Questions tagged [electromagnetism]
For questions on Classical Electromagnetism from a mathematical standpoint. This tag should not be the sole tag on a question.
169
questions with no upvoted or accepted answers
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The magnetic field of a spinning charged sphere
Evaluate $\displaystyle \int_{0}^{2\pi}\int_{0}^{\pi}\frac{(z_0-R\cos\theta)\sin^2\theta\cos\phi}{[(x_0-R\cos\phi\sin\theta)^2+(y_0-R\sin\phi\sin\theta)^2+(z_0-R\cos\theta)^2]^{\frac{3}{2}}}d\theta d\...
- 701
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How to solve $\sum_{n=-\infty}^\infty\frac{y^2}{[(x-n\pi)^2+y^2]^{3/2}}$?
I need to solve this sum:
$$\sum_{n=-\infty}^\infty\frac{y^2}{[(x-n\pi)^2+y^2]^{3/2}}.$$
Do you have any ideas for how I could do this?
I know that this sum:
$$\sum_{n=-\infty}^\infty\frac{y}{(x-n\pi)^...
- 1,027
4
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Deriving boundary conditions at a surface of discontinuity: $\int \mathbf{B} \cdot \mathbf{n} \ dS = 0$
I am currently studying Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light, 7th edition, by Max Born and Emil Wolf. Chapter 1.1.3 Boundary conditions at ...
- 4,322
3
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91
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First chern class of magnetic monopole
Example 3.5.5 in the Mirror Symmetry textbook (Hori-Katz-Klemm-et. al) states:
Let us compute the first Chern class of the line bundle defined by the $U(1)$ gauge field surrounding a magnetic monopole,...
- 569
3
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47
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An improper integral from Jackson's book involving the modified Bessel function
When deriving the angular distribution of energy for synchrotron radiation one has to evaluate two tricky improper integrals (see [1] below):
$$
I_1 \equiv \int_{0}^{\infty} x^2 [K_{2/3}(x)]^2 \, \...
3
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54
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Are there theorems in fiber bundle land and differential geometry land that make calculations in electromagnetism easier?
Some time ago while thinking about life and such, I thought to myself does recasting electromagnetism in bundle theory make certain calculations easier? To be precise are there theorems in ...
- 581
3
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81
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Solving cylindrically symmetric non-homogeneous wave equation $\nabla^2\mathbf{A}(s,t)-\frac{\partial^2}{\partial t^2}\mathbf A(s,t)=\mathbf J(s,t)$
I'm trying to solve a non-homogeneous wave equation in cylindrical coordinates
\begin{align}
\nabla^2\mathrm A-\frac{\partial^2\mathrm A}{\partial t^2}=\mathrm J,
\end{align}
where A and J are ...
- 1,685
3
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47
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Gauge condition in Maxwell's equation
Maxwell's equations (differential forms formulation) read
$$
dF = 0 \\
\partial^a F_{ab} = -j_b
$$
where $j_b$ is the current-density 1-form. The first equation tells us there is some 1-form $A$ so ...
- 5,141
3
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104
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Why is electric potential function in free space infinitely differentiable?
Electric potential function in free space of a continuous charge distribution $\rho'$ distributed over volume $V' \subset \mathbb{R}^3$ is denoted by:
$\psi (x,y,z): \mathbb{R}^3 \setminus{V'} \to \...
- 1,141
3
votes
0
answers
339
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Restricting a distribution to a non-open subset
If I have an open subset $U \subset \mathbb{R}^n$ and a distribution $\rho \in \mathscr{D}'(U; \mathbb{R})$, i.e. a continuous linear functional $\rho: \mathsf{C}_{\mathsf{c}}^\infty(U;\mathbb{R}) \...
- 303
3
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130
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Do Maxwell's equations (generalized) apply to _every_ $k$-form on a pseudo-Riemannian manifold?
Given a pseudo-Riemannian $n$-manifold and a $k$-form $F$ on the manifold, I will call its exterior derivative $J=dF$ the source of $F$ and the differential $K=dG$ the dual source of $F$, where $G={\...
- 716
3
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82
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Charge density of charged conductor with flat side
Given a charged conducting body with a flat side, can the charge density (and hence the normal electric field) be constant on the flat part?
According to physics lore, the charge density is greater ...
- 1,410
3
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130
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Radial fourier transform of gaussians
In this paper is calculated the square modulus of the radial fourier transform of the function $\rho(r)$
$$\left|F(q)\right|^2=\left| \int_{\mathbb{R}^3} e^{i\mathbf{q}\cdot\mathbf{r}}\rho(\mathbf{r})...
- 275
2
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29
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Does this family of curves appearing in the magnetic field of a coil have a name?
While attempting to express the magnetic field induced by a single coil of current (at any point in space, not just on the coil's axis), I tried visualising the set of the infinitesimal contributions $...
- 165
2
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67
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Evaluation of Fourier series $\sum_{n=1,3,5...} \left[\frac{1}{n}\text{e}^{-\frac{n \pi x}{a}} \text{sin}(\frac{n \pi y}{a}) \right]$
I was studying electromagnetism and followed 'Introduction to Electromagnetism' by David Griffiths. During his derivation of the solution to Laplace's equation in ch. 3.3, he derives the equation $$V(...
- 289