I would like to build a strong magnet using 100 6"x4"x1" permanent magnet blocks. What is the best way to place them so I get the strongest magnetic field? (Should I stack 2 row of 50 blocks and put them side by side? Should I place them like halbach array?...) I use this magnet to attract metal particles that are on a conveyor. The field must attract the medium sized particles(2"x3"x2" approx.) upon a fairly good distance. Thank You!

  • $\begingroup$ You answered your own question writing about Hallbach array, aren't you? $\endgroup$ – HolgerFiedler Jun 17 '16 at 17:34
  • $\begingroup$ You are going at this the exact wrong way. In engineering we don't start with "I have six brick, now how do I build a house?" but with "I want to build a house, how many bricks do I need?". The correct procedure here is experimental. Use one or a few of your magnets to measure the area in which they attract exactly the kinds of parts that you want, then scale it up. Using magnets alone, without a proper magnetic return path is not going to get you a good magnet, anyway, though. $\endgroup$ – CuriousOne Jun 17 '16 at 18:31
  • $\begingroup$ If you tie these magnets parallel to each other such that all the north are facing one direction you would likely to have a strong attracting force. It is just my gut feeling, in any case field very close to magnet pole remain same as of one magnet. $\endgroup$ – hsinghal Jun 17 '16 at 19:20
  • $\begingroup$ Ok thank you I'll make some your tests monday and I will come back with the results! $\endgroup$ – Jean-Gabriel Deshaies Morin Jun 17 '16 at 20:23

The permanent magnets are magnetic dipoles which means that their field goes down like $B\sim 1/r^3$ with the distance from the dipole. The number of such magnets in a volume goes like $r^3$, so regardless of the value of $r$, the magnetic field will have basically the same magnitude.

In particular, if you just double all the dimensions, the whole "picture" will just magnify but the magnitude of the magnetic fields at the corresponding points will stay the same.

Moreover, the magnetic field right at the top of each magnet will be the same regardless of the arrangement. There's basically no way to increase the magnetic field by combining many magnets. Different arrangements will produce different shapes of the magnetic field. One can make the field stronger above the magnets but a bit weaker on the sides, or vice versa, but you would have to describe exactly which quantity of the magnetic field you want to be maximized.

  • $\begingroup$ The place where I want the strongest magnetic field is the side parallel to the conveyor(seen as the bottom), so the particles get attracted. The four sides and the top are not important at all. Thank you $\endgroup$ – Jean-Gabriel Deshaies Morin Jun 17 '16 at 17:25
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    $\begingroup$ This is a cleverly simple answer without much math, very nice! Luckily we have iron. $\endgroup$ – uhoh Oct 30 '16 at 11:56

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