Increase magnetic field density near surface of magnet

[Waterfox]

I'm currently playing with diamagnetic pyrolytic graphite and I have created a small portion of a track similar to this video
I want to create a circular track for it travel on, but as rare Earth magnets are getting expensive I'm going to use thinner magnets that consequently have a weaker magnetic field.

I still want to have a small cosmetic payload so I'm asking how can I maximise the magnetic field density where it levitates about 1-3mm above the magnets' surface?
I know objects with high permeability can shape magnetic fields, so if I place the magnet track on a sheet of metal with high permeability, will it intensify the field strength in the area the graphite levitates, supporting better levitation and a better payload?
If so, looking at this list on wikipedia, will higher permeability work better? e.g using Mu-metal would be better than electrical steel which would be better than normal steel?

 

[Hassan2]

..so if I place the magnet track on a sheet of metal with high permeability, will it intensify the field strength in the area the graphite levitates, supporting better levitation and a better payload?

No, this way it doesn't strengthen the field. It even weakens it slightly. I you need a stronger field in a narrow air gap ( or inside the a ferromagnetic metal), high-permeability can help, but I guess you need it in an open region ( not a gap). Magnetic energy of the the magnet is constant. I don't think you can increase the field in the air without limiting the air region to a smaller volume.

 

[Waterfox]

I'm not entirely sure how the sheet will affect the field but I expected something like this:
http://img805.imageshack.us/img805/3425/magneticfield.jpg

Is this what will happen? To simplify things, will this increase the field density in the small volume above the magnet like in the picture? If I placed a magnetometer 1mm above the magnet's surface will I get a higher reading with the sheet of high permeability metal?
If not how can a concentrate the field so its closer to the surface of the magnet and not so spread out?

 

[Hassan2]

Yes such a configuration, it strengthen the field to some extent. Sorry, I misread you previous post as placing the metal sheet on the magnet and gave you the wrong answer.

I did a simulation of this problem with my finite element software. The simulation is not exact but the results shows the effect of the sheet to some extent. I replaced the magnet with a coil because my software doesn't support permanent magnet. It shows about 25% increase in the field ( for the relative thickness of sheet to magnet shown in the picture) . The image of the field distributions with and without the metal sheet is attached. The arrow size is proportional to the field magnitude at the corresponding point.

The sheet is iron here. A higher permeability would give have a better but i think the difference would little. The thickness of the sheet is important too but above a certain thickness ( depending on the the magnet's height) the different is negligible.http://www.uploadup.com/di-2O73.jpg

 

[Waterfox]

Thanks for going to effort of running a simulation, it seems my prediction was true despite my limited knowledge of magnetism. Also a 25% increase will actually make the thinner magnets slightly more effective than the thicker ones for my use, so given imperfections it should be about equivalent which is what I was hoping for.
Thanks for helping!

 

[Hassan2]

Yes you were right and you have a good common sense to predict this. I am looking forward to seeing the measurement result. Please share it with us once done.

 

[cmb]

With the steel sheet, you're essentially removing the magentic energy from the space on the other side of that sheet, so the space on the magnet side of the sheet is then filled with higher field level. The total magnetic energy in the space around the magnet is [much] the same, but it now occupies a smaller space, thus higher field.

 

[M Quack]

You could also try to insert your magnets into a U-shaped steel bar, especially if the fit is rather tight. This will give the same effect as in your sketch, but the field lines would be bundled even closer to the edge of the magnet.

If the U is a bit higher than the magnet, you should get higher field at the edges than in the center. This would stabilize the trajectory of the surfer. Obviously, the U has to be wider than the board.

 

[Robin07]

Off of left wall here. Look up nullflux 8 coil and fasion a coil above or underneath your graphite sheet/board. Start with a single layer or if Hassan2 would FEA it you may be able to find the correct wind. I could use FEA results write about now. Anyways it may work for you. Good luck.