All Questions
Tagged with electromagnetism mathematical-physics
71
questions
3
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1
answer
3k
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Proof of equality of the integral and differential form of Maxwell's equation
Just curious, can anyone show how the integral and differential form of Maxwell's equation is equivalent? (While it is conceptually obvious, I am thinking rigorous mathematical proof may be useful in ...
- 203
4
votes
4
answers
3k
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How to interpret the continuity conditions in the PDEs (for example, Maxwell equations) originated in physics?
I am currently working on PDEs in physics, mostly Maxwell equations. I am a mathematics graduate student, and this question has been haunting me for years.
In PDE theory, or more specifically the ...
- 203
3
votes
1
answer
79
views
generation of arbitrary potentials
Suppose you have as many electrically charged particles as needed (even countably many) and consider the open unit ball centered at some point in space. For every continuous real valued function on ...
- 33
3
votes
2
answers
330
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Why, intuitively, must a solution in physics be unique?
When solving Laplace's equation or Poisson's equation say, we require that the solution must be unique, which can be shown.
In general, what is the physics behind seeking a unique solution?
Are ...
- 17.1k
2
votes
1
answer
229
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What determine whether the dynamical equations are tensor equations or vector equations?
Newton's 2nd law which is central to Newtonian dynamics, is a vector equation
$\sum\textbf{F}_{external}=m\textbf{a}$
Same with Maxwell's equations in the covariant form.
On the other hand, ...
- 17.1k
6
votes
3
answers
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Can Laplace's equation be solved using Fourier transform instead of Fourier series?
Sorry for the long text, but I am unable to make my question more compact.
Any periodic function can be Fourier expanded. Usually, they say in mathematical physics books, if the function is not ...
- 17.1k
14
votes
1
answer
305
views
Theorems on instability of classical systems of charged particles?
Classically, a hydrogen atom should not be stable, since it should radiate away all its energy. I remember hearing from my favorite freshman physics prof ca. 1983 about a general theorem to the effect ...
user4552
1
vote
2
answers
183
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A question on a system of particles governed by laws of gravity and electromagnetic field
Consider a system of many point particles each having a certain mass and electric charge and certain initial velocity. This system is completely governed by the laws of gravitation and electromagnetic ...
- 2,152
7
votes
0
answers
443
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1-form formulation of quantized electromagnetism
In a perpetual round of reformulations, I've put quantized electromagnetism into a 1-form notation. I'm looking for references that do anything similar, both to avoid reinventing the wheel and perhaps ...
- 9,948
2
votes
2
answers
785
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Phase Accumulation of Hankel-waves upon propagation
Hankel functions are solutions to the scalar Helmholtz-equation $$\Delta\psi + k_e^2\psi = 0$$ in cylindrical and spherical geometry (with respect to a separated angular dependence). Thus, they are ...
- 4,311
1
vote
3
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591
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Electric field at a point being an $n^{th}$ derivative of electric (or magnetic) field at some other point
This is a theoretical question for which i would like to know an answer with an example.
I'd like to know if its possible to create a setup where the electric field at a point $P$ is $n^{th}$ ...
- 2,152