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 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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1answer
50 views

Could you make a Faraday cage with a different force law?

Gauss' law depends on the mathematical form of the Coulomb force. However, the phenomena that static charge resides on the surface of a conductor, and that you can't have electric fields within a ...
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164 views

Physical representation of magnetic vector potential

In electrostatics, for scalar potential $V$, we can represent the equipotential surface as a perpendicular surface of the direction of derivative. such as $$ {\bf E}~=~-\nabla V \tag{1} $$ & the ...
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1answer
40 views

Potential in the middle of a square [closed]

Find the electric potential in the middle of a square with side length $a$ and charge $Q$. If I put the origin in the middle of the square, for the potential I get: ...
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63 views

Effect of humidity on static electricity

I am looking for a reference to a scientific paper or textbook that explains the effect of humidity on static electricity (triboelectric effect). Any help will be highly appreciated.
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2answers
53 views

Charge inside a sphere

Suppose I have a sphere of radius $r$ with all the charge residing on the surface, distributed uniformly i.e. charge density $\sigma$ is constant. I want to find the electric field created by this ...
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2answers
93 views

Divergence of conservative electric field

I have a little doubt about the following: according Gauss law in the form of Maxwell's equation, we know that: $$ {\rm div} (D)~=~ \rho(v) $$ This just tells us that the electric field has nonzero ...
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1answer
110 views

Total number of electric field lines coming out of a proton?

I have to calculate the total number of electric field lines through a proton. I tried using Gauss' Law, i.e, $$\phi = \oint\boldsymbol E.d\boldsymbol s = {\frac{q}{\epsilon_0}} $$ $$So, \phi = ...
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2answers
147 views

Why does charge distribute evenly between two halves of a conducting sphere?

Always while studying I was told that if two identical spheres, one charged and the other uncharged, are brought together the charge in each one of them is halved. However, why does it happen? Is it ...
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2answers
59 views

Basic of Capacitor

I've 2 capacitors; plate area, difference between plates and dielectric is same. Only thing is that the metal used in plates is different. Since the formula $\displaystyle C=\frac{\varepsilon A}{d}$ ...
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3answers
183 views

Limitation of Gauss's Law

We can use Gauss's law to find out the electric field $\vec{E}(\vec{r})$ due to an infinite cylinder of charge. But if the cylinder is of finite length then it is said that $|\vec{E}(\vec{r})|$ is ...
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1answer
25 views

Why defects moderate (reduce) electric field?

I am running a simulation with drift-diffusion equation, Poisson equation and Fourier heat equation with a metal/insulator/metal structure. In my simulation, initially electric field is at the top of ...
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2answers
86 views

Gauss's Law for a Uniformly Charged Solid Sphere [duplicate]

We want to calculate $\vec{E}$ at a distance $r$ from the center $O$ of a spherical polar coordinate system. Let the point on the Gaussian surface at which we want to calculate $\vec{E}$ is ...
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1answer
70 views

What would be physics of a star totally consisting of electrons? [duplicate]

What is the minimum radius and mass (if any) for such a structure to be stable? What is the ultimate future of such structure? Will the electron repellation always be stronger than any gravitational ...
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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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380 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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1answer
51 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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99 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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1answer
64 views

Charging a metallic sphere positive by induction

Bring a negatively charged rod close to a metallic sphere placed on a insulated stand. As the rod is brought close to the sphere, the free electrons in the sphere move away due to repulsion and ...
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2answers
130 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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1answer
49 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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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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2answers
35 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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37 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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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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1answer
49 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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36 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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30 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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2answers
95 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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2answers
160 views

Grounded conductor inside a uniform electric field [duplicate]

I am working on a textbook problem of a grounded conductor inside a uniform electric field. The textbook states that "grounded" means potential = 0. In my opinion, "grounded" should mean "same ...
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0answers
18 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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1answer
75 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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1answer
57 views

How is the charge concentrated at the centre of shell for calculating potential from it? [duplicate]

While calculating electric potential due to a spherical shell at a point outside the shell, why do we say that the entire charge is present at the centre of shell? Is this true even if the charge on ...
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1answer
68 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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3answers
133 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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0answers
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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2answers
97 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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2answers
65 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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1answer
36 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
50 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
92 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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2answers
176 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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1answer
130 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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0answers
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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1answer
97 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
68 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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2answers
308 views

Grounded conducting sphere inside uniform electric field

The problem of a grounded conducting sphere inside a uniform $E$ field in the $z$ direction can be solved by imagining the field be produced by a pair of charges $Q$ and $-Q$ put on the $z$ axis, ...
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1answer
146 views

How do I place point charges when using the method of images with a sphere?

We have a point charge $q>0$ in vacuum at a distance $a$ from the center $M$ of an isolated metal sphere that has a total charge $-q$ and radius $R$. ($a>R$) A) Use the method of images ...
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1answer
106 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
133 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 ...