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Results tagged with electrostatics
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user 36793
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 the [electromagnetism] and/or [magnetic-fields] tags.
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Multipole expansion in electrostatics
A generic charge distribution need not be a monopole or a dipole. Multipole expansion of potential illustrates that the potential due to an arbitrary continuous charge distribution, is in general, a s …
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Proving Earnshaw's theorem is subtle in three-dimensions!
The Laplace's equation for the electrostatic potential $\phi(\textbf{r})$ is given by $$\nabla^2\phi(\textbf{r})=0.\tag{1}$$
Equation (1) is said to encode the fact:
A free movable charge cannot …
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Do we need a bounded domain for the Laplace equation to have a non-zero solution $u$?
I'm not sure that I understand what you mean by "bounded domain". This is an answer based on what I understand from the question.
To solve Laplace's equation uniquely, you have to specify either the …
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Can the electric field be made to penetrate the bulk of a metal?
When an external electric field $\textbf{E}_\textrm{ext}$ is externally applied to a metal, the free electrons move opposite to the direction of the field inside the metal and create an internal field …
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Electric potential energy of charges localized to the surface of an object
For instance, one could consider an object of fixed volume that could be deformed to assume shapes with different surface areas, with charge redistributing to maintain uniform charge density regard …
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Can I write a 2-dimensional electric field as an analytic function on the complex plane?
I am not sure about the question. But I'll give it a try. Since an electrostatic field is irrorational i.e.$\boldsymbol{\nabla}\times\textbf{E}(\textbf{x})=0$, it amounts to $$\frac{\partial E_x}{\par …
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Quantization of electrostatic $\vec E$ field?
Can a electrostatic field $\vec E=\vec E(x,y,z)$ (time-independent) or electrostatic potential $\phi=\phi(x,y,z)$ be quantized? If yes, will these quanta be photons again? But we don't have an electro …
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Facing a paradox: Earnshaw's theorem in one dimension
Consider a one-dimensional situation on a straight line (say, $x$-axis). Let a charge of magnitude $q$ be located at $x=x_0$, the potential satisfies the Poisson's equation $$\frac{d^2V}{dx^2}=-\frac{ …
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Does this example contradict Earnshaw's theorem in one dimension?
Consider electrostatics in $1$-dimension (say, the $x$-axis). Now consider a positive charge $+q$ located at $x=0$, and two equal negative charges $-q$ are held fixed at $x=+a$ and $x=-a$. …
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Is Gauss' law valid for time-dependent electric fields?
The Maxwell's equation $\boldsymbol{\nabla}\cdot \textbf{E}(\textbf{r})=\frac{\rho(\textbf{r})}{\epsilon_0}$ is derived from the Gauss law in electrostatics (which is in turn derived from Coulomb's law …
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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 t …
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