Which of the above setups would have the strongest attraction to a steel plate? You can assume the magnets are secured to a non magnetic structure. My intuition says that A (non alternating) would be stronger, but I don't know enough about magnets to confirm that. I know that the magnets would prefer to be alternating, but how does this effect the magnetic attraction to the steel plate?
I definitely choose B, especially when the magnets are on a strip of weak iron. Then one has a Halbach array. Ideally, the field would be twice as large, and there is also a large gradient.
In this image, the colored elements are the permanent magnets.
The results will likely depend on the geometry, specifically the separation between the magnets and the steel plate. When the plate is very close to the magnets, I suspect B with alternating magnets will yield the higher force.
In A, the magnetic flux is forced to "flow" through the sides, which will have higher reluctance compared to the gap between the magnets and the plate. Loosely speaking, this increases the total reluctance of the magnetic circuit, reducing the magnetic flux, and thus the magnetic flux density in the gap between the magnets and the plate. In B, the magnet in the middle can partially "sink" the magnetic flux sourced by the other two magnets, providing a lower reluctance path through the gap rather than forcing the magnetic flux to flow through the sides. The higher magnetic flux density in the gap translates to a larger force.
