How would the electrons flow in this case?

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Say you have a strong spherical magnet where the poles are along the Z axis, and this magnet is surrounded by a toroid of metal at the equator, if you spin this toroid very rapidly around the sphere in the θ direction (along the blue arrow, i.e it goes around the Z axis), how would the electrons be affected? theoretically speaking, if the magnetic field and the spinning were very very strong, would the electrons from the metal leave the metal and follow the field lines? (assuming it's in a vacuum) I'm very confused about this so please help me understand
250px-Toroidal_coord.png
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
mg50D.png
 

Answers and Replies

  • #2
35,500
11,949
Spherical magnets have complicated fields.
Assuming the metal is not ferromagnetic (that would make things complicated), the field lines would roughly follow the surface of the torus. You would get a potential difference between the interior and the exterior. To allow electrons to leave the metal, you would need really strong fields or really fast rotations. The electrons would not follow the field lines, I would expect them to fly off to infinity, but it might depend on details of the geometry.
 
  • #3
73
2
Spherical magnets have complicated fields.
Assuming the metal is not ferromagnetic (that would make things complicated), the field lines would roughly follow the surface of the torus. You would get a potential difference between the interior and the exterior. To allow electrons to leave the metal, you would need really strong fields or really fast rotations. The electrons would not follow the field lines, I would expect them to fly off to infinity, but it might depend on details of the geometry.

Googling field lines of a sphere I keep getting images of this
http://web.mit.edu/6.013_book/www/chapter8/ch8-853.gif
What does this represent then? it looks fairly straightforward to me
 
  • #5
73
2
That picture represents a Cross-section of a conductor at the moments of induction.

I do think you may need to read up a little more on induction, etc.
Read this and it will build the frameworks for induction in linear conductors, then continue on to learn about spherical/toroidal inductors.


http://www.electrical4u.com/lenz-law-of-electromagnetic-induction/

Oh I see, I thought the field lines of a sphere magnet would be the same.

Ok let's say the field we have is due to induction, then doing the same thing (spinning a toroid around it) how would the charges on the toroid be affected? also at an extremely high speed and very strong magnetic field, would the electrons fling out from the toroid?
 
  • #6
35,500
11,949
What I wrote in post 2 does not depend much on details of the field. A bar magnet of similar size would produce the same result.
 
  • #7
73
2
What I wrote in post 2 does not depend much on details of the field. A bar magnet of similar size would produce the same result.

Ok I'm asking that question because I'm trying to understand black hole jets, Kip Thorne explains it very simply here in page 105:

http://www.helli.ir/portal/sites/de...terstellar-norton_w._w._company_inc._2014.pdf

Of course there are many other models, but I'm using his interpretation and trying to figure out what equation describes such magnetic field, and how the black hole and its accretion disk work together to eject the material from the disk. Do you know what kind of equations might be involved? I would appreciate any insight
 
  • #8
35,500
11,949
There are no solid metal rings orbiting a black hole, and you cannot neglect gravity there.
See the relevant publications for formulas.
 
  • #9
Khashishi
Science Advisor
2,815
493
Electrons need to have energy exceeding the work function of the metal to leave the metal. For sufficiently extreme spinning and/or field, you should probably treat the metal as a plasma. The motional Stark effect can cause the metal to ionize. Then you have something like a dipole magnetic confinement device.
 

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