# What is the optimal disposition of coil to maximize the magnetic field created?

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?

• In which direction do you want the lines of flux to go thru the box? Is it a DC magnet or an AC magnet? Commented Sep 28, 2015 at 20:17

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.

• Isn't this solution technically similar to the third sketch of mine? Mine is probably more efficient. Why exactly does it have to be a toroid circle? Why not an U like in my sketch, with the gap in the U made to fit the box, and the rest made just right to cover the box without wasting too much space.
– Zee
Commented Sep 28, 2015 at 19:31
• No. Your third form (as drawn) concentrates the flux inside the U, where it appears outside the iron at the open ends of the U, forming a relatively weak field (since those open ends are relatively small and far apart) field, mostly off to the right of the cell. Some fringing will actually cross the cell, but most of it is effectively screened from the magnetic field by the inner sides of your winding.
– user16324
Commented Sep 28, 2015 at 19:36
• It doesn't have to be circular though. Using E's and I's you could create a strong field in a gap by shortening the central leg of the E, for example.
– user16324
Commented Sep 28, 2015 at 19:39
• I see, so I just need to curve out the U ends in some sort, thanks, I'll try it out. Or use your example of the E core, I like that much better.
– Zee
Commented Sep 28, 2015 at 21:25
• Have the U ends facing inwards towards each other. Directly between them is pretty much the only place (outside the iron) you'll have a strong field.
– user16324
Commented Sep 28, 2015 at 21:30