# Electromagnet lifting capability increasing unexpectedly

1. Jan 18, 2014

### aloman

Hello,
I have been performing an experiment in which I am observing the lifting capacity of DC electromagnets while changing variables including current, number of turns, and length of the core. It is a fairly basic experiment as all the theoretical values can be obtained using the formula F=N2I2μ2A/2μ0L2

However I am getting results that do not satisfy this equation and I am not sure why this may be.
Testing an electromagnet with a carbon steel core of length 6.5cm and 77 turns in the solenoid with currents of 5.04 A , 3.77 A and, 2.51 A I get average maximum lifting mass results of 0.7447 kg, 0.4179 kg, and 0.1875 kg respectively. However when I test the magnet with a core length of 12.25cm, 154 turns and the same currents, (which according to the theory should yield results of 1.126 times that of the first magnet) I get the following results of 1.7027 kg, 0.8407 kg, and 0.4036 kg respectively. The results of the second magnet are approximately two times greater than they should be according to the first magnet and the theory.

Could it be that I am missing something obvious, and if so what? Any input would be valued.

Last edited: Jan 18, 2014
2. Jan 18, 2014

### Baluncore

If there are other magnetic materials nearby, they may distort the field differently because the other pole is in a different position, depending on the length of your test core.

3. Jan 18, 2014

### aloman

I don't think the effects would be so extreme if that were the only reason. I am thinking it could be caused by the mass i'm lifting and its addition to the length of the system. If this is the cause than there is far to much complexity in the field path for my ability level and understanding of magnetic flux to make any creditable claims. Though Believe if I were to change my setup so the magnet was only ever in contact with a piece metal that remains constant and a variable non-magnetic mass suspended from the constant piece.

as follows:

Last edited: Jan 18, 2014
4. Jan 18, 2014

### OmCheeto

It looks as though you've used the wrong equation. According to wiki, that equation is good for a horseshoe type magnet:

Bolding mine

5. Jan 18, 2014

### aloman

That is true, I have an "i" magnet. What equation would I use then?

6. Jan 18, 2014

### OmCheeto

I'm not sure. I've been working on your problem on and off since you first posted, and the only answer I have is; "It's complicated".

I've never experimented with electromagnets, nor have I studied them since university, 30 years ago.

It might be possible for us to derive an equation for your system, if you were to provide us with the cross sectional area of your core.

7. Jan 18, 2014

### aloman

the cross-sectional area is 1.2668x10-4 m

I have also been wondering how direct the relationship between the magnetic force and lifting capacity is, If a electromagnetic force of 16 N is able to lift approximately 1.63 kg of steel then it becomes possible to estimate the relative permeability of my core.

8. Jan 18, 2014

### aloman

9. Jan 19, 2014

### OmCheeto

I was about to give up, but I ran across the equation for the pull force of a single magnet:

m=(B2A)/(2μogn)

From which you can derive "k", and subsequently μ, for the first phase of your experiment.

The following statement tells me that this is not a "plug and chug" problem, and is therefore not within my abilities to solve:

ref

Hysteresis curves always hurt my brain, as I recall.

And this:

indicates that although you doubled the length of your core, it really didn't matter.

10. Jan 19, 2014

### aloman

Thank you very much I think I have a fairly reliable approximation now. I was able to get a formula that seems simple enough.
lucky for me i'm not planing on going into electrical engineering.