All Questions
5
questions
6
votes
5
answers
705
views
How are vector quantities in three dimensions (velocity, electric field, etc.) modeled in mathematical physics?
In introductory courses, vectors are defined as objects with direction and magnitude. I guess everyone has arrows in mind when talking about vectors and that's probably the most intuitive description, ...
- 1,801
11
votes
3
answers
559
views
What are good non-paraxial gaussian-beam-like solutions of the Helmholtz equation?
I am playing around with some optics manipulations and I am looking for beams of light which are roughly gaussian in nature but which go beyond the paraxial regime and which include non-paraxial ...
- 134k
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 ...
0
votes
2
answers
407
views
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
15
votes
4
answers
2k
views
Electromagnetic field and continuous and differentiable vector fields
We have notions of derivative for a continuous and differentiable vector fields. The operations like curl,divergence etc. have well defined precise notions for these fields.
We know electrostatic and ...
- 1,578