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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Electric force between charges in two different media

As far as I know, Coulomb's law of electrostatic force is applicable on two different charges situated in same medium. But if two individual charges are in different media (say one charge on a iron ...
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15 views

How does the dieletric displacement change among two dieletric materials?

Here's a question I am working on. "A sphere of linear dielectric material with permittivity $\epsilon_1$ and radius $a$ is surrounded by an infinite region of linear permittivity $\epsilon_2$. In the ...
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52 views

What is the potential field of an ion near the Bohr radius?

I figure that at large enough distances, the potential field of an ion is just the Coulomb potential for its net charge. But what happens at scales comparable to the ion's Bohr radius? Could there be, ...
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64 views

Earnshaw Theorem for ionic solids

Is a single molecule of sodium chloride (say) or a cluster of molecules of NaCl unstable, although macroscopically NaCl is in fact, stable? How can I reason this based on Earnshaw's theorem?
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68 views

Usage of Poisson's equation?

I revisited electrostatics and I am now wondering what the big fuzz about Poisson's equation $$\nabla^2 \phi = -\frac{\rho}{\varepsilon_0}$$ is. Wiki says One of the cornerstones of electrostatics ...
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60 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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42 views

Charging a spherical capacitance

How could one charge a spherical capacitor with a battery or any other emf source?
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40 views

Relation between electric field and dipole moment

I want to show the following equality $$\int_{\left|\vec{r}\right|<R}d^3r\vec{E}\left(\vec{r}\right)=-\frac{\vec{p}}{3\epsilon_0}$$ where $\vec{p}$ is the dipole moment of a charge distribution ...
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231 views

How can I split a resultant force into its $x$ and $y$ components?

Point charge 3.5μC is located at x = 0, y = 0.30 m, point charge -3.5μC is located at x = 0 y = -0.30 m. What are (a)the magnitude and (b)direction of the total electric force that these charges ...
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264 views

How can one explain the Kelvin Water drop experiment without assuming the container to already possess a positive charge?

Kelvin Water Dropper experiment refers to the electrostatic generator invented by Lord Kelvin, which uses falling water to generate a voltage by electrostatic induction occurring between ...
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83 views

Energy Stored in a Capacitor with and without Dielectric

I have seen the equation $V = \frac {V_0}{K}$, but also the equation $V=\frac{1}{2}CV^2$. The values of C and V increase in the same linear ration with K (because $C=KC_0$). However, as the energy ...
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130 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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38 views

Influence of a Capacitance Matrix of a voltage measurment

I am having a problem in understanding how in a multiconductor system the Capacitance Matrix influences the measure of voltage between two electrodes. In the case that interest me we have 4 ...
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22 views

electrostatic force vs gravitational force [duplicate]

I have question regarding the forces caused by electrostatic charges and gravity. From the explanation here in the link just by existing an object with mass distorts space-time. Will there be a ...
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0answers
16 views

How does the Triboelectric effect work? [duplicate]

The general description for the Triboelectric effect (the main cause of static electricity in everyday life) is that when two certain materials come into contact, electrons are transferred between ...
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1answer
27 views

Finding energy stored in a capacitor

i am given a voltage time graph for a capacitor circuit. How to find energy stored in that capacitor at various time instants? Can we just calculate by using $\frac{1}{2}CV^2$ We are given capacitance ...
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58 views

Electrostatics and two electric charges

How can two identical metallic objects have the same but opposite charges (one loses electrons and one gains electrons) when we know that metals have the ability to lose electrons only?
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3answers
45 views

Explaining the current flow of the positive shunt clipper (diodes)

I am currently studying clippers or parallel limiters in the Navy and I was wondering if someone could clear up a few things for me. Here is a picture that fits my description: A clipper has a ...
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2answers
86 views

Electric potential energy and signs

I know that electric potential is negative near a negative charge and positive near a positive charge. But does this mean a small positive 'test' charge has a negative electric potential energy near a ...
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38 views

Polarization vector of dielectric electrostatics

I know two laws for Polarization vector of a dielectric material $$\vec P = N q \vec{\Delta L}$$ Where N is the number of dipoles per meter cube, $\vec{\Delta L}$ is the vector that represents the ...
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1answer
229 views

What determines how much electrical charge an object can hold?

What determines how much electrical charge an object can hold? Does increase voltage force more electrical charge to be store in an object (Van de Graaff generator), since electric field increase as ...
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280 views

Effect of charges near a parallel plate capacitor

If I charged a parallel plate capacitor. And then, I insert a charged body near one of the plates. Will there be any interactions like attraction or repulsion? What if I disconnected the battery?
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How does electrostatic force affect electronic devices?

How does electrostatic force generated by two seperate plates having opposite charges affect electronic devices? I know that magnetic fields have some harmful effects to electronic devices but I am ...
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28 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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1answer
81 views

Charge distribution on a doughnut shaped conductor

In a spherical solid conductor the charge is always on the outer surface.Even if the sphere has a cavity,the surface of the inner cavity can not carry a charge due to Gauss's Law. What would be the ...
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1answer
364 views

Taylor expansion of an integral in spherical co-ordinates

I've some difficulty deriving this equation from Jackson electrodynamics (The equation after 1.30) $$\nabla^2 \Phi_a\left({\textbf{x}}\right)=-\frac{1}{\epsilon_0}\int_{0}^{R} ...
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Where's the energy in a boosted capacitor?

Suppose I look at a parallel plate capacitor in its rest frame and calculate the electrostatic energy, $E$. Next, I look at the same capacitor in a primed frame boosted in the direction perpendicular ...
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39 views

Forces between charged particle

I am given two charged particle of same charge at distance of $r$ , they initially apply force of magnitude $F$ now infinite dielectric(of constant 4) of width $\frac{r}{2}$ is introduced between ...
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29 views

Tranverse electromagnetic waves

TEM waves do not exist in waveguide. Is this the correct explanation- Both curl and divergence of TEM are zero inside the waveguide and because of the boundary conditions (electric field zero at every ...
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1answer
2k views

The electric field of a conductive sphere containing a charge - grounded vs not grounded

Let's suppose we have a sphere but unlike theoretical ones it'll have some thickness say $\Delta r$ and inner radius $R$. What I was wondering about is how will it behave if we place some charge $q$ ...
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3answers
236 views

Why capacitance is given as constant value in Farads, and not as max charge in Coulombs?

The equation for capacitance is $Q=CV$ or $V={1\over C}Q$. I don't understand what is the physical meaning of this "$C$": Does the charge in a system changes linearly with voltage under all ...
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30 views

What are the consequences of connecting a non-ideal conductor to a battery in open loop?

Suppose I have a battery with $\Delta V=5[\mathrm{V}]$. Now I connect a piece of a metal wire to the "+" side of the battery only. Let's assume that the ambient air is not conductive at all: Are ...
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1answer
92 views

Phase difference between incident plane wave incident on a dipole and radiation fields from dipole

i have an incident plane wave and a dipole, consider that plane wave incident on dipole. at this moment what happens to dipole? We know that after incident of plane wave on dipole, the radiation has ...
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43 views

electrostatics particle charging

When ash particles are charged negatively ( corona charging, ionization, tribo electric ) and then collected on to the fabric; particles arrange themselves in porous dendritic structure whereas ...
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Magnitude of Electric field vector on the axis of a conducting half sphere

I need to calculate the electric field of a conducting half-sphere shell ( just the outer shell, it has no base ) of a radius $a$ and surface charge density $\sigma$ on the arbitrary point on axis ...
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Why can you make two repelling positively charged rods touch? Shouldn't the Coulomb force become infinite?

For a physics lab on the Triboelectric effect, we rubbed two rods with fur which gave both of them a positive charge. We then brought them close together, and they obviously repelled. We then held ...
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Using Coulomb's law to solve for a continuous charge distribution [closed]

I have been trying to evaluate this specific integral and have been completely stuck. $$\frac{1}{4\pi \epsilon_0} \int^L_0 \frac{2\lambda z}{(x^2+z^2)^\frac{3}{2}}dx.$$ I am a freshman and have been ...
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36 views

Why does energy rise in a constant voltage capacitor after inserting a dielectric?

For example from this link: http://te.fisica.edu.uy/fuerza_en_Capacitor.pdf we can deduce, that the work the electric field inside a constant-voltage capacitor does during the insertion of a ...
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43 views

How to find whether the electric field between capacitor plates is above or below the electrical breakdown limit of the insulator between the plates?

Let's say the two plates of a capacitor have charges $q_1$ and $q_2$. The separation between these plates is $d$. I know that I can calculate the electric field by dividing the voltage that is applied ...
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1answer
17 views

Find quantity of electricity of two circular faces

So, there are two circular conductive sheets with quantities of electricity of Q and -Q. If I know that the distance d between them is 0.002 meters and their radius is 0.1m and the voltage between ...
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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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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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113 views

Circuit breaker Trips during thunderstorm

The circuit breaker at the electrical mains trips at home when there is a thunderstorm outside. Why does this occur?
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104 views

Electric flux through nonspherical surphace

Here's an explanation from a book that I read: Now, I have a few problems with this explanation as well as with the "cone method". I guess that all my problems boil down to the concept of ...
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1answer
8 views

discharging static

Quick question, if you have a buildup of static charge causing sheets of paper to stick together, can you have a grounding foil touching the paper to dissipate the charge to prevent pages from ...
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1answer
73 views

Electrostatic Potential Energy Integral

I'm trying to calculate the total energy of a simple two charge system through the integral for electrostatic energy of a system given in Griffiths' book: $$U = \frac{\epsilon_0}{2}\int_V E^2 dV .$$ ...
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Electric field at a point [closed]

We consider a thin disk whose center is $O$ and radius is $R$, which has an electric surface charge density of $\sigma$. We want to find the expression of the electric field $\vec{E}$ at a point ...
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925 views

Why is the shape of lightning or an electric spark a zig-zag line?

Why is the shape of the lightning (or an electric spark) always of a zig-zag nature? Why is it never just a straight line? Image source.
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37 views

Electric field and potential between two charges [closed]

There are two point charges on the $x$ axis and $x'$ is a place where the potential, relative to infinity, is the biggest. Why is the electric field zero at this point?
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35 views

Calculate electric field without using Gauss law

Given a uniformly charged sphere ( total charge $5 nC$ ) of radius $R=10 cm$, write the equation of electric field vector for any distance $r (r > R)$ from sphere center and calculate total ...