5 ms·

I thought the strength of most(all?) fields is inversely proportional to the square of the distance from the center/source? I think this is called inverse squar

by kamaal 2y ago

I thought the strength of most(all?) fields is inversely proportional to the square of the distance from the center/source? I think this is called inverse square law. Its also for these reasons making a very large nuke is pointless, after some distance the effects are almost 0.

ChrisMarshallNY 2y ago
Yes, that's what I would think, but I remember reading that, and thought it sounded strange. The article made it seem as if the rules were different for superconducting magnets. Might just be a manifestation of the Inverse Square Law. Like I said, not my area of expertise.
hollerith 2y ago
Very large nuclear bombs are inefficient because most of the energy goes into heating up air, so not relevant to the current thread.
- taneq 2y ago
  They're only inefficient if you want them to do something other than heat up a lot of air by a very large amount very fast. :)
  - hollerith 2y ago
    OK: they're inefficient at killing people and destroying buildings and other structures relative to bombs with yields like 500 kilotons.
    - connicpu 2y ago
      Pretty efficient in their mass to destruction ratio, it's only inefficient if you compare it to how much energy the fissile/fusible material could be worth in a nuclear reactor.
      - hollerith 2y ago
        It's also an inefficient use of ICBMs or whatever "system" is being used to "deliver" the bomb to the target (which BTW is more expensive than the bombs themselves).
    - jajko 2y ago
      Well that heat does a lot of damage too, on top of other damaging radiation, blast wave, irradiating everything etc. which is proportional to bomb yield. Sure the biggest ones are comparatively ineffective, thats why the focus on manufacturing was on small/medium yield one, one can produce many more and saturate defenses more easily rather than one/few MOABs.
- kamaal 2y ago
  Agreed that I know very little about this subject. But heat itself can be imagined as a kind of field. For eg: A candle, the closer you move to the flame, every point closer to flame, the temperature is higher. The farther you move apart the temperature reduces. Same with the Sun. Take for eg- Sound. The closer you move to the source of it, the louder it sounds, the farther you move from it, the fainter it gets. Now you could call this a wave. Like the wavelength stretches with distance, also decreasing frequency and amplitude. Another way of looking at this a field. Imagine 3D space with points, like a lattice. Each point has a value, and the values get denser to the center, and move farther apart as move away from center. If Im not wrong a lot of physical phenomenon exhibit this behaviour. Including thing like light, sound, temperature, gravitation etc. While you can make a beam of light, I doubt you can make a beam of magnetic field(ray?) or gravity for that matter?
  - vlovich123 2y ago
    Heat is only a field in radiation because it’s literally being carried by electromagnetic waves. Heat is also conduction and convection - in those cases it’s decidedly not a field.
  - itishappy 2y ago
    The heat and wave equations have an important difference: heat: ∂u/∂t = k ∂²u/∂x² wave: ∂²u/∂t² = c² ∂²u/∂x² Note the extra time derivative on the wave equation. The heat equation is dissipative, moving towards the average value, spreading energy out over time. The wave equation, on the other hand, allows for solutions that oscillate and maintain their shape while they travel. This means that waves such as electromagnetic (light) or gravitational can in theory be focused and beamed significant distances without much loss. A plane wave solution is lossless, but requires an infinite emitter. Finally, note that this does not apply to static fields, such as magnetic, electric, or gravitational fields, which if not oscillating will still spread out and dissipate over distance.
    - barrenko 2y ago
      So the second equation does not cover my induction cooktop?
- naasking 2y ago
  There are many efficiency metrics. For instance, how much energy went into constructing and deploying the bomb vs. how much destruction it caused. I think large nuclear bombs would look quite ok on this metric.
  - hollerith 2y ago
    People have known how to make very large bombs for a long time (e.g., in 1961, the USSR tested a bomb with a yield of 50–58 megatons) so it says something that for decades, no military has had any bombs larger than about 1.3 megatons.
closewith 2y ago
Magnetic fields produced by dipoles have an inverse cube dependence, so dissipate much faster than gravity or other fields.
gus_massa 2y ago
If we ever find a monopole, the field will be inversely proportional to the square of the distance. Bug normal magnets and superconductor magnets have canceling magnetic charge, the same amount of S and N, so after a few math tricks [1] the field will be inversely proportional to the cube of the distance. [1] The filed from N decays as 1/r^2 and the field form S as -1/r^2 but they are indifferent places (the r is not the same on both), so the difference is almost like 1/r^3 more details in https://en.wikipedia.org/wiki/Multipole_expansion https://en.wikipedia.org/wiki/Multipole_expansion
- kamaal 2y ago
  Thanks for the link. Sometimes I wish Xanadu had actually happened. The moment I opened the article I saw something like |R^3. Honestly speaking I don't really know what |R means. And R keeps showing up all over the article. I will dig more into this using ChatGPT with time. But I could understand very little from reading the article.
  - card_zero 2y ago
    Blackboard bold R with a superscript 3? That's just space, like regular space that we inhabit. The 3 is the dimensions, the R is the real numbers, and this distinguishes it from other wacky kinds of space that mathematicians like to try things out in. Edit: we also have in there "the coefficients of the multipole expansion can be written as functions of the distance to the origin, r", so it sounds like r in italics is the origin - but that's usually (0, 0, 0), so maybe it's a distance to it. Anyway r in bold is probably a vector, vectors are usually in bold. And you're quite right about Xanadu, I wonder if there's some way to overhaul Wikipedia to put a key to notation in the sidebar of all pages with equations in.
    - kamaal 2y ago
      >>and this distinguishes it from other wacky kinds of space that mathematicians like to try things out in. What other space apart from 3 dimensional space exists? And what does that even mean?

by kamaal 2y ago

ChrisMarshallNY 2y ago

Yes, that's what I would think, but I remember reading that, and thought it sounded strange. The article made it seem as if the rules were different for superconducting magnets. Might just be a manifestation of the Inverse Square Law. Like I said, not my area of expertise.

hollerith 2y ago

Very large nuclear bombs are inefficient because most of the energy goes into heating up air, so not relevant to the current thread.

taneq 2y ago
They're only inefficient if you want them to do something other than heat up a lot of air by a very large amount very fast. :)
- hollerith 2y ago
  OK: they're inefficient at killing people and destroying buildings and other structures relative to bombs with yields like 500 kilotons.
  - connicpu 2y ago
    Pretty efficient in their mass to destruction ratio, it's only inefficient if you compare it to how much energy the fissile/fusible material could be worth in a nuclear reactor.
    - hollerith 2y ago
      It's also an inefficient use of ICBMs or whatever "system" is being used to "deliver" the bomb to the target (which BTW is more expensive than the bombs themselves).
  - jajko 2y ago
    Well that heat does a lot of damage too, on top of other damaging radiation, blast wave, irradiating everything etc. which is proportional to bomb yield. Sure the biggest ones are comparatively ineffective, thats why the focus on manufacturing was on small/medium yield one, one can produce many more and saturate defenses more easily rather than one/few MOABs.
kamaal 2y ago
Agreed that I know very little about this subject. But heat itself can be imagined as a kind of field. For eg: A candle, the closer you move to the flame, every point closer to flame, the temperature is higher. The farther you move apart the temperature reduces. Same with the Sun. Take for eg- Sound. The closer you move to the source of it, the louder it sounds, the farther you move from it, the fainter it gets. Now you could call this a wave. Like the wavelength stretches with distance, also decreasing frequency and amplitude. Another way of looking at this a field. Imagine 3D space with points, like a lattice. Each point has a value, and the values get denser to the center, and move farther apart as move away from center. If Im not wrong a lot of physical phenomenon exhibit this behaviour. Including thing like light, sound, temperature, gravitation etc. While you can make a beam of light, I doubt you can make a beam of magnetic field(ray?) or gravity for that matter?
- vlovich123 2y ago
  Heat is only a field in radiation because it’s literally being carried by electromagnetic waves. Heat is also conduction and convection - in those cases it’s decidedly not a field.
- itishappy 2y ago
  The heat and wave equations have an important difference: heat: ∂u/∂t = k ∂²u/∂x² wave: ∂²u/∂t² = c² ∂²u/∂x² Note the extra time derivative on the wave equation. The heat equation is dissipative, moving towards the average value, spreading energy out over time. The wave equation, on the other hand, allows for solutions that oscillate and maintain their shape while they travel. This means that waves such as electromagnetic (light) or gravitational can in theory be focused and beamed significant distances without much loss. A plane wave solution is lossless, but requires an infinite emitter. Finally, note that this does not apply to static fields, such as magnetic, electric, or gravitational fields, which if not oscillating will still spread out and dissipate over distance.
  - barrenko 2y ago
    So the second equation does not cover my induction cooktop?
naasking 2y ago
There are many efficiency metrics. For instance, how much energy went into constructing and deploying the bomb vs. how much destruction it caused. I think large nuclear bombs would look quite ok on this metric.
- hollerith 2y ago
  People have known how to make very large bombs for a long time (e.g., in 1961, the USSR tested a bomb with a yield of 50–58 megatons) so it says something that for decades, no military has had any bombs larger than about 1.3 megatons.

closewith 2y ago

Magnetic fields produced by dipoles have an inverse cube dependence, so dissipate much faster than gravity or other fields.

gus_massa 2y ago

If we ever find a monopole, the field will be inversely proportional to the square of the distance. Bug normal magnets and superconductor magnets have canceling magnetic charge, the same amount of S and N, so after a few math tricks [1] the field will be inversely proportional to the cube of the distance. [1] The filed from N decays as 1/r^2 and the field form S as -1/r^2 but they are indifferent places (the r is not the same on both), so the difference is almost like 1/r^3 more details in https://en.wikipedia.org/wiki/Multipole_expansion https://en.wikipedia.org/wiki/Multipole_expansion

kamaal 2y ago
Thanks for the link. Sometimes I wish Xanadu had actually happened. The moment I opened the article I saw something like |R^3. Honestly speaking I don't really know what |R means. And R keeps showing up all over the article. I will dig more into this using ChatGPT with time. But I could understand very little from reading the article.
- card_zero 2y ago
  Blackboard bold R with a superscript 3? That's just space, like regular space that we inhabit. The 3 is the dimensions, the R is the real numbers, and this distinguishes it from other wacky kinds of space that mathematicians like to try things out in. Edit: we also have in there "the coefficients of the multipole expansion can be written as functions of the distance to the origin, r", so it sounds like r in italics is the origin - but that's usually (0, 0, 0), so maybe it's a distance to it. Anyway r in bold is probably a vector, vectors are usually in bold. And you're quite right about Xanadu, I wonder if there's some way to overhaul Wikipedia to put a key to notation in the sidebar of all pages with equations in.
  - kamaal 2y ago
    >>and this distinguishes it from other wacky kinds of space that mathematicians like to try things out in. What other space apart from 3 dimensional space exists? And what does that even mean?