I have read the forum textbook about E/M, the relevant section of ARRL-2014 and have watched 2-3 videos on youtube. It's all clear how things work but I don't get a clue about what each magnetic unit of measurement really means.
In the attached diagram, I know that what I 'm really asking is the force (in kg or Newtons) that the electromagnet pulls the black rectangle, and from what I have understood so far this force is a function of:
1. Current through the coil (I) -Linear
2. Number of coil turns (n) -Linear
3. distance between coil and rectangle - inverse square (double distance = 4 times less force)
4. Properties of the material that the rectangle is made of (retentivity?)
5. Properties of the meterial in the center of the coil (permeability?)
6. Not sure if the diameter of the coil (d) and the surface of the rectangle are parts of the equation

Is there an equation to calculate Force taking account of all these variables and how all these variables relate to Gilbert, Maxwell, Oersted, Gauss . Is there any place to explain more extensively these terms?

 

Hi dk31,

Here's the equation

F = (N x I)² x k x a / (2 x l²)

F = electromagnetic force in Newtons
N = number of turns
I = current in Amperes
a = cross-sectional area of electromagnet in square metres
l = the distance between the electromagnet and the piece of metal in metres
k = 4 x 10⁻⁷x 22/7 = magnetic constant

Regards,

Nandu.

Thanks for the equation. Is this valid for coils without a core (air core coils)? Also, to calculate the cross-sectional area of the electromagnet, do you know if you have to use the inner diameter (core diameter), outer diameter or an average diameter of the coil?

 

Hi dk31,

No, it's not valid for air core coils.

The area is that of the iron core.

Regards,

Nandu.

Thanks for helping out. I have put your formula in an excel spreadsheet and I 'm playing around. Next step will be to try to confirm the figures on my primitive lab

 

Gilbert, Maxwell, Oersted, Gauss

You should not use these units as they are obsolete.

They belong to an older scheme of electromagnetic units, where the actual formulae and some definitions are different from the modern ones, which was called the CGS system.
Worse there was more than one CGS system which is partly why it was changed and all the formula brought into line.

The modern units are the rationalised MKS system.

Because of the change to the formulae and definitions the equivalents from one system to the other are confusing.

 

Sorry for the late response. What I really meant is what these unints measure and how the relate to force measured. I understand that the SI units are the standard now.

So, anyway that''s what I did to confirm the formula. I took a 6M threaded rod and added two blind nuts to define the room for the coil. Then, I took a 0.2mm wire and counted 1800 turns. Then I cut the the rod, and made a bridge so that I could see on the scale how the weight of a metal piece would become smaller when the E/M is turned on.

Then I played around with different Amps and distance between E/M and piece of metal. I wrote down some 20 different combinations and I get a more or less consistent 25% force reading compared to the formula.
For example at 310mA and 7mm above the scale:
F = (N x I)² x k x a / (2 x l²) =
(1800 turns * 0.31Amps)^2
* k --->(0.0000013)
* pi()*0.003^2 square meters -->(Screw diameter is 6mm so r = 0.003m)
/(2*0.007^2) --->(7mm above the scale)
-------------------
=0.108Newton or 11.1 gr
The real life measurement of force is only 2.7 gr (25% of the formula)
It could be that the 6mm thread is actually smaller in diameter compared to a solid 6mm rod (4.77mm inner diamter) but again this only changes the difference to 40%.
Last, it could be that the trhead is not pure iron, but I can't see any big difference between how the thread and a steel piece are attracted to a magnet.
Any thought on this would be great ...

 

Yes, reading about permeability, the material of the core can boost strength many times relative to air core.
I guess the above formula is valid only for iron core(?). Or it could be complemented by multiplying with a coefficient of relative permeability of the core compared to iron. In my case that coefficient would be ~0.25.

Could you also help substitute in the above formula any magnetic units? For example, NxI equals magnetomotive force in Amp-turns so another way of writing the formula would be:
F = (N x I)² x k x a / (2 x l²) <=> F = (mmf)² x k x a / (2 x l²)
If I had a way to measure flux density (in Tesla) how would the formula change?

 

I just found it. http://info.ee.surrey.ac.uk/Workshop/advice/coils/force.html

F = B2 A / (2 μ0)
where
B:flux density
μ0: magnetic constant
(Maxwell's pulling force formula)

Thank you all, I think now I have enough tools to play