All Questions
10
questions
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votes
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Charge Density Of A Conducting Strip
I am currently doing a project which requires me to figure out the charge density of a strip. Assume that the strip is isolated in a vacuum.
Assume the strip is 1 dimensional, kind of like a rod. What ...
1
vote
1
answer
30
views
Permissible Electrostatic Potential
Let us consider a $1D$ real function $V(x)$. When is this a classical electrostatic potential?
My take on the problem:
$V(x)$ must be differentiable everywhere. In fact, we should be able to ...
- 785
2
votes
1
answer
235
views
How to find convergence of conditionally convergent series obtained while calculating the electrostatic potential energy of a NaCl crystal?
I was reading Electricity and Magnetism by E M Purcell and there in the first chapter there is an attempt to estimate the electrostatic potential energy of the crystal lattice of a NaCl crystal.
...
- 1,147
3
votes
1
answer
455
views
Why are Cauchy boundary conditions an over-specification of boundary conditions for solving Poisson’s equation?
I was referred to Physics.SE by the following content published in Jackson’s Classical Electrodynamics:
This rather surprising result [the fact that the potential within a charge-free volume is ...
- 33
2
votes
3
answers
427
views
Mathematical rigorous definition for an electrical dipole
I've been reading Laurent Schwartz's Mathematics for the physical sciences, and in the chapter on distributions he makes many cool examples of ways to define in a mathematical rigorous way certain ...
7
votes
2
answers
1k
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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 $$\frac{d^2V}{dx^2}=-\frac{\...
- 26.8k
5
votes
3
answers
353
views
Obtaining the charge from the charge density using distribution theory
In electrostatics, for several reasons, it seems that the correct way to understand the charge density $\rho$ isn't as a function $\rho : \mathbb{R}^3\to \mathbb{R}$, but rather as a distribution $\...
- 36.4k
8
votes
2
answers
583
views
Calculating the potential on a surface from the potential on another surface
The question is short: If a charge (or mass) distribution $\rho$ is enclosed by surface $S_1$, I can calculate the electrostatic (or gravitational) potential on that surface by integrating $\rho(r') \ ...
- 6,273
2
votes
1
answer
97
views
Time dependent electric field: Mathematical expansion for local electric field
In many articles and books I see that local electric field is expanded as
$$\vec E_0(\vec r(t)) = \vec E_0(\vec R_0) − (\vec a(t) \cdot \nabla) \vec E_0(\vec R_0) \cos(\Omega t) + \ldots $$
For ...
- 1,593
6
votes
3
answers
2k
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Can Laplace's equation be solved using Fourier transform instead of Fourier series?
Sorry for the long text, but I am unable to make my question more compact.
Any periodic function can be Fourier expanded. Usually, they say in mathematical physics books, if the function is not ...
- 17.1k