing it to achieve some potential difference V0 across its plates, then disconnect it and allow both of its leads to float in ...
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772 views

Trying to understand Laplace's equation

I'm struggling here so please excuse if I'm writing nonsense. I understand that the gravitational potential field, a scalar field, is given by $$\phi=\frac{-Gm}{r}$$ where $\phi$ is the ...
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3answers
79 views

Calculating the Potential from the E-Field

I find that often times I'll be tripped up by questioning whether or not I can do something mathematically, and be unable to come up with a satisfying answer. This is, unfortunately, one of those ...
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1answer
182 views

Coulomb interaction as virtual particles exchange?

I've been reading about virtual particle exchanges in physics books and in Physics SA posts, where a particle interpretation of gravity and Coulomb interaction is established. The Feynman Diagram ...
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2answers
3k views

Electric Field Between Two Parallel Infinite Plates of Positive Charge and a Gaussian Cylinder

Is the electric field between two positively charged parallel infinite plates one with a charge density twice the other effect the electric field on the outside of the plates? I am thinking no, ...
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3answers
469 views

Potential Inside Conducting Cube

A cubical box with sides of length L consists of six metal plates. Five sides of the box { the plates at $x=0, x=L, y=0, y=L, z=0$ - are grounded. The top of the box (at z = L) is made of a separate ...
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1answer
149 views

Electrostatic charge leakage

What are the ways electrostatic charged objects leak charge in humid conditions? Can airborne particles pick up charge by contact, then be repelled hence removing charge? If so would it be a ...
2
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1answer
857 views

Minimizing potential energy of a dipole in an electric field

My test paper asked me which way a dipole should be orientated in an electric field to minimize its potential energy. My answer was that the dipole should lie parallel to the electric field with the ...
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1answer
380 views

What is the energy of interaction between a point charge and an infinite cylinder?

I don't remember enough from my electromagnetism course and I can't find any simple, full example on this subject. I know, that I can consider the cylinder as a wire with the same charge density ...
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1answer
140 views

electrostatic potential, analytic properties

An electrostatic potential associated with some delocalized charge $\int \rho(\mathbf{r}) d{\mathbf{r}}$ is given by: $$v_H(\mathbf{r}) = \int ...
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63 views

How can the potential on a cube's surface replicate the potential of a point particle?

If i have a cube (either hollow, or an insulating solid) and i want its surface have a potential such that it looks like a point particle outside of the box does that mean the exact potential on the ...
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1answer
82 views

Charging the plates before making the capacitor

Basically, a simple capacitor will consist of 2 plates and a dielectric material between them, what if i took 2 plates, charged one with a +ve charge and the other with equal -ve charge, then i put ...
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2answers
62 views

Can a liquid insulator be electrically charged by touching a charged conductor?

Can a liquid insulator be electrically charged by touching a charged conductor? I understand that solid insulator will only be charge on the surface where it is touch, but the case is different ...
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1answer
139 views

Potential of a dipole with actual physical extension?

I think everybody here knows the equation that gives the potential of a point like dipole, but how does the field look like if you have e.g. a metal sphere with radius $R$ and a certain dipol moment, ...
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1answer
140 views

What happens if we give a single electron charge to a hollow metal sphere?

I found this related question: What happens to 5 electrons on a sphere? But this question describes the case when there can only be 5 electrons on that sphere at all times. The answer linked to the ...
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1answer
92 views

Dielectric modification of electrostatic equations?

I have learnt that in cases of electrostatic fields inside a dielectric of any source charge, the field is reduced by a factor of K( if K, the dielectric "constant", is taken everywhere to be same). ...
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1answer
168 views

Battery and current confusion?

How exactly does a battery produce a current in the circuit connected across its ends? I dont want to know the chemical reactions in the battery core, but just the essence of it. I believe it doesn't ...
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1answer
190 views

Potential for charge distribution, finiteness

Consider a potential for charge distribution: $$v_H(\mathbf{r}) ~=~ \int \frac{\rho(\mathbf{r'})}{|\mathbf{r}-\mathbf{r'}|}d\mathbf{r'}$$ where $\rho(\mathbf{r'})$ is the charge density. This ...
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2answers
327 views

In which cases is it better to use Gauss' law?

I could, for example calculate the electric field near a charged rod of infinite length using the classic definition of the electric field, and integrating the: $$ \overrightarrow{dE} = \frac{dq}{4 ...
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4answers
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If something has zero resistance, does it have infinite amperage?

If amps = volts / ohms, and ohms is 0, then what is x volts / 0 ohms?
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1answer
44 views

Distribution of charge over a conductor?

Excess charge in a conductor is supposed to distribute itself evenly over the surface of the conductor. If the conductor has a charge of $2e$ how would the charge distribute itself? There's no way you ...
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0answers
114 views

Field inside a conductor?

If the above image is a cross section of a conductor, the field at the point shown is not zero. So the field inside a conductor is not zero at all points. You could argue that the electrons would ...
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0answers
61 views

Ideal metallic sphere in electric field

Assuming that you have a metallic sphere that is in an electric field $E=(E_r,E_\theta,E_\phi)^T$, $E_r,E_\theta=0$ and $E_\phi$ is some constant. Now I was wondering what the dipole moment in the ...
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159 views

Do black holes have charges?

Do black holes have charges? If so, how would they be measured? Also, does electricity behave the same way? Black holes affect photons, which are carriers of EM radiation, so do black holes have any ...
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Why does the area of the plates affect the capacitance?

Why does the area of the plates affect the capacitance? Lets say I have a parallel plate capacitor with a charge of 10C and a potential difference of 5V. By the definition $C=Q/V$, the capacitance is ...
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1answer
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Electric field due to nonconducting sphere

For calculating electric field outside a nonconducting sphere with a hollow spherical cavity. When I use the rule (Charge density= $dQ/dV$), I don't know exactly what is $dV$, is the volume here ...