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Results tagged with electromagnetism
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user 36793
The classical theory of electric and magnetic fields, both in the static and dynamic case. It also covers general questions about magnets, electric attraction/repulsion, etc. Distinct from electrical-engineering.
24
votes
2
answers
3k
views
What is the conclusion from Aharonov-Bohm Effect?
What is the conclusion that we can draw from the Aharonov-Bohm effect? Does it simply suggest that the vector potential has measurable effects? Does it mean that it is a real observable in quantum mec …
- 27.2k
15
votes
2
answers
4k
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Does classical electrodynamics have $U(1)$ symmetry? If yes, how?
Quantum electrodynamics (QED) is based on $U(1)$ symmetry. What happens to this symmetry in classical electrodynamics?
Addendum The books on classical electrodynamics such as J. D. Jackson, does not …
- 27.2k
14
votes
6
answers
5k
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How do we prove that the 4-current $j^\mu$ transforms like $x^\mu$ under Lorentz transformat...
Given that the position vector $\textbf{r}$ to be a vector under rotation, we mean that it transforms under rotation as $\textbf{r}^\prime=\mathbb{R}\textbf{r}$. Now, taking two time-derivatives of it …
- 27.2k
13
votes
6
answers
1k
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Charged particle as observed from an inertial and a non-inertial frame of reference
A charged particle fixed to a frame $S^\prime$ is accelerating w.r.t an inertial frame $S$. For an observer A in the $S$ frame, the charged particle is accelerating (being attached to frame $S^\prime$ …
- 27.2k
12
votes
3
answers
8k
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Hamiltonian and Energy of a charged particle in an Electromagnetic field
The Lagrangian of a charged particle of charge $e$ moving in an electromagnetic field is given by $$L=\frac{1}{2}m\dot{\textbf{r}}^2-e\phi-e\textbf{A}\cdot \textbf{v}$$ where $\phi(\textbf{r},t)$ is t …
- 27.2k
9
votes
4
answers
2k
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Why is the speed of light in a medium smaller than its value in vacuum?
The speed of electromagnetic waves in a medium is smaller than its value in the vacuum: $$v=\frac{1}{\sqrt{\mu\epsilon}}=c/n<c$$ with the refractive index $n=\sqrt{\frac{\mu\epsilon}{\mu_0\epsilon_0}} …
- 27.2k
9
votes
4
answers
2k
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Can we use the term "U(1) gauge invariance" for the free electromagnetic field?
Disclaimer: This question is probably based on a misconception or flaw in the understanding.
Can we use the term $U(1)$ gauge invariance for the free electromagnetic field? Let me explain why I ask t …
- 27.2k
9
votes
3
answers
12k
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Retarded and advanced Green's function and Feynman propagator
Is there a use of advanced Green's functions? If yes then when or in which context?
In quantum field theory, why do we always use Feynman's prescription for finding the propagator and not the retard …
- 27.2k
8
votes
3
answers
938
views
How do Maxwell's equations uniquely determine ${\bf E}$ and ${\bf B}$ despite no. of equatio...
Maxwell's equations in free space are given by $${\bf\nabla}\cdot\textbf{E}=0,~~{\bf\nabla}\cdot\textbf{B}=0$$
and
$${\bf\nabla}\times\textbf{E}=-\frac{\partial\textbf{B}}{\partial t},~~{\bf\nabla}\ti …
- 27.2k
8
votes
2
answers
2k
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Divergent self-energy of point charges in Classical Electrodynamics
Assuming the electron to be a classical point particle, if one calculates the self-energy one finds $$U=\frac{e^2}{8\pi\epsilon_0r}$$ which diverges as $r\rightarrow 0$. Therefore, the measured mass o …
- 27.2k
7
votes
2
answers
1k
views
What does the non-zero divergence of $\textbf{H}$-field say about magnetic monopoles?
It is always true that $\boldsymbol{\nabla}\cdot \textbf{B}=0$ (implying that there are no magnetic monopoles). However, $\boldsymbol{\nabla}\cdot \textbf{H}\neq 0$ when $\boldsymbol{\nabla}\cdot \tex …
- 27.2k
6
votes
5
answers
4k
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Is Gauss' law valid for time-dependent electric fields?
The Maxwell's equation $\boldsymbol{\nabla}\cdot \textbf{E}(\textbf{r})=\frac{\rho(\textbf{r})}{\epsilon_0}$ is derived from the Gauss law in electrostatics (which is in turn derived from Coulomb's la …
- 27.2k
4
votes
1
answer
124
views
Reaching equilibrium in a blackbody and light-matter interaction
Suppose we have a metallic cavity maintained at a fixed temperature. Suppose we start with any distribution of radiation that is not in equilibrium with the container. Gradually, when the equilibrium …
- 27.2k
4
votes
3
answers
5k
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Radiation gauge and choice of the gauge function
In electrodynamics, the scar potential $\phi$ and the vector potential $\textbf{A}$ satisfy the equations $$\frac{\partial}{\partial t}(\boldsymbol{\nabla}\cdot\textbf{A})+\nabla^2\phi=-\frac{\rho}{\e …
- 27.2k
3
votes
2
answers
292
views
How does friction and its velocity dependence arise from microsocpic interactions?
Friction arises as an effective macroscopic force, unlike the four fundamental interactions in nature which are there at the microscopic level. How can we understand, the appearance of friction as a d …
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