# How to concentrate magnetic fields using the least amount of material possible for a fixed area

So the goal is to a build a device that will redirect field lines from earths magnetic field at the magnetic north pole into a point.

The goal is to maximize the area / amount of magnetic flux redirected while minimizing the amount of material used in this device.

Initially the thought I had was a hollow cone shaped magnet whose magnetic orientation is the same as the earth's would be ideal for this. Image below with magnetic field lines in violet drawn for how I believe will happen the field would interact with the cone: Naturally an idea arises. Why use a cone at all? We could after all just have a flat disk that covers the same area and then just have a prong extending from it in the center to minimize the surface area used.

So I came up with this idea: But even then... why even have the disk? could we perhaps just have a cage of tentacles try to attract and trap magnetic field lines without even having a disk? So now the amount of material used scales linearly as opposed to quadratically So is it possible to do better than this for minimizing the amount of material one uses and still successfully redirecting field lines?

• Why did you label the disk as being diamagnetic ? What is the physics principle behind "tentacles try to attract and trap magnetic field lines" ? Question makes a lot f assumptions which are not justified IMHO.
– AJN
Dec 8, 2022 at 13:18
• The upper disk is diamagnetic since since I assumed the field lines would just pass through vertically if it weren’t (maybe they’d move closer to the center but not by much). The tentacle approach is basically each tentacle is acting as a magnet Dec 8, 2022 at 13:48
• I acknowledge the question somewhat sucks as it is currently written so I have a meta post trying to figure out how to properly state the question: engineering.meta.stackexchange.com/questions/666/… Dec 9, 2022 at 2:35

A limit on minimizing material is that the field will leak out if you exceed the material's saturation magnetic field, e.g. $$\sim 2$$ T in soft iron, or $$\sim 0.8$$ T in mu metal. This limits the thinness of your horizontal collector layer and how narrow your tentacles or central pillar can be. To minimize cost instead of material, you might want to use cheaper soft iron (with relative permeability $$\mu\sim 5000$$) for the collection areas and only use expensive high purity iron ($$\mu\sim 200000$$) for where the flux is most concentrated. (Metglas has even higher permeability, $$\mu\sim 10^6$$, but its saturation field is lower $$\lesssim 1$$ T.)