All Questions
Tagged with conservation-laws electromagnetism
153
questions
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2
answers
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Charge conservation in ohmic material - Apparent paradox
Consider an ohmic material with constant conductivity, which obeys the relation:
$$\vec J = \sigma \vec E$$
where $\vec J$ is the current density and $\sigma$ is the conductivity. Applying the first ...
- 1,616
0
votes
0
answers
20
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Energy and momentum conservation for light reflection [duplicate]
There is a radiation pressure which means that when light reflects from a surface, the surface will get some momentum/energy.
If so, what is the balancing change on the light/radiation side if light ...
- 155
5
votes
2
answers
643
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Theorem in mechanics relating energy flow and momentum
In Feynman's Lecture 27 on Vol. II it is written that
There is an important theorem in mechanics which is this: whenever there is a flow of energy in any circumstance at all (field energy or any ...
- 1,831
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votes
1
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58
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Stokes' theorem and vector continuity equations
I have been working with homogeneous continuity equations of the general form:
$$\frac{\partial \rho}{\partial t}+\vec{\nabla}\cdot \vec{J}=0$$
This has me wondering whether we can formulate other ...
- 1,616
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0
answers
28
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Solving continuity equation under specific conditions
I have been thinking about how to get a general solution for the continuity equation:
$$\frac{\partial \rho(\vec{r},t)}{\partial t}+\vec{\nabla}\cdot\vec{J}(\vec{r},t)=F(\vec{r},t)$$
and I figured the ...
- 1,616
0
votes
1
answer
61
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Poynting's theorem and continuity equation
I have recently come to realise that many of the most fundamental theorems can be reduced to a continuity equation. Doing some research on the topic of said equations, I have found out they have ...
- 1,616
1
vote
0
answers
33
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Charge conservation and $U(1)$-invariance [duplicate]
Let’s consider electromagnetic Lagrangian
$$\mathcal L=-{1\over 4}F_{\mu\nu}F^{\mu\nu}\tag{1}$$
Is charge conservation derived as a consequence of $U(1)$-invariance of this Lagrangian?
user394668
2
votes
1
answer
81
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Rotational quantum states for atoms
It is well-established that molecules possess rotational and vibrational quantum states, due to molecular symmetries, in addition to electronic states. In contrast, it is generally accepted that atoms ...
- 342
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votes
3
answers
205
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Deriving continuity equation from 4-current of a charged particle
how can i check that following 4-current for a single charged particle
$$j^{\mu}(x)=qc\int d\tau u^{\mu}(\tau)\delta^{4}(x-r(\tau))$$
satisfies continuity equation $$\partial_\mu j^\mu = 0.$$
user391340
-1
votes
1
answer
37
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Continuity Equation on a Non-Ideal System
I recently watched a video on the diffusion equation for neutrons in a fissile material, and at about 2:30 minutes into the video, the author points out that the right hand side of the continuity ...
- 11
2
votes
0
answers
68
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Early E&M problem revisited
In my first electromagnetism class we were given this problem: Suppose you take two electrons and bring them within a distance $d$ of each other. Then release them. What is their final velocity?
Early ...
- 2,728
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0
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Continuity equation in curved space-time: a point particle
Let us consider the action describing a point particle with charge $e$. The interaction term is equal to
$$
S_{int} = e\int A_{\mu}\dfrac{d{x}_e^{\mu}}{d\tau}d\tau = e\int A_{\mu}\dot{x}_e^{\mu}dt
$$
...
- 391
0
votes
2
answers
259
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What is the intuitive reason why Ampere's law is incorrect?
I don't understand why Ampere's Law for magnetic fields is wrong. So initially, we got taught it as the following:
$$\vec\nabla\times\vec{B}=\mu_0\vec{J}$$
and this turns out to be wrong. I also ...
4
votes
1
answer
952
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Why does a current loop obey Newton's third but a charged particle doesn't?
My super basic question is, the (magnetic) force between two steady current loops obeys Newton's third but the (magnetic) force between two charges doesn't. This is surprising given that the former is ...
- 1,095
1
vote
3
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105
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Electric field of an electron after it comes into existence
This is a followup of an older post I made here, whose main premise was not answered. Suppose than an electron is created in a scattering experiment, where other particles are created/destroyed in ...
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