I am trying to create a powerful magnetic field using coil, and possibly some ferromagnetic metal bars.
The white box with the X on it, is empty, or made of air.
Saying that I have no limits on how many metal bars I have, or their dimensions, but I have limited copper wire length that I can use, and through all examples, the current that I use is constant.
The examples in the image included, but I would gladly accept anything new you can think of, what is the best way to have the maximum possible magnetic flux go through the box?
Best Answer
Large pole pieces close together.
In your case one approach is a 10x20x(long) iron bar formed into an almost complete circle leaving a L=5 gap. This concentrates a relatively strong field enclosing your 10x20x5 volume in that gap. Wind copper round the bar, apply current.
Something like this...
Image from this page... Dimensions may not match your needs and material is ferrite rather than iron, but illustrates the principle.
EDIT : comparing this with your third option - there are some similarities if you concentrated the winding on the vertical arm of your core. (Spreading out the winding screens most of your cell from the magnetic field!). However this directs the flux almost equally across the gap, whereas with your "U" the RH end of the gap will see somewhat less field while the LH end next to the winding will see a bit more. You can probably reduce this effect by carefully shaping the core and pole pieces, and performing 3D simulations of the magnetic circuit...
Alternative form with a gapped E core...
Winding would be on the central limb of the E, and would be simpler if the gap was at one end of the central limb rather than in the middle. Image from this page though their focus is on creating efficient inductors rather than generating a concentrated magnetic field. Nevertheless, read their page - especially the section "Gap energy" - even though the magnetic path looks quite long, because iron (or ferrite) has such a low reluctance compared to air, its length is unimportant compared to the length of the gap.