4 ms·

What's the Deal with Magnetic Fields?

30 points by zdw 2y ago

bobchadwick 2y ago
69 Love Songs is brilliant as a concept album, but Charm of the Highway Strip is my personal favorite.
- werdnapk 2y ago
  Most of the crowd is here unlikely to get the reference, but since I do, 69 Love Songs is indeed great.
- cmiller1 2y ago
  I was at a Mark Mulcahy show in Hamden, CT and he started covering a Magnetic Fields song, it was the only time in my life where I just screamed in fan excitement.
- turadg 2y ago
  I was on a date when she asked “do you like magnetic fields?”. “Yes!” and we were both smitten. Took us a few conversational turns to realize we had different capitalization. (This was in the old days when courting was mostly by speaking in person.)
- deleted 2y ago
  [deleted]
- ihatemarketing 2y ago
  I like the House of Tomorrow
ijidak 2y ago
This article is also great. Linked in one of the comments: https://teoriaelektryki-pl.translate.goog/jak-szybko-plynie-prad/?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=pl&_x_tr_pto=wapp https://teoriaelektryki-pl.translate.goog/jak-szybko-plynie-...
pjc50 2y ago
This is really interesting as an explanation. It's not usually taught this way, because the formalization of Maxwell's Equations pre-dates General Relativity. Is it actually theoretically sound?
- programjames 2y ago
  Yes, this is how I learned it. Suppose you have a line of charges with density p moving up at velocity v, and want to find the force on a stationary particle with charge q and distance r to the right. The classical Gauss' law gives F = (p / 2πrε) * q If we switch to a moving reference frame (up at velocity v), the charge density decreases to p' = p*sqrt(1-v^2/c^2) = p - pv^2/2c^2 + O(v^4/c^4) (from Taylor series) The force should stay the same, so (p / 2πrε) * q = (p' / 2πrε) * q + F' where F' is some other magnetic force created by the current. Solving, to second-order we have F' = pqv^2/4πrεc^2 If we introduce a new constant µ = 1 / εc^2, we get F' = (µ / 4π) * pqv^2 / r Now, we know F' = B * qv where B is the magnetic field, so B = dF'/d(qv) = µpv / 2πr = µI / 2πr (where I is the current in the wire). This agrees with the Biot-Savart Law for an infinitely long wire.
- gattis 2y ago
  The article makes it sound as if magnetism arises because of a delay in the propagation of the electric field caused by a limit on the speed of light. It's kinda the other way around. Light is a alternating electric field and the speed of it's propagation is limited by the ε0 and μ0 (electric permittivity and magnetic permeability) in Maxwell's equations. From Maxwell you can derive c^2=1/(ε0*μ0). Lorentz and Einstein came along and realized that this changes all of mechanics, and that is special relativity.
- rnhmjoj 2y ago
  It's correct, but I think it's misleading. If you're now thinking that magnetic fields are just electric fields viewed from different reference frame and that the latter are the more fundamental, that's not right. There are situations in which you have both fields and you can't attribute the magnetic field to a purely electrostatic field in another frame. It turns out that all observers agree on the value of k=E²/c² - B², so if you have k<0, you can't possibly find a frame with no magnetic fields, because that would imply k≥0. So, you can use relativity to motivate the need for introducing a B field, instead of "pulling it out of the hat", but in general you need both E and B. In the modern formalist these are the components of a larger object called F, the field strength tensor.
KboPAacDA3 2y ago
Veritasium has a video: https://www.youtube.com/watch?v=1TKSfAkWWN0 https://www.youtube.com/watch?v=1TKSfAkWWN0
Eduard 2y ago
> "even though the average drift speed of electrons in a wire usually doesn’t exceed several centimeters per minute [...]". So on average, relativistic effects are negligible. Then how can relativistic effects then be used in the later arguments for where magnetic effects come from?
- wrs 2y ago
  There are a lot of electrons in a real piece of wire. As the author says, relativistic effects are usually negligible, but in this case the math does work out.
- madhadron 2y ago
  Because they're not negligible. It's worth calculating it out. Length contraction produces a very slight increase in charge density of the nuclei, but there are a lot of charges and electromagnetism is very strong.
- AlotOfReading 2y ago
  A very small force affecting the very large number of particles in a conductor balances out to the human scale phenomena we're familiar with.
- ben_w 2y ago
  Two things: 1) Lots of small things that interact constructively. IIRC, the conduction electrons in copper have something like -13600 coulombs of charge per cubic centimetre, but that all cancels out with the positive ions right next to them; the magnetic fields from each electron's motion don't cancel out*, but the motion of the ions is ~ isotropic*, so they do cancel each other*. 2) The strength of the electric (and by extension magnetic) force is also strong, which in turn also helps make this easier to notice. * in the lab frame
- bee_rider 2y ago
  I’m slightly confused by this question. The full quote is: > The effect is negligible in most contexts unless the objects are moving at very high (“relativistic”) speeds, but electric fields are a notable exception — even though the average drift speed of electrons in a wire usually doesn’t exceed several centimeters per minute. The point of the text you’ve quoted is to set up the seeming contradiction or unexpected idea. Then the hope is that the author explains it in the rest of the article. It is fine to say that the article doesn’t follow through with the implied promise of the quote, but the deficiency is in the answering if that is the case, not the quoted text.
deleted 2y ago
[deleted]
deleted 2y ago
[deleted]
pfdietz 2y ago
The electric and magnetic potentials combine to produce something called the electromagnetic four-potential, just as energy and momentum yield the four-momentum. https://en.wikipedia.org/wiki/Electromagnetic_four-potential https://en.wikipedia.org/wiki/Electromagnetic_four-potential
amluto 2y ago
Interestingly, the history of this kind phenomenon is the other way around. Einstein introduced special relativity in 1905. Well before that, around 1889, physicists started to notice that the Lorentz transformation was necessary to get a self-consistent description of electric and magnetic fields. In the 16 intervening years, physics classes must have been rather confusing: how did people feel about transforming coordinates into a moving frame in a manner that pretty much required length contraction, time dilation, and simultaneity violation before anyone really believed that the universe actually worked that way?
- bee_rider 2y ago
  I guess it would probably be similar to stuff like Dark Matter or whatever, right? Here’s a kludge; the professor doesn’t like it either but somebody is working on it… I often wonder about the “luminiferous aether”— it sounds a bit silly. If there were message boards form physicists back then, would there be a bunch of writing: “well, we think this is a bit dumb, we’re just using it to make the math work out” for us to read? I’m sure somebody’s checked their personal letters…
filoeleven 2y ago
I always thought this was real weird. https://en.m.wikipedia.org/wiki/Aharonov%E2%80%93Bohm_effect https://en.m.wikipedia.org/wiki/Aharonov%E2%80%93Bohm_effect
johnea 2y ago
The article sort of jumps straight from Faraday's law to special relativity. I would think it's at least worth mentioning that Maxwell's equations did unify the electric and magnetic forces prior to relativity. They aren't always taught as completely separate things, even in classical physics. I would also say, this is a great example of how once we have a word, or a an explanation for a thing, it pretty much becomes invisible to us. The magnetic phenomenon still amazes me, at 65 years old. It's what as a child, and a youth, inspired me to study electrical engineering. Holding two permanent magnets near each other, and physically feeling the force between them, even though they don't touch each other, really frikin amazes me! Still! Just drop everything you've ever learned or thought you knew, and hold those two magnets, and wonder at how do they know the other one is near? Reality is just so much more amazing than make believe. It's so sad to see so much of the modern world lost in make believe...

30 points by zdw 2y ago

bobchadwick 2y ago

69 Love Songs is brilliant as a concept album, but Charm of the Highway Strip is my personal favorite.

werdnapk 2y ago
Most of the crowd is here unlikely to get the reference, but since I do, 69 Love Songs is indeed great.
cmiller1 2y ago
I was at a Mark Mulcahy show in Hamden, CT and he started covering a Magnetic Fields song, it was the only time in my life where I just screamed in fan excitement.
turadg 2y ago
I was on a date when she asked “do you like magnetic fields?”. “Yes!” and we were both smitten. Took us a few conversational turns to realize we had different capitalization. (This was in the old days when courting was mostly by speaking in person.)
deleted 2y ago
[deleted]
ihatemarketing 2y ago
I like the House of Tomorrow

ijidak 2y ago

This article is also great. Linked in one of the comments: https://teoriaelektryki-pl.translate.goog/jak-szybko-plynie-prad/?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=pl&_x_tr_pto=wapp https://teoriaelektryki-pl.translate.goog/jak-szybko-plynie-...

pjc50 2y ago

This is really interesting as an explanation. It's not usually taught this way, because the formalization of Maxwell's Equations pre-dates General Relativity. Is it actually theoretically sound?

programjames 2y ago
Yes, this is how I learned it. Suppose you have a line of charges with density p moving up at velocity v, and want to find the force on a stationary particle with charge q and distance r to the right. The classical Gauss' law gives F = (p / 2πrε) * q If we switch to a moving reference frame (up at velocity v), the charge density decreases to p' = p*sqrt(1-v^2/c^2) = p - pv^2/2c^2 + O(v^4/c^4) (from Taylor series) The force should stay the same, so (p / 2πrε) * q = (p' / 2πrε) * q + F' where F' is some other magnetic force created by the current. Solving, to second-order we have F' = pqv^2/4πrεc^2 If we introduce a new constant µ = 1 / εc^2, we get F' = (µ / 4π) * pqv^2 / r Now, we know F' = B * qv where B is the magnetic field, so B = dF'/d(qv) = µpv / 2πr = µI / 2πr (where I is the current in the wire). This agrees with the Biot-Savart Law for an infinitely long wire.
gattis 2y ago
The article makes it sound as if magnetism arises because of a delay in the propagation of the electric field caused by a limit on the speed of light. It's kinda the other way around. Light is a alternating electric field and the speed of it's propagation is limited by the ε0 and μ0 (electric permittivity and magnetic permeability) in Maxwell's equations. From Maxwell you can derive c^2=1/(ε0*μ0). Lorentz and Einstein came along and realized that this changes all of mechanics, and that is special relativity.
rnhmjoj 2y ago
It's correct, but I think it's misleading. If you're now thinking that magnetic fields are just electric fields viewed from different reference frame and that the latter are the more fundamental, that's not right. There are situations in which you have both fields and you can't attribute the magnetic field to a purely electrostatic field in another frame. It turns out that all observers agree on the value of k=E²/c² - B², so if you have k<0, you can't possibly find a frame with no magnetic fields, because that would imply k≥0. So, you can use relativity to motivate the need for introducing a B field, instead of "pulling it out of the hat", but in general you need both E and B. In the modern formalist these are the components of a larger object called F, the field strength tensor.

KboPAacDA3 2y ago

Veritasium has a video: https://www.youtube.com/watch?v=1TKSfAkWWN0 https://www.youtube.com/watch?v=1TKSfAkWWN0

Eduard 2y ago

> "even though the average drift speed of electrons in a wire usually doesn’t exceed several centimeters per minute [...]". So on average, relativistic effects are negligible. Then how can relativistic effects then be used in the later arguments for where magnetic effects come from?

wrs 2y ago
There are a lot of electrons in a real piece of wire. As the author says, relativistic effects are usually negligible, but in this case the math does work out.
madhadron 2y ago
Because they're not negligible. It's worth calculating it out. Length contraction produces a very slight increase in charge density of the nuclei, but there are a lot of charges and electromagnetism is very strong.
AlotOfReading 2y ago
A very small force affecting the very large number of particles in a conductor balances out to the human scale phenomena we're familiar with.
ben_w 2y ago
Two things: 1) Lots of small things that interact constructively. IIRC, the conduction electrons in copper have something like -13600 coulombs of charge per cubic centimetre, but that all cancels out with the positive ions right next to them; the magnetic fields from each electron's motion don't cancel out*, but the motion of the ions is ~ isotropic*, so they do cancel each other*. 2) The strength of the electric (and by extension magnetic) force is also strong, which in turn also helps make this easier to notice. * in the lab frame
bee_rider 2y ago
I’m slightly confused by this question. The full quote is: > The effect is negligible in most contexts unless the objects are moving at very high (“relativistic”) speeds, but electric fields are a notable exception — even though the average drift speed of electrons in a wire usually doesn’t exceed several centimeters per minute. The point of the text you’ve quoted is to set up the seeming contradiction or unexpected idea. Then the hope is that the author explains it in the rest of the article. It is fine to say that the article doesn’t follow through with the implied promise of the quote, but the deficiency is in the answering if that is the case, not the quoted text.

deleted 2y ago

[deleted]

deleted 2y ago

[deleted]

pfdietz 2y ago

The electric and magnetic potentials combine to produce something called the electromagnetic four-potential, just as energy and momentum yield the four-momentum. https://en.wikipedia.org/wiki/Electromagnetic_four-potential https://en.wikipedia.org/wiki/Electromagnetic_four-potential

amluto 2y ago

Interestingly, the history of this kind phenomenon is the other way around. Einstein introduced special relativity in 1905. Well before that, around 1889, physicists started to notice that the Lorentz transformation was necessary to get a self-consistent description of electric and magnetic fields. In the 16 intervening years, physics classes must have been rather confusing: how did people feel about transforming coordinates into a moving frame in a manner that pretty much required length contraction, time dilation, and simultaneity violation before anyone really believed that the universe actually worked that way?

bee_rider 2y ago
I guess it would probably be similar to stuff like Dark Matter or whatever, right? Here’s a kludge; the professor doesn’t like it either but somebody is working on it… I often wonder about the “luminiferous aether”— it sounds a bit silly. If there were message boards form physicists back then, would there be a bunch of writing: “well, we think this is a bit dumb, we’re just using it to make the math work out” for us to read? I’m sure somebody’s checked their personal letters…

filoeleven 2y ago

I always thought this was real weird. https://en.m.wikipedia.org/wiki/Aharonov%E2%80%93Bohm_effect https://en.m.wikipedia.org/wiki/Aharonov%E2%80%93Bohm_effect

johnea 2y ago

The article sort of jumps straight from Faraday's law to special relativity. I would think it's at least worth mentioning that Maxwell's equations did unify the electric and magnetic forces prior to relativity. They aren't always taught as completely separate things, even in classical physics. I would also say, this is a great example of how once we have a word, or a an explanation for a thing, it pretty much becomes invisible to us. The magnetic phenomenon still amazes me, at 65 years old. It's what as a child, and a youth, inspired me to study electrical engineering. Holding two permanent magnets near each other, and physically feeling the force between them, even though they don't touch each other, really frikin amazes me! Still! Just drop everything you've ever learned or thought you knew, and hold those two magnets, and wonder at how do they know the other one is near? Reality is just so much more amazing than make believe. It's so sad to see so much of the modern world lost in make believe...