The magnetic field emitted by the magnet falls off at a rate equal to the square of the distance:
>"Magnetic force obeys an inverse square law with distance. ... If the distance between two magnets is doubled the magnetic force between them will fall to a quarter of the initial value. (F/4) If the distance between two magnets is halved the magnetic force between them will increase to four times the initial value."
That is, magnetism is an "Inverse Square Law" effect:
So now, here's my question:
If you have a non-magnetic iron or steel screwdriver, or other piece of iron or steel -- you probably have at one point in time or another connected this item to your magnet, and observed that magnetic objects -- could now be attracted with the tip of the previously non-magnetic ferromagnetic metal item...
Simple enough, right?
But here's the thing:
You see, I observe that in addition to this happening, via the non-magnetic iron or steel screwdriver or via a non-magnetic iron or steel bar, or other piece of metal --
THE MAGNETIC FIELD HAS BEEN EXTENDED, IN SPACE, AWAY FROM THE MAGNET
So now, my question can be formulated thusly:
What's the maximum length a magnetic field can be extended, via a non-magnetic metal, from itself?
Also, what's the mathematical equation, the mathematical relationship, for such field extension?
Because it's not the inverse square law anymore...
In other words, I have a magnet.
It's field falls away as the inverse square root of the distance.
Now I connect it to my non-magnetic iron or steel screwdriver, or my non-magnetic iron or steel bar.
It's field is extended (although it might lose some strength) -- to the end.
Now the inverse square law, via the non-magnetic iron or steel item -- does not apply, because we've actually "moved"/"extended through" the magnetic field, through the ferrous metallic item.
Of course, at the end of this extension -- the inverse square law applies again... But it applies how it always did, that is, through space!
But, through an object made with a ferromagnetic metal or alloy (Iron, Steel, ?) --
what's the max distance a magnetic field can be extended, and what's the exact mathematical equation for such field extension?
How does the shape of the non-magnetic, ferromagnetic metal -- affect the max distance?
For example, let's say that a non-magnetic, ferromagnetic metal object -- was cone shaped or pyramid shaped -- if the base of the cone or pyramid was placed on the magnet, then the other end, due to it being pointy in nature -- would collect the magnetic field at that point, and extend it farther into space than a structure like a beam or bar of the same length...
Conversely, if the pointy end was placed near the magnet, the flat end would dissipate the magnetic field, which should mean that it would travel (from that point onward) a less amount in space...
Also, a related question to this is, what's the best shape of the non-magnetic, ferromagnetic metal -- such that it extends the magnetic field for the max distance from it?
Also, if a specific shape is good at blocking/dissipating the magnetic field -- perhaps that makes it a candidate for such things as Hallbach arrays, etc. (I don't know -- this is pure speculation...)