Questions tagged [electromagnetism]
For questions on Classical Electromagnetism from a mathematical standpoint. This tag should not be the sole tag on a question.
435 questions
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Magnetic Field of Cylinder with Uniform Current Density
Though this is a problem from physics, I think it is more about mathematics.
Suppose an infinite cylinder $V$ of radius $a$ with its center aligned in $z$ axis carrying a current density
$$
\...
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Are induced electric fields relatively localised to changing magnetic fields?
Let $\mathbf{d} \colon \mathbb{R}^3 \to \mathbb{R}^3$ be a divergence-free $C^\infty$ function such that $\mathbf{d}=\mathbf{0}$ outside a bounded subset of $\mathbb{R}^3$. Define $\mathbf{E}\colon \...
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References for continuous Thomson problem in disk
Consider problem of minimizing total Coulomb energy of configuration of $N$ particles inside unit disk:
$$\sum\limits_{i\not =j}\frac{1}{|x_i-x_j|}\longrightarrow \min\limits_{|x_i|\le 1}$$
I think we ...
- 536
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Electrostatic potential formula
The electrostatic potential $\phi\left(\boldsymbol{r}\right)$ is given as
$$
\phi\left(\boldsymbol{r}\right) = \frac{1}{4\pi\varepsilon_0}\int\limits_{V'}\frac{\varrho\left(\boldsymbol{r'}\right)}{\...
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Solving the double integral $\int_0^{2\pi}\int_0^a \frac{z_0 \rho}{(\rho^2 + \rho_0^2+z_0^2 -2\rho \rho_0 \cos \phi)^{3/2}} d\rho d\phi$
I came across this integral while solving for the axial component of the field due to a uniformly charged ($\sigma_S$ is charge density) thin disk at an off-axis point P. If $k_E = \frac{1}{4\pi \...
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Surface charge distribution on a conductor - does it exist mathematically?
Physics told us that when a conductor reaches the electrostatic state
all charges reside on its surface, and
the electric potential is constant within the conductor
Viewing this statement from a ...
- 12k
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How to write the dipole energy radiated by two charges in elliptical motion in terms of Bessel functions?
For two charges $(q_i,m_i)$, $i=1,2\ $ in bound motion, the energy radiated by their dipole in the center of mass frame:
$\vec{p}=\mu\vec{r}\left(\displaystyle\frac{q_1}{m_1}-\frac{q_2}{m_2}\right)\ ,\...
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Curie-Weiss partition function seems to be written wrongly in a book
I'm working on Statistical Physics Methods in Optimization and Machine Learning by Krzakala and Zdeborova, which can be accessed here: https://sphinxteam.github.io/EPFLDoctoralLecture2021/Notes.pdf.
...
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Only vanishing solution at $r \rightarrow \infty$ of the wave equation
I'm reading a proof that the fields $\vec{E} \ \& \ \vec{H}$ in continuous medium are independent of time when the sources of the fields are themselves stationary (independent of t). The exact ...
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Computing the work to bring two charged particles together using translated spherical coordinates
Consider a charge $ q_1 $ sitting at the point $ p_1 $. Take another charge $ q_2 $. I'm trying to compute the work needed to bring $ q_2 $ from "infinity" down to the position $ p_2 $, but ...
- 1,017
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Inverse of the divergence operator
Given the volume charge density is $10^{-8}\cos(50\pi \rho) ~ \rm C/m^3$ in the region $0.01 ~ \mathrm m<\rho<0.03 ~ \mathrm m$, determine the electric flux density in the region.
It’s a simple ...
- 9,329
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Arranging 8 positive and 8 negative charges to produce $1/r^5$ potential in 3D
Short version of the problem:
Given 8 +Q charges and 8 -Q charges in 3D, can I find an arrangement in which their potential has its leading non-zero term proportional to $1/r^5$?
Step by step ...
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Electric Flux Through a Cube via Surface Integration [duplicate]
I am trying to compute the electric flux through the surface of a cube due to a point charge $ Q $ at its center, using direct integration rather than Gauss’s law.
Problem.
A cube of side length $ 2s $...
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Griffiths Helmholtz Theorem Corollary Explanation
In Griffiths' Intro to Electrodynamics textbook, in the appendix C, the Helmholtz Theorem states that:
If the divergence D(r) and the curl C(r) of a vector function F are specified, and if they both ...
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How to interpret difference between vector summing and normal summing over magnitude.
I am reading a book where the resultant electric field is given by $E_\text{TOT}$ and is the vector sum of two components, i.e. $E_\text{LOS}$ and $E_g$, and the resulting envelope is given by:
$$|E_\...
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