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eightplusonefingers

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Hence this question.

On the left we have a disc magnet diameter D attracted to a much larger lump of steel with force F (when there is no gap between).

If I add a second similar magnet, a website selling magnets I found tells me the force increases to about 70% of the sum of the two - shown on the right.

If I arrange the magnets as shown with the spacing a little more that the magnet diameter and a bridging steel pole piece straddling the two as shown. Note the right hand magnet has been flipped N-S

What is the force between each magnet and the lump of steel at the bottom?

Does that force vary much with the thickness of the pole piece T?

Does the pole piece even do anything useful?

Without the pole piece I assume the attraction of the two magnets in isolation would be F each but

Does the pole piece help increase this? if so how much by?

In my mind I have the idea that there is now a "magnetic circuit" via the pole piece and the steel lump at the bottom but is a magnetic circuit even a real thing.

Not looking for pages of maths just a real world idea of what it means

TIA