How does the shape of an electromagnet pole affect the field produced?

[ptabor]

I'm attempting to get a rough estimate on how the shape of an electromagnet pole will affect the field produced. Most of the poles you see in labs are tapered, and not simply cylindrical - I'm wondering how this affects the field. After all, there has to be a reason why they would do such a thing.

physically, I imagine that a very very narrow pole would have field lines concentrated strongly at the tip, giving a high B density but at the expense of uniformity. On the other side of the coin, a large flat cylinder will have field lines which are less dense, but more uniform.

My understanding falters in the middle, with a "conical" shaped pole.

If anyone can provide some insight i would be appreciative

 

[NoTime]

Magnetic circuit design, with open poles, tends to be a black art.
Less so for closed magnetic circuits.
The rules for magnetic circuits are much like those for electric circuits.
As I understand it, some of the recent software can do a fair job of modeling, but there are no closed form solutions due to somewhat ambiguous multiple leakage paths.

My guess is that a larger core has less saturation, so tapering the core can reduce field leakage over the body of the coil, giving an effective increase in field strength at the pole.

 

[Phrak]

hmm. I thought I posted an analytic solutions, or sorts, here.

 

[NoTime]

hmm. I thought I posted an analytic solutions, or sorts, here.

There were a bunch of these mag questions all at once, you posted to a lot of the other ones.
I don't remember you posting to this one.

I think there are commercial products that can get an iterative approximation to a question like this.
If you have an analytic solution feel free to post it.
AFAIK, there are only analytic solutions for closed magnetic circuits.

 

[Phrak]

There were a bunch of these mag questions all at once, you posted to a lot of the other ones.
I don't remember you posting to this one.

I think there are commercial products that can get an iterative approximation to a question like this.
If you have an analytic solution feel free to post it.
AFAIK, there are only analytic solutions for closed magnetic circuits.

Thanks, NT. Re:analytical; I think I've been abusing the language

The magnetic field is had by summing over infintesimal dipoles, but which way do they all point? If I had to, i'd approach the problem like this: assuming no hysteresis, the minimum energy occurs when there's no torque on any dipole, so it may amount to finding the extremal in one variable, the energy. It's a two dimensional problem in r and z, with the diople magnitudes scaled by r.

I'm actually more curious as to how this is normally calculated, then my own suppositions, so I wonder if this is the usual method.

 

[NoTime]

Looks like it's valid only for air core where L<<D, but I did find this

http://ieeexplore.ieee.org/Xplore/l...8/04475321.pdf?tp=&isnumber=&arnumber=4475321

Unfortunately, I don't have an Id for IEEE.