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!
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.