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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Solving by using Gauss law [closed]

Task: find the vector $ \mathbf E $ in the center of the sphere with radius $R$, which has charge volume distribution $\rho$ , $$\rho = \mathbf a \cdot \mathbf r ,\qquad \mathbf a = ...
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1answer
80 views

Which symmetry for which distance function

For evaluating the electric field of some charge distribution one can use $$\phi(r):= \frac{1}{4 \pi \varepsilon_0}\int_{\mathbb{R}^3} \frac{\rho(r')}{||r-r'||_2} dr'.$$ My question is: What symmetry ...
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49 views

Inconsistent integral and distance in spherical coordinates

I am currently studying this problem: 14 b) There you see an integral $$A(r) = \int f(\theta) (-\sin(\phi), \cos(\phi),0) d \Omega$$ where $f$ is the function containing all the rest of the integrand ...
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133 views

Electric Potential due to conducting sphere and conducting shell

The problem statement, all variables and given/known data A solid conducting sphere having a charge Q is surrounded by an uncharged concentric conducting hollow spherical shell. Let the potential ...
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87 views

Has this approach to Coulomb force/Newton gravity unification ever been published?

Introduction: When toying with gravitational and electromagnetic equations in my undergrad days I stumbled upon this interesting relationship. With the very childish hopes of unifying gravitation ...
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423 views

Conductors and their charge?

Why does excess positive charge stay on the surface of a conductor? This is what I understood from: How does positive charge spread out in conductors? and other resources on the web: If there is a ...
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1answer
125 views

Neutral shell(with a charge inside) in an electric field

A positive point charge $Q$ is kept eccentrically inside a neutral conducting shell. An external uniform field E is applied. Then: a) Force on Q due to E is zero b) Net force on Q is zero ...
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134 views

The Ultimate Hand Dryer

I have come across many hand dryers that attempt to dry your hands really fast after you wash them. Here are two of them: XLERATOR http://www.exceldryer.com/ Dyson Airblade ...
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99 views

Does a AAA battery have a dipole moment?

Does a AAA or D battery have an electric dipole moment? Why don't the opposite poles of two batteries attract each other like that of magnet's?
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50 views

Potential Around Suspended Particles

In my textbook, the classic example of a dielectric sphere suspended in a dielectric solution is solved, and a general form for the potential inside and outside of the potential is given without ...
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42 views

Finding the direction of the electric field of several charges? [closed]

A clock has negative charges -q, -2q, -3q,...., -12q fixed at a the position of the corresponding numerals on the dial. The clock hands do not disturb the electric net electric field due to pont ...
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46 views

Finding V in a electric field? [closed]

How will we find $V_{ab}$ when $\vec E = (2i+3j+4k)$ N/C , $\vec R_a = (i-2j+k)$ m and $\vec R_b = (2i+j-2k)$ m ? I know $\vec E= -\frac{d V}{d\vec r}$, but I don't know what should be my initial ...
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34 views

Which charge value to use and Why [closed]

$1\mu C=10^{-6}C$ vs $e=1.60\times10^{-19}C$. I am having trouble understanding when to use for $q$, $10^{-6}C$ or $1.60\times10^{-19}C$. I had a problem where $a=Eq/m$. I don't know which value of a ...
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36 views

What would happen if…? (Scenarios involving a ball in an electric field) [closed]

First I shall define two table tennis balls: Ball $A$ is coated with a conducting material and ball $B$ is an insulator. Then I'll define two scenarios: Scenario $I$ is a ball held from a ...
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666 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
62 views

Finding out the Potential difference

Find the potential inside and outside a uniformly charged solid sphere whose radius is $R$ and whose total charge is $q$. Use infinity as your reference point. Compute the gradient of $V$ in each ...
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36 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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26 views

Charge Image Problem: Work done on charges on the plate

Assume there is an infinite grounded conducting plane in the $xy$-plane. Assume also that a point charge is being brought slowly from $z=\infty$ to $z=z_0$, slowly enough that the problem is treated ...
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21 views

Why is the Poisson - Boltzmann equation not suitable for high potential?

The Poisson - Boltzmann equation is to find the potential whose charge density obey the Boltzmann distribution. If the potential is not large compare to $k_BT$, the PBE can lead to the Debye–Hückel ...
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76 views

Meaning of “Grounded”

In my opinion, "grounded" means having the same potential as the potential at infinity, which is usually set to zero. Now if we consider a conductor inside a uniform electric field, what is the ...
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1answer
89 views

Electric Field at surface/side of cylinder [closed]

I know I can use Gauss's law to find the Electric Field inside and outside the cylinder very easily. We can select Gaussian surfaces for different cases (i.e. $r \lt R$ and $r \gt R$, where $R$ is the ...
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3answers
95 views

Capacitance: How to increase total charge drawn from a battery?

I can't seem to find any information about how parallel capacitors or capacitors in a series affect how much a capacitor can charge, not in my textbook or online. Here is the question I am trying to ...
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14 views

Questions regarding rubbing catfur on glass

I have certain questions regarding the electrostatic charge developed by this rubbing effects: 1-what is the threshold for electrostatic charges by this process? 2-can we define potential energy ...
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95 views

Where are exactly the charges of charged capacitor?

If a capacitor is connected to a battery and is charged, are there charges inside the wires or do they just accumulate on the surfaces of capacitor?
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88 views

Electric field of a dipole

I'm trying to find the electric field due to an electric dipole $\mathbf{d}$. There are plenty of approaches to doing this online, but I want to do it "my way," which doesn't seem to be working (and I ...
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527 views

What do we mean exactly by the positive/negative charges in cathode and anode?

In batteries, what exactly do we mean by negative and positive charges? My understanding is that the negative charge of the anode is basically an atom with an extra electron in the last orbital and a ...
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1answer
61 views

Integration over $S^2$ in electrostatics

I'm studying for a test in electrostatics and I'm always failing on putting up the correct integrals. In one problem I have the surface of a sphere with radius $a$ and an opening angle of $2\theta$. ...
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210 views

Method of images tutorial?

I'm having an exam in Electrodynamics soon. I think I have most of it under control, but the method of images I'm not quite sure about. There is not much in my book about, so I was thinking some of ...
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39 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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2answers
62 views

What will happen when “earthing” is not an option?

I know that earth has a very high capacitance (of about 711$\mu$F) and it would take a lot of time for this but since we earth almost all our appliances for safety, wouldnt one day come when earth ...
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4answers
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Delta Dirac Charge Density question

I have to write an expression for the charge density $\rho(\vec{r})$ of a point charge $q$ at $\vec{r}^{\prime}$, ensuring that the volume integral equals $q$. The only place any charge exists is at ...
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33 views

Is there a way to induce a net negative electric charge in an electrically conductive material, and If not why?

From what I've been reading, moving electrons don't compress relative to the protons within the atom, For reasons that I'm having difficulty understanding. Seeing that this is the case I would like to ...
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1answer
49 views

Electric field of half a wire

I am trying to calculate the electric field of a half wire in polar coordinates. At $y=R$ is a wire going from $-\infty$ to $0$ with charge density $\rho$. I want to calculate the electric field at ...
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3answers
103 views

Why is the void devoid of an electric field?

For a region devoid of charge, maxwell's equation yields $\nabla \cdot \mathbf{E} = 0$ which still allows a constant field. So why is in electrostatics for the vacuum always $\mathbf{E} = 0$ assumed? ...
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71 views

Why the electric field inside a conductor is zero? [duplicate]

In electromagnetism books, such as Griffiths or the like, when they talk about the properties of conductors in case of electrostatics they say that the electric field inside a conductor is zero.
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115 views

Electric potential of spherical water droplet [closed]

I'm trying to answer the following: 1000 spherical water droplets, each of radius $r$ and each carrying a charge $q$, coalesce to form a single bigger spherical drop. If $v$ is the electric ...
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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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How do we make symmetry assumptions rigorous?

I have, for instance, a problem with a spherically symmetric charge distribution. I deduce here, in order to solve the problem easily, that the corresponding electric field must be symmetric. How is ...
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964 views

Can two electrons never touch each other?

The Coulomb's force is given by $$ F = {k q^2 \over r^2} $$ When $ r \rightarrow 0 $, $ F \rightarrow \infty $ Does this mean two electrons never touch each other?
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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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91 views

Jackson equation 2.9; How to derive it?

I wanted to understand the derivation of Jackson's equation (2.9) that you can find here on page 31 (50/661) from the potential given earlier. This equation is written as: $$ ...
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1answer
58 views

Gaussian surface and and Gauss law

Can we consider a cube as a Gaussian surface, for a point charge located at its center.since,Gaussian surface is a closed surface which has a constant electric field but in this case the both the ...
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1answer
141 views

A dielectric sphere in an initially uniform electric field and representation theory of SO(3)

I learned recently that the highest order spherical harmonic required to represent the spatial distribution of decay products of a particle can be used to determine its spin, by using arguments ...
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40 views

What are eigenfunctions in a box which includes two kinds of medium?

I have to solve a problem of mathematical physics. There is a simple case which can inspire me to solving a more complex case. Considering a metal box in 2D $0<x<a$ and $0<y<b$. And ...
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1answer
70 views

The force on an infinite line of charge perpendicular to a on a rod of charge

Essentially the question is to calculate the force exerted by a charged rod perpendicular to an infinite line of charge: $\vec{F}_{\text{rod}\rightarrow \text{line}} =\dots$ My question is it okay to ...
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1answer
103 views

Simulate / plot electrostatic field

I have something like this: For given voltage (9 V red wire, 0 V blue wire) I want to simulate electrostatic field. I already know, for example that in the point (10.5;0) there are 10 V and etc. I ...
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What are electromagnetic fields made of?

I am trying to understand electromagnetic fields so I have two question related to them. What is a electromagnetic field made of? Is it made of photons / virtual photons? How about a static electric ...
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159 views

Boundary conditions of this problem

We have A point charge, a homogeneously charged insulator with total charge $Q''$ which is a ball with radius $R$, a conducting metal ball with charge $Q'$, radius $R$ and a grounded metal (no ...
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80 views

Find the points where potential is null

Let's say we have two charges called $q_1$ and $q_2$, respectively $20 \, C$ and $-40\,C$, at a distance $d=1\,m$ We want to find all the points where electric potential is null. I solved the ...
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A little question about Gauss' Law

So I've just learned Gauss' Law a few days ago. I also worked out some applications of Gauss' Law. But I have a little confusion. In a couple of books that I referred, I found a statement that I don't ...