All Questions
Tagged with electromagnetism mathematical-physics
71
questions
5
votes
1
answer
596
views
Different possible solutions for the wave equation?
The Wave equation is:
$$\nabla^2\psi(\mathbf{x},t)-\frac{1}{c}\frac{\partial^2 \psi(\mathbf{x},t)}{\partial t^2}=f(\mathbf{x},t)$$
The Green function is then
$$\nabla^2G(\mathbf{x},t)-\frac{1}{c}\...
- 937
2
votes
1
answer
213
views
Physical accuracy of Hankel function solution to cylindrical voltage wave propagation?
The well-known solution to an outward-travelling wave in cylindrical coordinates (in an unbounded medium) is the Hankel function of the first kind:
$$H^{\left(1\right)}_n (\rho,t) = \left(J_n (\rho,t)...
- 123
0
votes
1
answer
629
views
Transformer universal EMF equation derivation
At this Wikipedia page, we've that the 'Transformer universal EMF equation' looks like:
$$\text{E}_{\text{rms}}=\frac{2\pi\times\text{f}\times\text{n}\times\text{a}\times\text{B}_{\text{peak}}}{\sqrt{...
- 291
0
votes
0
answers
279
views
Is mathematical rigour irrelevant in most physics fields? [duplicate]
Are mathematical notions like closed sets, limits of sequences, measures, and function spaces basically irrelevant in the day to day work of a physicist? Naturally, such concepts are the foundations ...
- 659
8
votes
2
answers
583
views
Calculating the potential on a surface from the potential on another surface
The question is short: If a charge (or mass) distribution $\rho$ is enclosed by surface $S_1$, I can calculate the electrostatic (or gravitational) potential on that surface by integrating $\rho(r') \ ...
- 6,273
6
votes
2
answers
2k
views
Proof of Ampère's law from the Biot-Savart law for tridimensional current distributions
Let us assume the validity of the Biot-Savart law for a tridimensional distribution of current:$$\mathbf{B}(\mathbf{x})=\frac{\mu_0}{4\pi}\int_V \mathbf{J}(\mathbf{y})\times\frac{\mathbf{x}-\mathbf{y}}...
1
vote
1
answer
237
views
response function and Fourier transform
A response function defined as the kernel of the following integral:
$\rho(t) = \int_{-\infty}^t \chi(t,t') E(t')dt'$ (1), where $\chi(t,t')$ is the response function.
Physically, it relates ...
- 171
3
votes
0
answers
966
views
Mathematics of Surface Divergence and Surface Curl
While studying electrodynamics I found two functions - Surface Divergence and Surface Curl - that seem to condense the formulas for superficial discontinuities of the electric and magnetic fields ...
- 88
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
2
votes
1
answer
166
views
Are there Non-conformal maps encountered in Physics?
We always encounter Conformal maps in Physics, may be they are easier to study, but are there Non-Conformal transformations encountered in Physics anywhere?
if they are encountered, where are they ...
- 595
3
votes
1
answer
497
views
Is EM interpreted in a principal or vector bundle?
I've read in a few places that EM is a $U(1)$-principal bundle; but is this correct? Isn't it rather an associated vector bundle using the adjoint representation of $U(1)$?
- 13.1k
0
votes
0
answers
203
views
Regarding Ampere's Circuital Law
If I am to show that Ampere's Circuital law holds true for any arbitrary closed loop in a plane normal to the straight wire, with its validity already established for the closed loop being a circle of ...
3
votes
1
answer
537
views
Divergence Theorem, mathematical approach to Gauss's Law?
Let $D$ be a compact region in $\mathbb{R}^3$ with a smooth boundary $S$. Assume $0 \in \text{Int}(D)$. If an electric charge of magnitude $q$ is placed at $0$, the resulting force field is $q\vec{r}/...
user81012
5
votes
2
answers
417
views
Path dependent phase in quantum mechanics
In elementary treatments of quantum mechanics, we are taught that the wavefunction of a single particle is complex valued ($\Psi : \mathbb{R}^3 \to \mathbb{C}$). In particular, the wavefunction has a ...
- 281
0
votes
2
answers
407
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Do there exist functions $\phi$ and $A$ such that $\vec E$ satisfies the Helmholtz Theorem $\vec E = -\nabla \phi + \nabla \times \vec A$?
Helmholtz Decomposition theorem stats:
"Let $\vec F$ be a vector field on a bounded domain $V$ in $\mathbb R^3$, which is twice continuously differentiable, and let $S$ be the surface that encloses ...
- 1,734