All Questions
Tagged with electromagnetism mathematical-physics
71
questions
16
votes
2
answers
2k
views
Why isn't the path integral defined for non-homotopic paths?
Context
In the Aharonov Bohm effect, there is a solenoid which creates a magnetic field. Since the electron cannot be inside the solenoid, the configuration space is not simply connected.
Question
I'...
- 12.4k
28
votes
1
answer
1k
views
Electric charges on compact four-manifolds
Textbook wisdom in electromagnetism tells you that there is no total electric charge on a compact manifold. For example, consider space-time of the form $\mathbb{R} \times M_3$ where the first factor ...
- 401
1
vote
3
answers
128
views
What is the relationship between $V(t)$ and $V(x,y,z)$
I was recently asked this by a friend.
He told me that coming from a physics background, he does not understand $V(t)$ and he believes it is purely theoretical construct made up by circuit theorists....
- 1,734
0
votes
1
answer
108
views
Charge and current density fields
The charge and current density fields in classical electromagnetism are scalar real number fields on space time manifold. But these fields diverge/become infinite in case of point charges, how is this ...
- 1,578
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
14
votes
1
answer
6k
views
How do you go from quantum electrodynamics to Maxwell's equations?
I've read and heard that quantum electrodynamics is more fundamental than maxwells equations. How do you go from quantum electrodynamics to Maxwell's equations?
- 344
0
votes
1
answer
547
views
Magnetic field of a Herzian dipole antenna
If I am given the dipole moment of very short dipole antenna as $P = P_0 sin (\omega t)$, what will be the magnetic field and polarization of far field radiation?
Do I need to consider the time ...
15
votes
1
answer
3k
views
Why is the Hodge dual so essential?
It seems unnatural to me that it is so often worthwhile to replace physical objects with their Hodge duals. For instance, if the magnetic field is properly thought of as a 2-form and the electric ...
- 1,452
0
votes
1
answer
85
views
Finding charge (electromagnetism course) [duplicate]
I'm a maths undergrad taking a course on electromagnetism, I've drawn a diagram to represent this following question, but I'm having a bit of trouble approaching it:
"Two tiny balls of mass m = 0:1 g ...
- 615
0
votes
1
answer
131
views
How magnets create electricity in conductors?
what are the reasons for current appearing in a wire when wire is in a changing magnetic field?
- 195
1
vote
0
answers
148
views
Boundary conditions for 2D helical waveguide
I'm interested in looking at standing wave solutions for the wave equation on a 2D annulus, with the twist that the annulus is "streched" in to a helix in 3D, but so that the rings themselves are 2-...
- 300
9
votes
2
answers
1k
views
Vector Potential for Magnetic field when the field is not in simply-connected region
According to Poincare's Lemma, if $U\subset \mathbb{R}^n$ is a star-shaped set and if $\omega$ is a $k$-form defined in $U$ that is closed, then $\omega$ is exact, meaning that there's some $(k-1)$-...
- 36.4k
2
votes
0
answers
305
views
Doubts about the Aharonov-Bohm effect
In F. Schwabl, Quantum Mechanics p.148 it is explained that if we have a particle in an electromagnetic field given by potentials $\varphi$ and $\mathbf{A}$ with wave function $\psi$, then a gauge ...
10
votes
2
answers
8k
views
Greens function in EM with boundary conditions confusion
So I thought I was understanding Green's functions, but now I am unsure. I'll start by explaining (briefly) what I think I know then ask the question.
Background
Greens are a way of solving ...
- 585
15
votes
3
answers
7k
views
Electromagnetism for mathematicians
I am trying to find a book on electromagnetism for mathematicians (so it has to be rigorous).
Preferably a book that extensively uses Stokes' theorem for Maxwell's equations
(unlike other books that ...