winding a electromagnet

[Honk]

That will be impossible to calculate unless the exact airgap distance is known.

[z_p_e]

Honk,

Surely knowing the number of turns, the current (DC), the core permeability, and the core length, one can determine what the Gauss reading would be at one end of the coil?

There must be a relationship?

I know it could be determined empirically, so why not mathematically?

Isn't the air-gap distance just the length of the solenoid?

[Honk]

No, one must also calculate especially on the airgap to get to know the flux, but the formula just show average flux, not face flux.
And yes, the length of the solenoid is part the airgap, but the total size and area matters to.
This is why a long solenoid have less face flux compared to a short solenoid, but inside the core the flux will be extremely high.
If you bend a solenoid into a C, with a very narrow opening between ends, then it is easy to reach high flux levels.
Actually, in a closed electromagnetic system (no airgap) it just takes a few hundred milliwatts to reach really high flux levels.
But as soon a an airgap is introduced the flux levels drop like a rock.

If you look at the cores used for switched power supplies you can get them at various permeabilities and inductances.
But increased permeability gives less power throughput due to easier saturation of the material.
This is why I on daily basis calculate the cores I use to fit the chosen design perfectly, but I never calculate face flux
because there is no need for me to know this when I design my electronics. It is very difficult to calculate this when using
an open solenoid electromagnet. There's just to many uncertain parameters to get an accurate result.

The best I can do is to maximize the magnetizing force, then use the best core possible and measure the face flux using a gaussmeter.

[z_p_e]

metalspider,

This may help. Shows you how to calculate the field strength both inside (in the middle) of the solenoid, AND at the end (which is the one you want).

I was confident there would be a formula out there...just had to find it. I hope it is accurate.

Have fun.

http://www.physics.rutgers.edu/ugrad/276/21-Ampere-S00.doc

uo is the permeability of free space (4Ïâ,¬ x 10-7), but I think you want to use the ur of your core material. Soft iron is about 5000 (I've seen anything from 1000 to 7000)

B is in Tesla (T). 1T = 10,000 Gauss

[Honk]

Yes, this is right, but the solenoid Paul wants has a rectangular metallic core, not circular.
This complicates the calculations. A rectangular metallic core and a return air gap of "uncertain" proportions.
But I don't know if this affects the formula. Kind of hard to calculate. But I wish Paul the best of luck.
(My bet is to go for the strongest magnetizing force possible at manageable cooling)