All Questions
9
questions
1
vote
0
answers
65
views
Non-homogeneous wave equation, retarded potentials and causality
Consider the non-homogeneous wave equation in three dimensions with homogeneous initial conditions:
$$
\begin{align}
& \square f(\underline{x}, t) = g(\underline{x},t), \hspace{3mm} \underline{x} \...
- 1,179
0
votes
0
answers
24
views
Beam propagation in an optical fiber with a $\tanh(\cdot)$ refractive index profile
The differential equation for a optical fiber with a refractive index $n(r)$ is given as
$$\nabla^{2}_{\perp}A(r,\theta)+(k^{2}n(r)^2-\beta^2)A(r,\theta)=0.$$
which is separable in cylindrical ...
0
votes
0
answers
221
views
Deriving the wave equation
Given:
$$\nabla \times \mathbf H = \frac{4\pi}{c} \mathbf j \ \ \ \ \ \ \ \ \ (1)$$
$$\nabla \times \mathbf E = -\frac{1}{c} \frac{\partial \mathbf H}{\partial t} \ \ \ (2)$$
$$\...
- 1,139
0
votes
0
answers
459
views
Deriving the wave equation out of $\nabla \times \vec H = \frac{4\pi}{c} \vec J$
I am trying to derive the wave equation presented by Alfven in his 1942 paper
Based on the electrodynamic equations:
$$\nabla \times H = \frac{4\pi}{c}J$$
$$\nabla \times E = -\frac{1}{c} ...
- 1,139
0
votes
0
answers
72
views
Image Theory in Electrodynamics
I'm searching for a rigorous mathematical proof of the image theorem for electric/magnetic currents distributions. A proof that, I think, shows that removing the reflecting surface and placing ...
- 79
-1
votes
1
answer
282
views
5
votes
1
answer
569
views
Deriving analytic expression for magnetic field & flow lines of bar magnet.
How can we analytically derive the flow-lines of a normal permanent bar-magnet?
Physics context & own approach:
In classical electromagnetics we have the legendary Maxwell's Equations:
$$\begin{...
- 26.1k
3
votes
2
answers
94
views
Can we motivate mathematically why wind turbines almost always have 3 flappers and aeroplane propellers can have any number of flappers?
Firstly I know some might frown upon a question so very broad and applied as this one. It really may not be a well defined mathematical question as some people would prefer on the site. I am okay with ...
- 26.1k
4
votes
1
answer
412
views
solution to $\square\chi=f$.
For an open set $U \subseteq \mathbb{R}^4$, if $f:U \to \mathbb{R}$ is a "good" (for example, smooth) function, is there a solution to the following equation?
$$\left( \Delta - \frac{1}{c^2}\frac{\...
user53216