The magnetic field emitted by the magnet falls off at a rate equal to the square of the distance:

https://socratic.org/questions/how-does-distance-affect-magn...

>"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:

https://en.wikipedia.org/wiki/Inverse-square_law

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.

But,

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?*

?