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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186 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 $$ ...
5
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127 views

Fluctuation interaction between two uncharged spheres

I'm trying to figure out quantitatively what is the force, acting between two uncharged conducting spheres and I've got stuck. It is not a kind of homework - it is just a simple act of curiosity. I'd ...
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231 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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0answers
65 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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197 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 ...
3
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63 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 ...
2
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45 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 ...
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18 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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69 views

Physical interpretation related to a non-linear partial differential equation

I am doctoral student in pure mathematics working on a particular problem. My question is if this problem has applications to real world phenomena. I will try to explain the direct problem starting ...
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26 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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58 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 ...
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100 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 ...
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86 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 ...
2
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257 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 ...
2
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0answers
125 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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174 views

Where can I find a database for dielectric constants in the visible range?

I am looking for a database of dielectric constants in the visible range and I could not find them by Googling, so I was wondering whether anybody here knows where I can find those parameters for some ...
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87 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 ...
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148 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 ...
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71 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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428 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} ...
2
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774 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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32 views

Human between capacitor plates

I was wondering what would happen if we were to put a person between two ideal capacitor plates such that electric field between plates is for example $10^{10} \frac{V}{m}$ and the plates are at a ...
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40 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 ...
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29 views

Divergence in interaction between induced dipoles

Suppose I have two polarizable point-particles 1 and 2 arranged on the z-axis and separated by $r$. Each particle has a dipole moment $\mathbf{p}_i=\alpha \mathbf{E}_i$. If we apply an external field ...
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52 views

How does a battery work?

How does the positive terminal of the battery attract electrons? Does the electric field emitted by the positive terminal attract the electrons?
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10 views

Would the charges on a superconductor near an another charged conductor move and produce magnetic field?

When there is a charged conducting object near an another charged conducting object the charges on these objects accumulate to the sides where the closest points between these objects are. However, ...
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44 views

Charge distribution over a finite plate

Let's say we have a tube(simply a cylinder with no top or bottom) with charge $q_1$, radius $r_1$ and length $l_1$ made out of insulating material. There is also a finite conducting plate with sides' ...
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43 views

Contradictory boundary conditions in electrostatics problem?

Consider the following problem: A conducting cube of side $a$ is grounded. Inside there's a horizontal (i.e., perependicular to the $z$ axis) sheet with uniform surface charge density $\sigma$. The ...
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110 views

How to calculate the electrostatic force between two dielectric rings of charge?

Let's say there is a dielectric ring of charge with radius $a$ and charge $q_1$. I could calculate the electrostatic force applied on a point charge with charge $q_2$ and which is collinear with the ...
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15 views

How to calculate the electrostatic force applied on an object that is along the axis of a charged tube's surface?

Let's say there is a charged tube(a cylinder with no top and bottom) with radius r and length l, charge q1 which also made out of insulating material. And also if there is an object with charge q2 ...
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36 views

How to calculate the electrostatic force applied on an object that is along the axis of a charged tube?

Let's say there is a charged tube(a cylinder with no top and bottom) with radius r and length l, charge q1 which also made out of insulating material. And also if there is an object with charge q2 ...
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26 views

name for 2D Electrostatics as Integrable System

I am trying to understand 2D electrostatics of $n$ point charges. Roughly, $$ H = \sum_{i=1}^N n_i \ln |z- z_i|$$ However, I keep bumping across the Gaudin model instead with this Hamiltonian $$ ...
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69 views

Sign error in calculating the electric field of point charge

I have to determine the electric field of a point charge, I get a true result except for a sign. Here is my passages. $$\nabla \cdot e = \frac{\rho}{\epsilon}$$ $$e = - \nabla u$$ $$\nabla^2 u = - ...
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38 views

Polarizable molecule in E-field

If we have a linear molecule with a dipole moment $\mu$ in a static electric field $E$, the potential is given by $V = - \langle \mu,E \rangle$. What is the appropriate equation for the potential if ...
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26 views

Surface potential resulting from the charge transfer between insulator and conductor

Common non-contact electrostatic voltmeters are used to measure the surface potential. Imagine we place a charged insulator on top of the conducting plate (insulated from the surrounding) and measure ...
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35 views

What causes charge buildup in a cloud before a lightning storm?

I am curious what causes the charge build up in a cloud before lightning occurs. I have seen in a few places such as this, that the process is not fully understood. Is this some form of static ...
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43 views

Potential generated by a hollow sphere with a hole

The sphere has radius $R$ and is missing its "pole" - meaning that in the area $\theta\leq\alpha$ there is nothing. The object has a homogenous charge density $\sigma=\frac{Q}{\pi R^2}$ I'm trying to ...
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41 views

Electromagnetic energy with P and M

In many books, for a linear dielectric medium in which we have Maxwell's equations and the relationships $${\mathbf D}=\varepsilon({\mathbf x}){\mathbf E}$$ and $${\mathbf B}=\mu({\mathbf ...
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156 views

Infinite chain of alternating charge

The problem There is an infinite chain (1d) of alternating charges that are in a distance a from each other. That is there is one charge +q and next to it -q and so on. Now calculate how much work it ...
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45 views

Electric field due to charge in one direction

I am supposed to calculate the electric field due to the charge density $\rho(x) = Ax e^{-\lambda |x|},$ where the density is supposed to be homogenous in $y,z$ direction. The problem is, that the ...
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147 views

How to solve the Laplace equation in ellipsoidal coordinates?

It seems that popular textbooks on electrodynamics do not discuss how to solve the Laplace equation in ellipsoidal coordinates. I could not find any reference, but there must be references about this. ...
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27 views

An EM problem of polarized sphere

Today, I'm doing an EM problem and my question is exactly the same as this site shows: http://www.physicsforums.com/showthread.php?t=133501 To reiterate my confusion, why we can't use that integral ...
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57 views

What is conductivity?

I read that if we have spin $\frac{1}{2}$-particle, where a magetic force acts on, then the force is given by a drift speed times a conductivity. This conductivity is determined to be $\frac{kT}{D}$, ...
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76 views

Debye Hückel Theory valid for ions?

I am wondering about the following: Is Debye Hückel Theory only used if you look at how an external "strong" field(like a potential by a sphere that has a charge that is 1000times higher than the ...
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400 views

Electric potential on a uniformly charged tube

A hollow cylinder, with no top or bottom, of radius $R$ and length $L$ is uniformly charged with density $\sigma>0$. I have to find the point on space where a point charge $q>0$ has to be drawn ...
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0answers
69 views

Electrostatic potential of a proton

I have been working on a quantum mechanical problem regarding the ground state of the Hydrogen atom. It appears that the best way to solve the underlying problem is to modify the electrostatic ...
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50 views

Does all electrical insulator can be electrostatically charged?

Does all electrical insulator can be electrostatically charged, or insulator with only dielectric property can? Thank you.
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148 views

Force and Energy of interaction of conducting sphere and point charge

A completely isolated neutral conducting sphere of radius $R$ is kept such that its center is at a distance of $r\left(>R\right)$ from a point charge $+Q$. How can I find the force of ...
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49 views

Do these steps demonstrate that acceleration of charged particle is proportional to current?

One formulation of Maxwell's Gauss Law for electric field is: $$\bigtriangledown E = 4 \pi k \rho $$ This can be worked into the Divergence Theorem as follows: $$\int\int_{A} F_\perp \:dA= 4\pi k ...
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97 views

Understanding unit vectors

Trying to understand how the unit vector ${\mathcal{\hat{r}}}$ defined as $\frac{r' - r}{|r' - r|} $ (where $r'$ is the source point) works in this problem: Work out the electric field, $E$, at point ...