Increase Electromagnet Strength Without Additional Energy

[Malverin]

Hello,
If we have an electromagnet

with some lifting force, for example 10N, and make core area smaller at the ends, to concentrate the magnetic field (without saturating the core)

according to the formula, for magnetic flux

magnetic field density B , will be greater.

For example if we make area, 4 times smaller we will get 4 times greater B

Then electromagnet force will increase too, and become 4 time greater

So we get more force, without puting in additional energy.
But I have made a magnetic field simulation in FEMM
http://www.femm.info/wiki/HomePage

and there is an increase in B, but much smaller than this according to the formula.
Is there something wrong with the simulation, or my thoughts are wrong...?

http://en.wikipedia.org/wiki/Magnetic_flux

http://en.wikipedia.org/wiki/Electromagnet

 

[mfb]

and there is an increase in B, but much smaller than this according to the formula.

What do you get as result?

Is your distance between the magnets much smaller than the length scale of the surface, even with the smaller surface?
Is B homogeneous within that surface?

 

[Malverin]

What do you get as result?

Is your distance between the magnets much smaller than the length scale of the surface, even with the smaller surface?
Is B homogeneous within that surface?

The result was about 2 times increase in B, with area ratio of 5
Yes, the distance is much smaller than the length scale of the surface.
I have measured the field in the core too (in point near the smaler surface, and in point near the big surface)
Inside the core B change should be according to formula I think (there are minimum or no losses inside), but it is not...

 

[Malverin]

Here is a screenshot of Neodymium magnet simulation. Area ratio is 19 , B increase is about 3 times. So this means more then 80 per cent flux loss! How is that possible?
Permeability of air is so much smaller. Where did the flux go?

 

[mfb]

That lacks the opposing magnet, the return yoke, and it looks too sharp. As you can see at the field lines, most of the field goes through the sides.

 

[Malverin]

That lacks the opposing magnet, the return yoke, and it looks too sharp. As you can see at the field lines, most of the field goes through the sides.

The return yoke to close the loop makes things worse...

This has no sense...

 

[mfb]

This does not look like your original sketch. And 2 Tesla is a typical saturation strength... are you sure you do not have saturation?

 

[Malverin]

This does not look like your original sketch. And 2 Tesla is a typical saturation strength... are you sure you do not have saturation?

Saturation is not the problem. I have used weaker fields and the ratio is the same.
There can be many variants of this setup. The principal is important.
I have tried differen forms and ratios, and increase in B is never equal to this in the formula.
Not even close...

 

[mfb]

Hmm well, it cannot be exact, but I would have expected that you can get a reasonable amplification. Well okay, you get an amplification...