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 ...

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Can someone give an intuitive way of understanding why Gauss's law holds?

Gauss' Law of electrostatics is an amazing law. It is extremely useful (as far as problems framed for it are concerned :D. I do not have a real world-problem solving experience of using Gauss' Law). ...
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Why doesn't $\vec{E} =\frac{1}{4\pi\epsilon_0} \int\frac{\rho \hat{r}\;dxdydz}{r^2}$ blow up at $r=0$, when $\rho$ is finite?

Electric field at $(x,y,z)$ produced by a continuous distribution of charges is given by:$$\mathbf{E}(x,y,z) =\dfrac{1}{4\pi\epsilon_0} \int\dfrac{\rho(x',y',z') \mathbf{\hat{r}} ...
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Why is electric flux defined as $\Phi = E \cdot S$?

Flux, as I understand it, is the amount of substance passing through a particular surface over some time. So, from a simple perspective, considering photons that go through some virtual surface $A$ ...
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Charge inside conductor

I know that the $E$ field inside a conductor is zero. What happens if I put a source of charge inside the conductor? Say the conductor was spherical centered on the origin and there exists a charge ...
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Electric field of a negative charge

How was it discovered that the electric field of a negative charge points towards the charge itself? Is it true? (Courtesy of wikipedia)
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Dirichlet and Neumann Boundary condition: physical example

Can anybody tell me some practical/physical example where we use Dirichlet and Neumann Boundary condition. Is it possible to use both conditions together at the same region? If we have a cylindrical ...
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Is an electron/proton gun possible?

In the 1944 SF story “Off the Beam” by George O. Smith, an electron gun is constructed along the length of a spaceship. In order to avoid being constrained by a net charge imbalance, it is built to ...
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Electric field outside a capacitor

I know that the electric field outside of a capacitor is 0 and I know it is easy to calculate using Gauss's law. We create cylindrical envelope that holds the same amount of charges (of opposite ...
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Gauss's law in a uniform charge distribution extending infinitely in all directions

Let us assume the universe filled with positive charge. About a particular point, all the positive charged particles will be symmetrical. Now consider a sphere of radius $r < \infty$ and apply ...
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Surface charge density for an off-centre charge in a spherical shell?

How would I evaluate the surface charge density on the inner and outer surface of a neutral, spherical, conducting shell which has an off-centre charge $q$ inside? I believe that we can not use the ...
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What is the first non-vanishing multipole moment of this configuration?

Imagine that you have a triangle where each side has the length $a$ and a charge $q$ sitting at every vertex. Additionally, we have a charge $-3q$ sitting in the center of the triangle. What is the ...
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Potential of arbitrary charge distribution

Imagine this: You have a sphere of air where you have no charge and around this sphere you have a charge distribution $\rho(r,\theta,\phi)$. (For instance, this could be ...
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Metal sphere and charged ring

I think this is an interesting question, to which I don't really know the answer to. (Also, not a homework question.) Say you have an uncharged metal sphere constrained to move in the z-axis. There ...
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Is the electric field at the edge of a uniformly charged disk infinite?

Consider a disk with a radius $R$ (I'll use $R=1$ at various points here) that has a constant surface charge density $\sigma$. Unlike the similar problem of the field in the vicinity of a infinitely ...
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How beam focusing looks like in electron microscope?

I mean I know there are electrostatic/electromagnetic lenses which does focus the beam, but I am not sure how it is possible to foсus beam down to a few 10nm while emitter might be 1mm thick while ...
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Can the electric or gravitational potential be discontinuous? Why?

I was solving the Laplace's equation for the charger thin spherical shell and noticed that the field is discontinuous at the surface (inside it is zero and outside it is proportional to $1/r^2$) but ...
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Flux of electric field through a closed surface with no charge inside? [duplicate]

I'm reading the Feynman lectures on electromagnetism and in Vol II, Chapter 1.4 Vol. II, Chapter 1-4 he talks about the flux of the electric field and says that flux of $E$ through and closed surface ...
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Is there such thing as an evenly-charged sphere?

Let's begin with a very typical model seen in almost every electromagnetics textbook: a solid, evenly-charged sphere. First it cannot be a conducting sphere because charge will automatically ...
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Why is electric potential positive?

If there is a positive charge $q$ at the origin of a coordinate system, the electric potential $\phi$ at a distance $r$ from $q$ is (by definition, if we take the point of zero potential at infinity): ...
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Charged particle between two parallel likely charged plates, is it affected by the plates?

Imagine two parallel conductive plates. Charge up both to have the same amount of positive charge. Then put positive test particle between the two. The Coulomb's law is an inverse square law, so one ...
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872 views

Electric field in a wire?

The electric field in a wire is parallel to the wire's surface (it is always pointing "to the front"). If the electric field did not point in this direction, surface charges would build up and ...
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Relation between Gauss' law and Coulomb's law

In Coulomb's law if the relation was as if electric field intensity was to vary inversely $1/r$ with distance rather than the inverse $1/r^2$ of square of distance, would the Gauss's law still be ...
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Flux through side of a cube

I am looking at Griffiths introduction to Electrodynamics 3rd ED. Problem 2.10 asks for the flux of $E$ through the right face of the cube, when a charge $q$ is in the back left corner of the cube. ...
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Two electron beams exert different forces on each other depending on frame of reference?

I am sure there is a simple explanation for my confusion, but I am a little puzzled: We are dealing with two parallel electron cannons that each produces a straight beam of electrons. They are placed ...
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Will the positive ions in an aqueous solution be attracted to a charged body ?

If I had a negatively charged body , say an electret , and i put it in a container of NaCl solution . Will the positive ions of sodium be attracted to it ? and why? If no, why do the positive ions ...
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Will two magnets lose magnetism if they stick to each other for infinitely long time?

Here we have two magnets and they are sticking to each other. What I've learned that could possibly explain it is one magnet holds positive charge and the other one holds negative. But when the ...
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Why does the induced charge have to have the same magnitude as the inducing charge?

Why is it that the total induced charge on a conducting, grounde,d infinite plane must be of the same magnitude as the inducing charge?
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Why would a rotating charged sphere not have time varying electric field?

I have seen Gauss Law being used for a uniformly charged hollow sphere rotating with $\omega$. How is that valid to use Gauss law since it is an electrostatic law and if it is valid, why do we get a ...
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Intuitive explanation of difference in $r$-dependence between dipole and monopole

For an electric monopole, its potential scales with $\frac{1}{r}$, where $r$ is the distance from the point of interest to the charge. However, for a dipole, its potential scales with $\frac{1}{r^2}$. ...
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120 views

Why is charge $q$ symmetrically distributed?

Simple question: Why is charge $q$ outside symmetrically distributed? The material is a conductor.
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Electrostatic energy integral for point charges

The electric energy stored in a system of two point charges $Q_1$ and $Q_2$ is simply $$W = \frac{1}{4\pi\epsilon_0}\frac{Q_1Q_2}{a}$$ where $a$ is the distance between them. However, the total ...
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Why is the radial direction the preferred one in spherical symmetry?

I am learning about electricity and magnetism by watching MIT video lectures. In the lecture about Gauss's law, while trying to calculate the flux through a sphere with charge in it, the lecturer ...
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Electric field and electric potential of a point charge in 2D and 1D

in 3D, electric field of a piont charge is inversely proportional to the square of distance while the potential is inversely proportional to distance. We can derive it from Coulomb's law. however, I ...
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The appearance of volume $V$ in the Fourier series representation of a periodic cubic system

In the textbook Understanding Molecular Simulation by Frenkel and Smit (Second Edition), the authors represent a function $f(\textbf{r})$ (which depends on the coordinates of a periodic system) as a ...
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874 views

Solving Poisson-Boltzmann equation for flat surface without excess salt

I'm trying to understand the solution of Poisson-Boltzmann (PB) equation as I read it in a review. The surface is uniformly charged and flat. I am only considering the $x$ direction. The PB equation ...
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55 views

What does a hexadecapole look like

Two dipoles can form a quadrupole, two quadropoles an octopole. The textbook by Griffith then says ' and so on'. So how would a hexadecapole really look like? My impression was that the construction ...
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Semiconductors and energy bands

The valence and conduction band of a semi-conductor are often drawn as here click. This plot has essentially two features and I would like to understand them. The peak and the valley of the two ...
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Is a capacitor in an open circuit charged?

Say I have a circuit consisting of a battery, a wire, an open switch, and a capacitor. The circuit is open since the switch is open. My book says that the capacitor will only be charged when the ...
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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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Motion of a dipole in an electric field

Assume that we have some non-constant electric field $E(x,t)$ and a point-dipole at a position $q$ with a constant dipole moment $\vec{p}$. How would you describe the time evolution, i.e. the motion ...
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Why 3 dipole terms in a multipole expansion?

As can be seen on this page http://en.wikipedia.org/wiki/Multipole_expansion when we take a multipole expansion without assuming azimuthal symmetry we end up with $2l+1$ coefficients for the $l^{th}$ ...
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Prove a dielectric with infinite dielectric constant behaves as a conductor for static fields

I read the following problem: Prove that a dielectric medium for which $\varepsilon \to \infty$ behaves as a perfect conductor in the presence of static electric fields. So, the easy part is that the ...
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614 views

Electric field lines

If electric field lines cannot terminate in empty space, in the simple example of two equal charges what happens to the line starting from one of the charges toward the other in the middle?
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Revealing Electric field lines through Grass seeds in mineral oil

In one of Walter Lewin's famous lectures, he takes a small container almost completely filled with mineral oil and grass seeds (I'll keep looking for the video to link to it). He connects two ...
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1answer
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Electric Potential of a Charged Sphere

Problem Consider a sphere with radius $R$, and with a charge distribution $\rho(r)=\rho_0r$. Using Poisson's equation, calculate the electric potential inside and outside the sphere. Solution I don't ...
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208 views

Capacitance of two cocentric spheres, contradicting results

Suppose we are given two conducting, cocentric spheres of radius $a_1$ and $a_2$ respectively. The inner sphere with charge $q$, the outer sphere with charge $-q$. I can calculate the capacitance of ...
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Some confusions regarding electrostatic shielding

A spherical conductor A contains two spherical cavities as shown. The total charge on conductor itself is zero. However, there is a point charge q1 at the centre of one cavity and q2 at the centre ...
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Electric Field “at” the surface of a conductor

It has been pointed out to me that the Electric field exactly on the surface of the conductor is conventionally taken to be $E=\frac{\sigma}{2\epsilon_0}$; does this come from taking the midpoint of ...
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Gauss Law Not Working Inside Cavity

When I apply gauss law inside a cavity within uniformly charged solid sphere then I get that $$\oint E.dA =Q _{enclosed}/{\epsilon_{0}}$$ Which should imply that $E=0$ since enclosed charge is 0. ...
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Static electricity: Why did this happen?

The other day I experienced a discharge of static electricity. It was unusually strong, so strong that it almost hurt. I would like to hear your answers to how such a strong static charge could have ...