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Registered Member #162
Joined: Mon Feb 13 2006, 10:25AM
Location: United Kingdom
Posts: 3140
suppose I have 1000 cube magnets, all N-S always alligned in the same direction, I could make one line of 1000 x 1 x 1 or (with glue) a 10 x 10 x 10 cube, or a 1 x 50 x 20 sheet .... any numbee of possibilities.
When far away (say >1,000,000 x block dimensions), does the arrangement make any difference to the nett magnetic field strength ?
OR
for a given ammount of 'magnet material', what shape causes the strongest remote magnetic field ? or by superposition, is shape irrelevant ? my maths is not up to this :(
Registered Member #58215
Joined: Wed Dec 30 2015, 11:27AM
Location: Boise, Idaho
Posts: 65
If you're greater than 1,000,000 block dimensions away, then no, arrangement has virtually no impact on strength, but only because you are so far away. If the magnets formed an infinite plane, then I think there would be a difference.
If you're much closer than that, (relatively close) then you would want a 1 cube thick sheet of magnets with the poles facing the same way and to be above (or below it) right in the center. By superposition, that's the shape and location of the strongest field, I think, because that's how you manage to get the most magnetic material closest to the point you are measuring. Depending on the distance, the sheet might be 2 or three units deep in the center and taper out to the edges.
You could sum up the magnetic material as dipoles and integrate over the sheet to confirm, I guess, but I think that's the best way: the most magnetic material as close as you can possibly get.
What you can also do if you just care about max strength is to guide the flux into a concentrated zone like so: for more field strength but I think it falls off more quickly as well in that case because flux doesn't like getting shoved together. Maybe this is a better way, I'm not sure.
Mostly I agree with what Karmaslap says. But there might be also a non linear effect, i.e. the magnetic field of one block might affect the field of another one. This would be the case, if the permeability of the magnets differ from 1. Then the field of one block will influence the field generated by another block since it will cause an additional magnetisation there.
Consider a case of one magnetic block and four other non magnetic ones with a high mu. Place the four blocks around the sides of the magnetic block. The flux of the magnetic block will go mainly through the other ones and not into free space, effectively shielding the magnetic block. The far field should be reduced by this.
Now we do have only magnetic blocks in Sulaimans experiment, but if the blocks have a high mu a sequential arrangements of blocks might produce a larger far field.
Registered Member #72
Joined: Thu Feb 09 2006, 08:29AM
Location: UK St. Albans
Posts: 1659
Yes, the arrangement of magnets does affect the far field.
Consider 4096 magnets arranged as >>>>>>>>>>>>>>>>, you now have a magnetic dipole of moment 4096d, where d is the length of a magnet. That field will be detectable at whatever distance, but of course it gets smaller as you move away. As long as all the blocks point the same way, it doesn't matter whether they are in a 16x16x16 cube, or whatever orientation of a 64x64 plane or 4096x1 line, the dipole moment is still 4096d, as all the blocks add up. Of course the very near field for those shapes will be different.
Now consider the 4096 magnets arranged as >>>>>>>><<<<<<<<. There is NO magnetic dipole, only a quadrapole field. The quadrapole field falls off faster than the dipole field. That's far less field to detect at any distance.
You can cancel the quadrapole field by an arrangement like this >>>><<<<<<<<>>>> leaving only a hexapole field, which falls off yet faster.
When magnets are shipped by freight, they are arranged in the box like this, or the 3D equivalent thereof, to cancel as much external field as possible, to protect peoples' cards and pacemakers, and so the box doesn't get stuck to forklift trucks! I've seen a forklift truck stuck to an MRI magnet before, which really slowed things down!
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A question on magnetics is bugging me ... help
