I core vs U core electromagnet

[eddielnl]

I am interested in calculating the magnetic field strengths of electromagnets with a couple of different core geometries, and I have been making some calculations that I think have gone wrong somewhere and I was just wondering if someone could kindly point out where/how I have made a mistake.

I am trying to calculate the field strengths of a straight cylindrical core electromagnet and also a U shaped electromagnet. I have assumed that the U shaped electromagnet is going to produce a stronger field, given the poles are closer and the magnetic field has less distance to travel through free space than the cylindrical core electromagnet.
However, when I do the calculations, I get a lower value (in Tesla) for the U shaped electromagnet than the straight cylindrical core electromagnet. Either my initial assumption the U shaped electromagnet would be stronger was incorrect, or my calculations are wrong (given my lack of scientific knowledge, either are pretty likely!)

For both magnets, the number of turns, the length of the core, the current, and the core material permeability are the same values.
Number of turns = 60
Core length = 0.0152 meters
Current = 0.001 Amps
μ Core Permeability = 50
μ0 Free space Permeability = 0.0000012566

For the straight cylindrical core electromagnet, I used the formula I got from here

http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/solenoid.html

permeability*turn density*current = B

so I did the following calculation
permeability (50 * 0.0000012566) * turn density (60 / 0.0152) * current 0.001 = 0.00024801315 Tesla

For the U shaped electromagnet, I used the formula I got from here

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

Under the heading "Magnetic field created by a current" it says "For an electromagnet with a single magnetic circuit, of which length Lcore of the magnetic field path is in the core material and length Lgap is in air gaps, Ampere's Law reduces to:

turns*current = B((Lcore/μ)+(Lgap/μ0))

Which I changed to
(turns:60 * current:0.001) / ((Lcore:0.0152 / μ:50) + (Lgap:0.0008 / μ0:0.0000012566)) = B = 0.00009424495 Tesla

0.00009424495 Tesla for the U shaped electromagnet vs 0.00024801315 for the straight cylindrical core electromagnet seems incorrect to me. I feel like, if anything, it should be closer to the other way around. I have checked each equation using an online calculator, with Excel, and through simply typing each equation into the google search window
eg
(50 * 0.0000012566) * (60 / 0.0152) * 0.001 =
and
60*0.001/((0.0152/50)+(0.0008/0.0000012566)) =

BUT I can't seem to find where I have gone wrong. Do these results seem strange to anyone? Am I using the wrong formulas perhaps?
Any suggestions would be most welcome!

 

[Skogsgurra]

Your second result seems plausible.
Your first one does not. For a rod, there is a huge air gap (from one end of the rod to the other). I can't see that "gap" anywhere in the first calculation. Also, there is nothing but "fringe effects", so you cannot use that simple formula.

Your feeling is good. The U shape shall give you more Teslas.

Gunnar Englund

http://www.gke.org

--------------------------------------
Half full - Half empty? I don't mind. It's what in it that counts.

 

[eddielnl]

Thanks Skogsgurra,
Yeah, I originally assumed that the "gap" in the first formula was accounted for by multiplying the core permeability by the free space permeability (50 * 0.0000012566) which I thought represented when the magnetic field travels from one end of the rod to the other. Now I am not sure!

 

[eddielnl]

Also,
Changing the permeability of the core material value in the second, U shape core formula has only a very small effect. (For example changing the core permeability from 50 to 1000)
from
(60 * 0.001) / ((0.0152 / 50) + (0.0008 / 0.0000012566)) = 9.4244955 × 10-5
to
(60 * 0.001) / ((0.0152 / 1000) + (0.0008 / 0.0000012566)) = 9.42449977 × 10-5
this difference seems so small for what I thought was such a big change. Does this seem plausible?