Magnetization of Permanent Spherical Magnet

[Michael Lin]

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

 

[Meir Achuz]

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.

 

[Michael Lin]

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?

 

[Meir Achuz]

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.

 

[Michael Lin]

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?

 

[Meir Achuz]

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.