Magnetization of Permanent Spherical Magnet

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Discussion Overview

The discussion revolves around the magnetization of spherical permanent magnets, particularly when multiple magnets are combined. Participants explore the implications of magnetization calculations, configurations of magnets, and the forces exerted on an iron plate in various arrangements.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • Mike questions whether the magnetization of four spherical magnets attached together would simply be 4M, referencing a specific formula for magnetization.
  • One participant clarifies that magnetization M is defined as magnetic moment per unit volume, suggesting that while magnetic moments may add, the effective power depends on the configuration due to the rapid fall-off of the magnetic field with distance.
  • Mike inquires about calculating the effective magnetization when using four vertically attached magnets and seeks references for further reading.
  • Another participant discusses the force between a spherical magnet and an iron plate, stating that the force can be calculated using a specific formula related to magnetic dipoles and that using four magnets touching the plate would increase the force proportionally.
  • Mike expresses concern about whether the effective force on the iron plate would still be four times greater if only one of the four magnets is in contact with it.
  • A participant responds that the arrangement of the magnets affects the force, indicating that if all four magnets are touching the plate, the force would be four times that of a single magnet, but if they are aligned in a row with only one touching, the increase in force would be minimal.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the exact calculations for effective magnetization or force, with differing views on how configurations of magnets influence the outcomes.

Contextual Notes

There are unresolved assumptions regarding the configurations of the magnets and their interactions with the iron plate, as well as the dependence on specific definitions of magnetization and magnetic moment.

Michael Lin
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Dear all,

1) For a spherical permanent magnet, the magnetization M is defined to be pi/4u0*Br*d^3. My question is: if I attach 4 such spherical magnets together, would the magnetization simply be 4M? Where (website) can I find a good reference for these type of material?

2) I have read in an article, "Magnet levitation at your fingertips" (please google) that for a setup with a solenoid creating a magnetic field, B that B/B' can be approximated by R (for short solenoid) and 1.2 R (for long solenoid). However, I can not find any articles or books that support this claim. How did the author came up with that?

Thanks,
Mike
 
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The magnetization M is usually defined as the magnetic moment per unit volume.
Your formula gives the magnetilc moment, usually designated by m or mu.
The magnetic moments of 4 such magnets would tend to add, but the effective power would be determined by the configuration. They could not be brought close enough to give 4m effectively, since the field falls off quickly with distance.
 
Thanks for your response to (1).
Is there any way I can calculate the effective M? I can properly simulate or measure the field around 4 such vertically attached magnets and derive M from that. Do you have any good reference that I can look up?
 
The force between a spherical magnet of radius R with magnetic moment m and a touching iron plate will equal the force between magnetic dipoles a distance 2R apart. This F=6m^2/(2R)^4 dynes (if m is in gauss).
If you use four such spheres, all touching the iron plate, the force will be 4 times as large.
 
Thanks for your response.
Your explanation is very clear. My concern is, however, if the iron plate is touching only one of the four spherical magnets oriented vertically, will the effective force on the iron plate still be 4 times?
 
If you put the magnets like this OO
OO, with all four touching the plate,
the force will be four times that of one magnet.
If you line them up like OOOO, with the plate touching only one, it will be only slightly stronger than one magnet.
 

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