Force exerted by an iron core electromagnet on a ferrofluid

[EmeraldPlatypus]

I am trying more generally to find the equation of the fore exerted by an electromagnet. The one that I keep finding is
F=((NI)^2 A mu0)/2X^2.
N is turn number, I is current, Mu0 is permeability of free space, A is the area of the core and X is the distance from the electromagnet.

I take issue with for a number of reasons. Firstly, surely it depends on the material I am trying to attract. I know from experience that a magnet that can lift a few hundred gram of iron can barely lift a gram of ferrofluid, and the equation just gives a flat force.

It also doesn't account for any core material. As far back as GCSE I have been told that "an iron core makes the electromagnet stronger" Well how much stronger? And to what property of the material does this strength increase correlate??

Can anyone give me an equation that shows some dependence on core material and the material that will be attracted to the electromagnet, as well as all the stuff listed in the (as I see it) in complete EM force equation

 

[rude man]

You hold a short, thin rt. circular cylinder , length l, made of hi-mu metal, e.g. iron, coaxially and near a solenoid (not inside). The axial B field will be stronger near the solenoid & weaker as you move away axially.

There will be a force applied to the near end surface of the cylinder "sucking" it towards the solenoid, and a lesser force sucking it away from the solenoid on the far end. If the cylinder has very high permeability the net pressure on the cylinder will approximate $Bl \nabla B/\mu_0$ since each side sees suction pressure $B^2/2\mu_0$ with B the respective value at each cylinder end.

If the cylinder has zero relative permeability then there is no force. If its permeability is finite but not arbitrarily high then there is a force on the cylinder but the computation becomes difficult.

 

[alan123hk]

As far back as GCSE I have been told that "an iron core makes the electromagnet stronger" Well how much stronger?

Because the relative magnetic permeability of pure iron is around 5000, it is ideally 5000 times under certain conditions. However, in most practical situations, it is believed that this maximum value will not apply.
https://en.wikipedia.org/wiki/Permeability_(electromagnetism)

Can anyone give me an equation that shows some dependence on core material and the material that will be attracted to the electromagnet, as well as all the stuff listed in the (as I see it) in complete EM force equation

This is closer to an engineering problem than a physics problem, and is a more complex case involving multiple parameters. It may be difficult to give a complete calculation formula. Maybe you should study the physics of electromagnets first. This should help you understand the problem thoroughly.