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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potential inside a cylindrical shell in terms of the surface potential?

Given a potential distribution $V(\phi)$ at the surface of an infinite cylindrical shell, is there an easy way to derive the potential inside the cylinder. No charges or currents anywhere.
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Electricity. I'm finding difficulty answering this question [on hold]

Consider 3 identcal spheres, A,B,C. A carries a +5q charge. B carries a -q charge. C carries no net charge. Spheres A and B are touches together and then seperated. Sphere C is then touched to Sphere ...
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39 views

Paradox in electrostatics in relation to Gaussian surfaces?

I have encountered something that is very confusing. My problem is this. I am assuming two infinite cubical Gaussian surfaces sharing a common side. One of the cubes contains a charge $q_1$ at a ...
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How to calculate surface density of conducting plates, given zero potential condition and another conducting plate [on hold]

Suppose there are three conducting plates at $z=6,3,0$(m) surface. The surface at $z=3$ has static surface-charge of $2C/m^2$, and the surfaces at $z=6$ and $z=0$ have zero electrostatic potential. ...
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How can I use volume charge density to find charge density constant knowing charge Q

I have an insulating sphere of radius R that has a total charge Q. It is distributed as $\rho$= $\rho_0*r^4$. I know that the charge is equal to Q and I'm trying to solve for $\rho_0$. I've tried to ...
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What charge will accumulate on an aluminium rod when rubbed with amber? [on hold]

An aluminium rod is held with an insulating handle.Then the rod is rubbed with amber.What will happen to the rod and why?(with reference to triboelectric series)
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Electromagnetism and static electricity

What is the difference between electromagnetism and static electricity? Also electromagnetic waves are mediated by photons , what mediates static electricity?
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Potential due to infinite plate carrying a finite charge

I've solved many problems where something is grounded and you've to figure out the charge distribution. The general strategy is to set the potential of the grounded thing equal to zero and solve. ...
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42 views

What are some open problems in classical electrodynamics? [duplicate]

I am about to finish reading 'Introduction to Electrodynamics' by David Griffiths. Throughout the textbook, Griffiths makes frequent references to current literature (mostly articles from American ...
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16 views

Defining the region in Laplace's equation

1) Consider a sphere S centered at the origin O, where a charge q is present. Is Laplace's equation applicable in the region S? No, right? 2)This is where I go crazy.... Instead of considering the ...
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26 views

How can a potential step be modelled?

a potential step is given by function $V(x) = V_o, x\geq 0$ and $V(x) = 0, x\leq 0$ Using the relation $- \frac{dV}{dx} = \vec E$ I take the negative derivative of this function, i'll get ...
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What's the Relation between Potential of mechanics and electricity?

As we know that for a conservative force field, there is associated a Potential with the force. But we know there is a potential in electricity (That's voltage). My question is that is there any ...
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Accelerating an electron to a high speed

Suppose there are two vertical metal plates. They are separated apart by a small distance. While one is grounded, the other one has a potential of some $V$. Now suppose electrons are produced at the ...
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Electric field on a rod [closed]

We are given a stick of length $L$ with uniformly distributed charge $Q$. One end is at $x = -L$ and the other at origin. A point charge is placed at $x = L$ we have to find a point inside the ...
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Anyone know of a flow chart or list of common/useful consequences of Maxwell's equations?

I just recently started to appreciate the Maxwell equations. I had never really take the time to study them but I feel like I'm finally more familiar with them. I've noticed that it seems like a lot ...
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Work done by electric field at large to small distances [closed]

Question: How much work is done by the electric field bringing a particle with charge +q from $(x, y) = (0,\infty)$ to point P (origin) by sliding it down the +y-axis? There is a dipole on the x-axis ...
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Electric Flux - What is the point?

Electric flux is a defined quantity that is proportional to the no. of field lines passing through a given area element for a given electric field. It is not proportional to the relative density of ...
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how can find the electrostatic force when the two identical charge are placed in different medium [closed]

Charge are placed in different medium and their distance between them is $r$. The identical charges are $q$. Then, what is the formula to find out the force between them?
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Electric field and charge density outside two coaxial cylinders

I am working on a problem of electrostatics, and I am having troubles in trying to figure out one part of it. It consists of an inner solid cylinder of radius $a$ with a voltage $V_A$, and an outer ...
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21 views

Why are trampolines more likely to give you a static shock when it is sunny?

It could just be in my head but I have noticed that I am more likely to get a static shock from my tramp when it is sunny than when it is not sunny. Is there a reason for this?
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Gauss's Law - Field with constant direction [closed]

Doing some exercises in the topic of Gauss's Law, I found this problem which I can't seem to understand: Suppose that an electric field in some region is found to have a constant direction but to ...
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1answer
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Plastic and Iron - static and magnetic

I'm wondering if when you have a ball that is made out of plastic but has an inner core of metal. Would that ball if given friction produce static? Or would the static from the outerside of the ...
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Wait… why exactly does farady's ice pail experiment prove Gauss's law?

You'll notice there are no equations in this: that's because this is a question of morale, not of math. But a humble one at that! I come to learn, not to expound. But don't let that limit the form ...
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37 views

Electric Flux through cube from point charge

"A point charge is located at the origin. Calculate the flux of E through a cube centered on the origin and aligned with the Cartesian axes. Evaluate the surface integral directly and verify that the ...
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Why does excess of charge in an isolated conductor move to the surface?

A remark in my textbook goes as follows: "If an excess charge is placed on an isolated conductor, that amount of charge will move entirely to the surface of the conductor. None of the excess charge ...
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Is work needed to bring a test charge from a higher potential to a lower potential?

I don't understand whether work is needed to bring a test charge from a higher potential to a lower potential. It seems that no work is needed because the positive test charge will be under the ...
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Finding potential of conducting sphere coated by a dielectric shell

An uncharged conducting sphere of radius $a$ is coated with a thick insulating shell (dielectric constant $\epsilon_r$ out to radius $b$. This object is now placed in an otherwise uniform electric ...
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Calculating flux of axisymmetric electric field through a sphere [closed]

The following problem and its solution is taken from I. E. Irodov's book basic laws of electromagnetism : I do not understand how the fact that field is axisymmetric leads to the conclusion that ...
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What is the essential concept behind the difference in the fundamental solutions of the Stokes and Poisson equations?

The fundamental solutions, i.e., the solution with a point source, of the Poisson's equation and the Stokes equations in 3D are: $$\nabla^2 f=\delta(\boldsymbol x) \ \Longrightarrow\ G(\boldsymbol ...
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Calculation of triple integrals like $ \int_{V'} \frac{ \mathbf{r} - \mathbf{r'}}{\mid \mathbf{r} - \mathbf{r'} \mid ^3} dV' $, on spherical domain [migrated]

How could one solve integrals in the form: $$ I(\mathbf{r})= \int_{V'} \frac{ \mathbf{r} - \mathbf{r'}}{\mid \mathbf{r} - \mathbf{r'} \mid ^3} dV' $$ where the domain of integration is the ...
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Can a charge moving in an open trajectory qualify as current?

It is sometimes said that a point charge is equivalent to an electric current. If it were a steady current, I should be able to find it from Ampere’s law or Biot-Savart’s law. Even if the current is ...
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Rigorous proof of Gauss' law for an arbitrary charge distribution from Coulomb's law

Most of the books about electromagnetism prove Gauss' law for a point charge in vacuum: $$ \Phi = \int_{\Sigma} \mathbf{E} \centerdot d \mathbf{S} = q/\epsilon_0 $$ and then simply state that for ...
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Relativity Paradox involving two charged particles

Suppose there are two charged particles separated by some distance $d$ both with an equal positive charge of $q$. The particles also have equal masses of $m$. $m$ and $q$ are chosen so the ...
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Energy density in electrostatics

Imagine two hollow spheres with radius $R$ with charges $q$ and $-q$. $L>2R$ is distance between them. Potential energy of the each sphere is \begin{equation*} W_1=\frac 1{8\pi \epsilon_0}\frac ...
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Divergence of a vector field, going through the math [closed]

The example I'm working on has this given identity: $\bigtriangledown \cdot \mathbf{\bar{r}}=3$. The question is: find the divergence of a vector field $\bar{\mathbf{E}}=\frac{\mathbf{r}}{r^{3}}$. ...
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Why does charge build up at the boundary surface of two media?

On a homework problem, we are asked to to use the first two Maxwell equations, $$\nabla\cdot \mathbf{B} = 0$$ $$\nabla \cdot \mathbf{D} = \rho$$ to show that along the boundary surface of two ...
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Energy density what volume?

In a derivation of energy density for an electric field (see here) We get rid of the $$\epsilon_0\oint(V \vec E \cdot d\vec a)$$ term by choosing a surface sufficiently far away so that this term ...
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Motion of charge particle under electric and gravitational fields

I am working on one experiment in which the charged particle falls under the effect of gravity and passes through the electric field in between. I want to know what is the charge of the particle? ...
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Is it inevitable to compute the quadruople tensor in components? Why? [closed]

I was trying to determine the quadrupole tensor for a given charge distribution in one go from this equation: $$\overleftrightarrow{D}=\int d^3r \varrho(\vec{r})\left(3\vec{r} \circ ...
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Are centrifugal fans subject to triboelectric effects, and if so can the increase in charge be predicted and measured?

A centrifugal blower is a device that moves gas, usually under power of an electric motor. The blower housing and impeller may be metallic, but often are made of plastic materials. My question is ...
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1answer
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Electrostatic induction in spheres

if we have a charged sphere with charge Q and radius r, the voltage on it's surface is calculated by gauss's law, what if we approach to it another sphere with radius R , R>r, earth it, remove earth, ...
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How to determine electric field strength without Gauss's Law

For objects which do not subscribe to Gauss's Law, I don't understand how one would determine the electric field strength. I know that the equation $E=k\int \frac{\mathrm{d}q}{r^2}$ can be used to ...
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1answer
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What is the charge density in the proof of Earnshaw's theorem?

I am trying to understand the proof for Earnshaw's theorem. Though the theorem states that a collection of point charges cannot be maintained in a stable stationary equilibrium configuration ...
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Electrostatics Basic Question

Why ,if we increase the charge on a conductor its potential also increases? That is, Q directly proportional to V. Why ,if an insulated conductor is given some charge it acquires a certain ...
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28 views

Potential at infinity due to a point positive charge

I know it is quite basic for this site, but I am confused...is it just a convention to take it as zero, or there is some logic? I really dont think that V = kq/r r->infinity, v -> 0 is right, because ...
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Current flow through car struck by lightning

It is safe to sit under a car rather than to stand under a tree during lightning. The electric field inside the car is zero when the lightning falls on it so, after falling on car, where do the ...
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Using Electric Potential to Float an Object

I've been trying to answer the following question but I'm stuck at one step. The question essentially states that a magician is trying to perform a "floating objects" act, for which she has a thin ...
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Gauss's Theorem in electricity and its gravitational counter part [duplicate]

We all know the Coulomb's law is the electrostatic counter part of the Newton's law of gravity.So by considering a gravitational potential,is there a gravitational counter part for Gauss's theorem in ...
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Why does a conductor shield its inside from its outside, but not vice versa?

A point charge outside a hollow conducting sphere will produce no field in the hollow interior: the metal shields the interior. But a point charge inside the hollow interior will produce a field ...