Electrostatics is concerned with the electrical fields and scalar potentials of stationary electrical charges and charge distributions. Use this for questions about electromagnetic situations in which currents and magnetic fields are absent, otherwise use [tag:electromagnetism] and/or [tag:magnetic-...

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224 views

Electric potential of a spheroidal gaussian

I'm looking for results that compute the electrostatic potential due to a spheroidal gaussian distribution. Specifically, I'm looking for solutions of equations of the form $$ \nabla^2\Phi=N\exp\left({...
5
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186 views

Fluctuation interaction between two uncharged spheres

TL;DR: The problem is to determine force, acting between two uncharged conducting spheres, induced by correlated fluctuations of charge densities in these spheres. I've got stucked along the way and ...
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95 views

Charge over 2 layer dielectric, image method

If I have a charge $Q$ located over a 2 layer dielectric as represented: According to the image method : the charge $Q'1$ will be located at a distance $h_1$ under the first interface and the $Q'2$ ...
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54 views

Lightning sprites

Lightning usually occurs due to an electrostatic discharge between an electrically-charged cloud and the Earth's surface, or between clouds. There are also sprites, electrical discharges that occur ...
4
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340 views

Can spheres leaking charge be assumed to be in equilibrium?

I am struggling with the following problem (Irodov 3.3): Two small equally charged spheres, each of mass $m$, are suspended from the same point by silk threads of length $l$. The distance between ...
4
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268 views

Electron hopping among molecules - Marcus equation

I'm running out of professors to talk to, and I need to clarify a couple of things for the sake of making a realistic model of electron travel through a mesh. This is about calculations of electron ...
3
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43 views

Is it true that it is a misconception that the Van de Graaf generator works with the Faraday's ice pail principle

I found some interesting papers which claim that it is a misconception that the charge accumulation on the top is due to the Faraday's ice pail principle but rather just as in Volta's condensing ...
3
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46 views

Why is the susceptibility $\chi(t)$ real?

So my question is quite simple I suppose, and perhaps trivial. It is known that the frequency domain susceptbility $\chi(\omega)$ is complex, and that the two parts can be related with the Kramers-...
3
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31 views

Scale-covariant decomposition of capacitance

I'm wondering if there is any good insight of how to evaluate a given capacitive geometry in such a way that it would be expressed as a function that depends only on two components: as a geometric ...
3
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75 views

What would be the charge distribution in a Klein bottle?

We know that for any conductor the charge lies on the outer surface at electrostatic equilibrium. What would happen if a Klein bottle is made up of a conductor and a charge is placed on it?
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88 views

What are the parameters for Pauli's repulsion pseudo-force?

I have found the following formula for the repulsion potential due to the overlap of the electron clouds arising from Pauli's exclusion principle: $$V = A\exp(-r/\phi)$$ where r is the distance ...
3
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287 views

How to set up Schrodinger's equation for an electron (as a charge distribution) under its own electrostatic field

After reading about the hydrogen atom and understanding how Schrodinger's equation explains most part of the atomic spectrum of an hydrogen atom, and also came to know that, it explains most of the ...
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68 views

Modeling the formation of a stellar system and matter accretion

I am trying to figure out what do I need to know to properly simulate the creation of a solar system from a particle cloud with random distribution of hydrogen atoms. Being more of a programming ...
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46 views

What is the charge density for line and surface charges?

In electrostatics it is common to see line, surface and volumetric charges being described differently. A line distribution is a function defined on the line, a surface charge distribution is a ...
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42 views

Method of image charges — Why is a *grounded* plate needed?

In the classic image charge problem of a charge $q$ above an infinite grounded plane, it is well known that the field lines essentially behave as though there were a negative charge behind it, and the ...
2
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0answers
54 views

Gauss' Law and Electric Field Close to a Ball

So I've learned about Gauss' law and I have something in my head. Why does electric field that is very close to a ball is not close to infinity. Take a look at this image: As we can see, if we make ...
2
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101 views

Current Density Boundary Conditions and its Implications

According to Ohm's Law, one can say $ \overline{J} =\sigma \overline{E} $ if the field is in a conductor, and $ \overline{J} =0 $ if it's in empty space. Now if we take the surface of a conductor and ...
2
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95 views

Why does Hauksbee orb or a similar device produce light?

This essentially fits well to the question asked earlier but had to placed as a separate question... An interesting and detailed answer was provided. However, there are few points, originating from my ...
2
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0answers
71 views

What is the essential concept behind the difference in the fundamental solutions of the Stokes and Poisson equations?

The fundamental solutions, i.e., the solution with a point source, of the Poisson's equation and the Stokes equations in 3D are: $$\nabla^2 f=\delta(\boldsymbol x) \ \Longrightarrow\ G(\boldsymbol x,\...
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32 views

Approximating electrostatic grids as a multipole expansion

Is there a known good summary, or a succinct algorithm to compute the far-field approximations of an arbitrary set of electrostatic surfaces set at different potentials? I'm looking to model a ...
2
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74 views

What is “above” and what is “below” the surface of a sphere?

When studying Electromagnetism using D.J. Griffith's Introduction to Electrodynamics, the boundary conditions for the electric potential across a surface charge density are expressed using the normal ...
2
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67 views

Why does electrolysis require a base electrolyte instead of an acid electrolyte?

I am in the process of using electrolysis to remove rust from some old tools. This is the process where you submerge the rusted item in a bath along with a sacrificial piece of metal. You connect a ...
2
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0answers
101 views

Electric field in a “concave” conductor

I am aware that the electrons are distributed across charged conductor surface so that the areas with smaller radius of curvature have more charge per surface area. But what happens when the ...
2
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48 views

Electrochemical cell potential - Prigogine book

I'm trying to understand equation 10.2.14 from Prigogine book "Moder thermodynamics": $V=\frac{\tilde{A}}{nF}=\frac{1}{nF}\left(\mu_X^R+\mu_Y^L-\mu_{Xred}^R-\mu_{Yox}^L\right) - \left( \phi^R-\phi^L \...
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111 views

Gravitational redshift of temperature and electrostatic potential

Consider a charged black hole in four-dimensional Minkowski spacetime, with charge $Q$, mass $M>Q$: $ds^2=-f(r)dt^2+\frac{1}{f(r)}dr^2+r^2d\Omega_2^2$, with $f(r)=1-\frac{2M}{r}+\frac{Q^2}{r^2}$. ...
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795 views

Types of electrostatic force

In some references, electrostatic force is said to have 3 types: Coulombic force, image force, and gradient force. I really would feel grateful if anybody can explain to me the difference between them,...
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149 views

Equivocal boundary conditions for Laplace equation of 2D “V”-shape conductor

A two dimensional infinite "V"-shape wedge conductor is earthed, wherein $\beta$ is the intersection angle. We can solve Laplace equation so as to get the electric potential inside the "V" zone, as is ...
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389 views

Calculating Electric Field from a Potential Difference w/o Charge

So here is my homework question: Two long cylindrical shells of metal (radii $r_1$ and $r_2$, $r_2 > r_1$) are arranged coaxially. The plates are maintained at the potential difference $\Delta\...
2
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246 views

mathematical model of one electrostatic problem

I am trying to find direct-current electric field in a specific domain: it is a brick made from a low-conductive material with a number of more conductive inclusions of different shapes - spheres, ...
2
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0answers
95 views

Consistency of equation with special relativity?

The following is the equation which, I want to know, if it is valid in relativistic domain. Consider two equal charges moving in same direction with velocity $v$ and charge $q$ at a separation of $d$....
2
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0answers
1k views

How the value of permitivity of free space is determined?

when electric charges are placed on the medium then force of interaction between them decreases. We say this factor permitivity of the medium. The force of interaction between the charges is max if ...
2
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0answers
73 views

Semi-conductors and induced charge

Can a semi-conductor ( germanium or silicon) or a semi-metal ( graphite ) carry an induced charge ?
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1k views

Electrostatic Dust Removal

I have been recently reading a paper on dust removal and I have a few basic questions regarding it. First off, I am citing this paper - "Dust removal system with static electricity" Basically, an ...
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556 views

Dielectric in Parallel Plate Capacitor

Given a parallel plate capacitor of width $w$, length $l$, with a dielectric moving along the length $l$. Let the dielectric be from $x$ onwards. The capacitance will be $\frac{w \epsilon_0}{d} (\...
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1k views

How to calculate the electric field and potential inside a dielectric surface placed into a homogenous field

In an experiment we placed a long dielectric cylindrical shell (cylindrical tube)(with inner and outer radii r1 and r2, respectively) in a homogenous field such that its axis was orthogonal to the ...
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24 views

Simple Van de Graaff generator with friction only

I have found an interesting picture about different versions of the Van de Graaff generator: (Source: http://www.coe.ufrj.br/~acmq/vdgself.jpg) I know the Wimshurst system on the right but I have ...
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0answers
52 views

Electric potential due to surface charge distribution on a conducting sphere

Let's consider a conducting sphere. If we charge the sphere, it is understood that there will form a surface charge distribution such that the surface of the sphere is an equipotential surface $ 0=\...
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0answers
35 views

Determine potential function given initial conditions?

Assuming a radially symmetric circular disk (let's say r=1). Given two simple initial conditions: Potential at the centre is 4 V Potential at the edges is 0 V How would I determine the potential ...
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21 views

Reversibility of uniqueness theorem

If we use uniqueness theorem then we know that if the boundary conditions and the charge distribution is same in 2 setups in a certain region then the electric field and potential in that region in ...
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37 views

Does wearing a metal hat does increase your chance of being struck by lightning?

Does wearing a metal hat does increase your chance of being struck by lightning? Prompted by this video. My view is that it makes no difference as to the conductivity of the head or the field ...
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19 views

With the help of a given charge is it possible to obtain a charge many times greater in magnitude

Consider a spherically conducting sphere. If a charge(say positive) is placed near the sphere, then it will lead to separation of charges inside the sphere.My question is, can we create charges more ...
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0answers
28 views

How does air density affect corona discharge?

I'm wondering how local air pressure and density affect the amount of ionizations occurring in a corona discharge. Also, does the threshold voltage required for a corona discharge vary with air ...
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0answers
25 views

Is frictional heat just electromagnetic interactions creating infrared radiation?

Example: Rub your index finger on a sheet of paper and you will feel that it will get noticeably hotter Is the reason you feel this increase in heat (technically an increase in kinetic energy of the ...
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0answers
8 views

Why x-axis E field exist in Electroosmosis Example

The explanation in Wiki said it is because the surface charge will induce electrical double layer at top and bottom surface, so that if we apply x direction E field, there will be a flow between two ...
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35 views

Flux through a face of a cube for an arbitrary position of a charge

Consider an imaginary cube with edge length a in space. A charge q is placed at the centre of one of the faces of the cube. So, what is the electric flux through the face opposite to the charge? ...
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32 views

Surface bound charge density in dielectric displacement

In Griffiths, it derived that the electric potential caused by Polarization $\bf {P}$ is written $$V({\bf r}) = \frac{1}{4\pi \epsilon_0} \int_{\mathcal{V}} \frac{\hat{\gamma} \cdot {\bf P}{({\bf r'})...
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160 views

distribution of electric charges

In electricity courses, in the lesson on static fields, at some point all teachers say "let's consider a large rectangular metal plate where the density of charges is uniform", and then they proceed ...
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111 views

Divergence theorem and discontinuous vector fields in electrostatics

Wikipedia defines Gauss Divergence Theorem for a continuously differentiable vector field; but in many idealized physical situations, we use it for non-differentiable fields. For example, the electric ...
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60 views

Gauss's law giving incorrect answer

Let's consider two concentric spherical shells, one of radius $R$ and one of radius $R - \Delta R$. The outer shell is negatively charged and the inner shell positively, but both the shells have net ...
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0answers
37 views

Induced charges, electric potential

Consider a solid spherical conductor with charge Q on it, a charge q is placed at a distance r from the centre of sphere. Find the electric potential at the centre of sphere due to induced charges on ...