Timeline for Electromagnetism problem: where does the magnetic field come from?
Current License: CC BY-SA 3.0
19 events
| when toggle format | what | by | license | comment | |
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| Jan 14, 2018 at 9:16 | vote | accept | Adrian | ||
| Jan 12, 2018 at 20:06 | comment | added | freecharly | @Anton Fetisov - For the formation of the shielding charges on the metal wires, and thus the validity of your reasoning, it suffices to have a finite resistivity $\rho \neq 0$ as long as the dielectric relaxation time of the metal related to the formation of the shielding charges is short compared to the time scale of the experiment. | |
| Jan 12, 2018 at 16:35 | comment | added | Anton Fetisov | @Nicol It looks like there will be no current under non-zero resistance. This won't affect the argument: I only need that the vertical component of electric field is $0$ on the boundary, which is true in all cases since there can be no vertical current and $\mathbf J = \rho \mathbf E$. | |
| Jan 12, 2018 at 16:12 | comment | added | Adrian | @AntonFetisov I have thought about something. If we consider the wire not to be a perfect conductor, but a material with resistance $R$, couldn't we argue, by Ohm's law, that since the EMF around the circuit is $0$, then there is no current? I think this may also affect your argument for the changing $E$. Of course this wasn't stated in the problem itself, it's just something I've been thinking about. | |
| Jan 12, 2018 at 15:25 | comment | added | Anton Fetisov | @Ben Ok, let's go to h bar. | |
| Jan 12, 2018 at 15:22 | comment | added | Ben51 | @Anton Fetisov But B is an axial vector and E is a polar one. I do not yet understand why symmetry cannot be used. Would you be willing to explain further in chat? | |
| Jan 12, 2018 at 13:23 | comment | added | Ben51 | @Anton Fetisov can one not prove that there can be no current by a symmetry argument? Given that Maxwell’s equations are parity invariant, how could the current choose a direction? | |
| Jan 11, 2018 at 14:27 | history | edited | Anton Fetisov | CC BY-SA 3.0 |
I don't know if the current exists
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| Jan 11, 2018 at 14:25 | comment | added | Anton Fetisov | @freecharly I don't think I can actually show it, I tried calculating the current but without success. But I also see no reason why there shouldn't be a current, and my analysis in the post shows that there is some nontrivial magnetic field. It's possible that it is entirely caused by the change in $\mathbf E$. | |
| Jan 11, 2018 at 14:17 | comment | added | freecharly | Although I agree with your analysis of the $\frac{\partial{\bf E}}{\partial t}\neq 0$ due to the induced shielding charges on the wire, I still cannot see how you come to the conclusion, if I understand you correctly, that there exists an induced current along the wire which should also causes a magnetic field. Could you, please, add an explanation for this? | |
| Jan 11, 2018 at 4:53 | comment | added | freecharly | I have read your detailed answer and think that your analysis of the integration contour in the metallic wire is correct! This is really surprising to me and I am grateful for your insights how to tackle this obviously not so "simple" problem. | |
| Jan 10, 2018 at 18:10 | history | edited | Anton Fetisov | CC BY-SA 3.0 |
case of non-zero resistance
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| Jan 10, 2018 at 18:08 | comment | added | Anton Fetisov | The important part is that the boundary term in the derivative of the integral is 0, since the vertical component of the electric field is 0. Now that I'm thinking about it, it will be true even if $\rho \ne 0$ since there can be no vertical current. | |
| Jan 10, 2018 at 17:55 | comment | added | Anton Fetisov | @Nicol I have written out the answer more thoroughly than is really required, just to make sure I didn't miss anything and explain all details. You don't really need delta functions, there are certainly no delta functions microscopically, they are an artifact of large-scale approximation and you can do the same things if you have a proper intuition about the structure of large-scale limit, but I felt the need to elaborate on the apparent zero time derivative paradox and the origin of magnetic field, especially since it's a common source of error and confusion. | |
| Jan 10, 2018 at 17:42 | comment | added | Adrian | [...] that this was a little oversight of my professor's, and that he got the right solution by chance. (I hope this doesn't sound condescending, but I've been obsessing with this problem for quite a while!) | |
| Jan 10, 2018 at 17:37 | comment | added | Adrian | Dear Anton, thanks for the detailed answer. I think I got the gist of it, but nonetheless I'm still perplexed. I'm studying engineering and the one I'm attending is a basic course in classical EM. We haven't covered delta functions, time-dependent surface integrals and the like. I can see my professor making this kind of reasoning, but for his students it would be pretty out or reach. Moreover, this was part of an easy quiz, and the other questions could be solved in minutes! Therefore, unless there is a more immediate way of seeing why the solution is correct, it seems more likely tome [...] | |
| Jan 10, 2018 at 15:43 | history | edited | Anton Fetisov | CC BY-SA 3.0 |
added 42 characters in body
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| Jan 10, 2018 at 15:37 | review | First posts | |||
| Jan 10, 2018 at 17:15 | |||||
| Jan 10, 2018 at 15:36 | history | answered | Anton Fetisov | CC BY-SA 3.0 |