# Attraction of magnets to ferromagnetic materials with distance?

• carmatic
In summary, the conversation discusses the relationship between distance and attractive force between a magnet and a piece of iron. The only available source for this information is Wikipedia, which provides a complicated mathematical expression for the force between two magnetic dipoles. It is possible to calculate the energy stored in a magnetic field and determine how it changes when a ferromagnetic material is placed around it, but the math can be messy and complicated.

#### carmatic

all i can find on the internet are the attractive and repulsive forces between 2 magnets... where can i find the relationship between distance and attractive force , between a magnet and i.e. a piece of iron?

Dr_Morbius said:
Magnets, how do they work?

Like this http://en.wikipedia.org/wiki/Magnet

as i have said, it only contains information on the force between 2 magnets, not between a magnet and a piece of ferromagnetic material

Any luck with this?
I'm looking for this answer as well.

The force between magnets as a mathematical expression is complicated.

What I have found is the force between magnetic diople moments.

The only source that I remember specifically is wikipedia:

http://en.wikipedia.org/wiki/Magnetic_moment#Forces_between_two_magnetic_dipoles

which gave the force acting on $\vec{m}_{2}$ as being

$\frac{3\mu_{0}}{4\pi \left\|\vec{r} \right\| ^{5}} \left[ (\vec{m}_{1} \cdot \vec{r})\vec{m}_{2} + (\vec{m}_{2} \cdot \vec{r})\vec{m}_{1} + (\vec{m}_{1} \cdot \vec{m}_{2})\vec{r} - \frac {5 ( \vec{m}_{1} \cdot \vec{r} )( \vec{m}_{2} \cdot \vec{r} ) \vec{r} }{ \left\| r \right\| ^{2}} \right]$

with $\vec{m}_{1}$ and $\vec{m}_{2}$ being the two magnetic dipole moments, and $\vec{r}$ is the displacement vector from the location of m1 to m2

Last edited:
You may be able to obtain a dipole based representation of each magnet. The permanent magnet would have "bound current", which is which is obtainable from the magnetization.

It is complicated to determine the attraction between a magnet and a piece of iron (or other ferromagnetic material). What you can do, if you know exactly how the magnetic field is configured, is to calculate the energy stored in that field and then calculate how much that energy would change when you place a ferromagnetic material around it. This is totally analogous to the problem Feynman analyzed on the Feynman Lectures, volume 2, chapter 10, section 10-5, with the difference Feynman did the math for electric fields and dielectrics. But the reasoning is precisely the same.

Anyways, unless you have a very simple system (such as a uniform magnetic field and a ferromagnetic plate), the math you will need to solve your problem can be quite messy.

## 1. What is the mechanism behind the attraction of magnets to ferromagnetic materials with distance?

The attraction between magnets and ferromagnetic materials is due to the alignment of magnetic domains within the material. These magnetic domains are microscopic regions where the atoms are aligned in the same direction, creating a net magnetic field. When a magnet is brought close to a ferromagnetic material, the magnetic fields of the two objects interact, causing the magnetic domains in the material to align with the magnetic field of the magnet. This alignment creates a strong attractive force between the two objects.

## 2. How does the distance between a magnet and a ferromagnetic material affect the strength of the attraction?

The strength of the attraction between a magnet and a ferromagnetic material is inversely proportional to the square of the distance between them. This means that as the distance increases, the strength of the attraction decreases at a rapid rate. For example, if the distance between a magnet and a ferromagnetic material is doubled, the strength of the attraction decreases by a factor of four.

## 3. Can the attraction between a magnet and a ferromagnetic material be blocked by other materials?

Yes, the attraction between a magnet and a ferromagnetic material can be blocked by other materials that are not ferromagnetic. These materials, such as wood or plastic, do not have aligned magnetic domains and therefore do not interact with the magnetic field of the magnet. This means that the attraction between the magnet and the ferromagnetic material will not be able to pass through these non-magnetic materials.

## 4. Why do some ferromagnetic materials attract to magnets while others do not?

The ability of a material to be attracted to a magnet depends on its composition and structure. Ferromagnetic materials, such as iron, nickel, and cobalt, have a specific arrangement of their atoms that allows them to have strong magnetic properties. Other materials, such as copper or aluminum, have a different atomic structure and therefore do not have strong magnetic properties.

## 5. Is the attraction between a magnet and a ferromagnetic material affected by temperature?

Yes, the attraction between a magnet and a ferromagnetic material can be affected by temperature. As the temperature of the material increases, the motion of the atoms within the material also increases. This can cause the alignment of the magnetic domains to become disrupted, reducing the strength of the attraction between the magnet and the material. At very high temperatures, the material may lose its magnetic properties altogether.