# Force on a ferromagnetic material attracted by a magnet

From the Lorentz force equation we know that the magnitude of the force between a current carrying wire and a magnet field is defined as $F = ILB$. This implies that there must be a current across the wire in order for there to be a force. Now let's take a look at ferromagnetic materials such as iron for example. Let's assume that I have an iron nail which when it gets close enough to a magnet it gets attracted by the magnetic field of the magnet. How is this force (attraction) possible if there isn't any electric current across the nail?

The only conclusion I've come to is that as soon as the iron nail (or any other ferromagnetic material) gets close enough to the magnet there is a change in magnetic flux. From Lenz's law we know that a change in flux induces an EMF: $V = -N\frac{d\phi }{dt}$ If we divide that voltage by the resistance of the iron nail (which is almost 0) we should get the current across the nail which then satisfies the Lorentz force equation. Is this assumption correct? I've found one drawback from my own conclusion though, if this were true then copper should also get attracted and it doesn't.

If someone could explain how this attraction force works and if there is a mathematical expression for it I'd greatly appreciate it.

• excellent question, most of the litterature focuses on explaining magnetic force upon a moving charge but then that give us no clue about magnet to magnet or magnet to ferromagnetic forces. I believe the answer lies in atomic current, something about electrons rotating around the atom preferentially in a way or another. But I eagerly await for the experts answers – Manu de Hanoi Sep 19 '18 at 18:34