Questions on ferromagnetism and attraction

[FieldOpsGirl]

I have questions about magnetic attraction in both conceptual and application. I am not a physicist (medical background) so I may have insufficient understanding of the concepts involved, but any clarification would be helpful.

Suppose I have a field source, such as a permanent magnet, and a ferrous object is rigidly held at a fixed distance from the source. I want to know how to calculate the force of attraction for a particular material and particular shape (i.e. a cube of iron). As the iron approaches the source, it is pulled in with increasing force up to the point of contact.

My current understanding of ferromagnetic materials is that, when exposed to a field, (1) permeability greater than that of a vacuum (or air as the case may be) allows flux to be ‘conducted’ through the material. At the same time, (2) the ferromagnetic material begins to act a magnetic sources itself, and (3) at a point of saturation can channel no greater amount of the flux.

As the distance between two magnets increases the pull should increase in an inverse squared relationship, but the “magnetic strength” of the iron is increasing as well so is there a different (cubic or other) relationship in the case of ferromagnets? If so, in the case of “saturation” does the regular inverse squared force relationship resume? The real question then is, given enough information about the materials involved, are there mathematical formulae to represent the interaction of iron and magnet, namely force?

 

[Naty1]

I want to know how to calculate the force of attraction for a particular material and particular shape (i.e. a cube of iron).

I'm not anywhere near current on magnetic designs and calculations, but I'm pretty sure that's quite a complex undertaking.

You can take a look at Wikipedia http://en.wikipedia.org/wiki/Permanent_magnet#Calculating_the_magnetic_force
for some ideas...

Permanent magnets come in dozens if not hundreds of materials and strengths and shapes, and likewise "ferrous" describes a wide range of materials as well. I'd guess this kind of question is answered in tables of magnet types and ferrous material relationships where results have been experimentally measured rather than theoretically calculated. Maybe somebody knows the latter; I've never seen such theory.

 

[astrokreng]

I can understand your confusion about the concept of magnetic attraction and ferromagnetism. To answer your first question, the force of attraction between a permanent magnet and a ferrous object can be calculated using the equation F = (μ0 * m1 * m2)/(4π * d^2), where μ0 is the permeability of free space (a constant value), m1 and m2 are the magnetic moments of the two objects, and d is the distance between them. The magnetic moment is a measure of an object's strength and orientation of magnetization. In the case of a cube of iron, the magnetic moment can be calculated using its magnetic susceptibility and volume.

Your understanding of ferromagnetic materials is correct. They have a higher permeability than air, allowing them to conduct magnetic flux and become magnetic sources themselves. The point of saturation refers to when the material can no longer increase its magnetization, and the flux remains constant. This saturation point can be affected by factors such as temperature and external magnetic fields.

As for the relationship between distance and force, it follows an inverse squared relationship, but it can also be affected by the shape and orientation of the objects. In the case of two magnets, the force can also be affected by their alignment (i.e. if they are aligned in the same direction, the force will be stronger). In the case of saturation, the force may not necessarily resume the inverse squared relationship, as the material is already at its maximum magnetization.

In terms of mathematical formulas, there are many equations that can be used to represent the interaction between iron and a magnet, including the one mentioned above. However, these equations can become more complex when considering other factors such as the shape and orientation of the objects. It is important to have a good understanding of the properties and behavior of the materials involved in order to accurately calculate the force of attraction. I hope this helps clarify some of your questions about ferromagnetism and attraction.