# Force exerted by an iron core electromagnet on a ferrofluid

• I
• EmeraldPlatypus
In summary, the conversation discusses finding an equation for the force exerted by an electromagnet, taking into account factors such as turn number, current, permeability of free space, core material, and distance from the electromagnet. The speaker also questions the accuracy of the commonly used equation and asks for a formula that considers the core material and attracted material. The response suggests that the problem is more complex and advises studying the physics of electromagnets for a better understanding.
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

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.

EmeraldPlatypus said:
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)

EmeraldPlatypus said:
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.

## 1. What is an iron core electromagnet?

An iron core electromagnet is a type of electromagnet that uses a core made of iron or other ferromagnetic material to enhance the strength of the magnetic field it produces.

## 2. How does an iron core electromagnet exert force on a ferrofluid?

When an electric current is passed through the coils of an iron core electromagnet, it creates a magnetic field. This magnetic field interacts with the magnetic particles in the ferrofluid, causing them to align and be attracted to the electromagnet, resulting in a force being exerted on the ferrofluid.

## 3. What factors affect the force exerted by an iron core electromagnet on a ferrofluid?

The force exerted by an iron core electromagnet on a ferrofluid is affected by the strength of the magnetic field produced by the electromagnet, the distance between the electromagnet and the ferrofluid, and the magnetic properties of the ferrofluid.

## 4. How can the force exerted by an iron core electromagnet on a ferrofluid be increased?

The force exerted by an iron core electromagnet on a ferrofluid can be increased by increasing the strength of the magnetic field produced by the electromagnet, decreasing the distance between the electromagnet and the ferrofluid, and using a ferrofluid with higher magnetic properties.

## 5. What are some practical applications of iron core electromagnets and ferrofluids?

Iron core electromagnets and ferrofluids have various practical applications, such as in magnetic levitation systems, loudspeakers, and magnetic separation processes. They are also used in medical devices, such as MRI machines, and in engineering and scientific research for their ability to control and manipulate fluids.

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