You should get lots of answers on these questions. I believe that in theory what you have stated has a limited amount of truth in it. For it to be substantial, however, you would need very strong magnets, possibly making any benefit cost prohibitive.

In some ways this sounds like a magnetic bottle. Have you examined those? Do a search.

GA I agree; not sure about case 1) though; sounds feasable, but if the OP wants to save a lot of theoretical work, he should do the experiment.

Oh wait, I have still another question for him (or you):

When you break a rectangular magnet, you can't re-join the two broken ends, they become of the same pole, right ? well, which of the two halves reverts its field ?.

I don't think that is correct. I think the magnetism is linear along the bar, if the north is to the right, when you break it, both ends have north to the right and the broken ends attract each other.

One of the best ways I've found of answering such questions on paper is by drawing the magnetic field, represented as directional flux lines.

Draw the magnet as a simple rectangle and draw each flux line as a complete, closed, directional loop which exits the magnet at one pole, arcs round the magnet's exterior, enters the magnet at the other pole and continues on through the magnet, forming a closed loop. You've seen these diagrams a zillion times I'm sure (except that in many of them the flux lines stop at the poles, as if to suggest that the field originates there, which it most certainly does not).

Mark the pole where the flux lines exit the magnet as 'North', and where they enter the magnet as 'South'.

Now 'cut' the magnet by erasing its midsection, whilst leaving the flux lines in-place. Mark where they exit the new piece as 'North' and where they enter the other new piece as 'South'. Repeat as necessary.

You can buy flexible magnetic sheets, I use them to attach business cards to the insides of control panels I work on. Why not experiment with them?

http://www.magnetking.com/#magnetsheet

Play with magnets and iron filings.

If you imagine you are putting your reputation on the line, then do the experiments first. I can't imagine that you live somewhere where you cannot get access to magnets.

I'm having a hard time parsing "a conical sheet of paper." Is the sheet of paper 1 x 100 or is the cone rolled from that piece 1 x 100. In either case this would be a difficult cone to work with and to roll. Perhaps you could just roll a cylinder from a less extreme piece of paper?

Sounds like you are thinking about a magnetic bearing.

Hi Folks;

Thanks for the great feedback. I am going to look online to see where I can buy lots of low cost magnets. I like the iron filing idea as well.

The conical dimensions are somewhat arbitrary save it to say that the cone is long enough to approximate a cylindar of uniform thickness for conical sectional lengths that have a length equal to the average radius of the section.

Regards and thanks!

Jim

Edmund Scientific also sells a magnetic-field 'visualiser'. Like iron filings, but using liquid crystal material instead (some kind of ferrofluid* I think). For a coarse-but-cool (vector field) visualiser, use lots of little cheap compasses, like these.

Home-brew magnetic levitation (maglev) using (highly-diamagnetic) pyrolytic carbon sheet, Halbach arrays and/or other techniques is lots of fun, too.

* If you like playing with magnets, you're gonna love what you can do with ferrofluid (which you can make yourself, btw).

Refrigerator magnet is lots of little magnets. Both poles are on the side that sticks to the Frig.