Work done by permanent magnets

[xareu]

I recall that the energy stored in a magnetic field is half the volume integral of the dot product of magnetic field and flux density vectors (H and B). When you place a piece of iron near a magnet, it does a work by attracting it. If H is 0 (I think there is only the magnetic moment vector M and the flux density B), where does this energy come from?. Is not HxB always applicable?
If the answer is that it was stored when the magnet was "created", how is it "replenished" when the piece of iron is removed (since the magnet can attract pieces of iron again and again)?

 

[Hesch]

If H is 0 (I think there is only the magnetic moment vector M and the flux density B), where does this energy come from?

H = B/μ , so if B>0 and H=0, μ must be infinit.
A magnet will always attrack the material/liquid that has the greatest μ-value surrounding it, and will repel the materials/liquids with lower μ-value.

So say that you submerge a magnet in a liquid containing iron particles, and that the liquid has the greatest μ-value, the magnet will repel the iron particles and will substitute the left volume by liquid, hence doing work to the liquid instead.

 

[xareu]

Yes, I do know that the magnet does a work. Here is where my question comes from: where does this work (energy) come from?

 

[Hesch]

Here is where my question comes from: where does this work (energy) come from?

Say you have a magnet in vacuum/air and that within a small volume close to a pole,
there is a magnetic energy density = ½*B*H [ J/m³ ].
Closing up a piece of iron ( with the same small volume ), the B-field will be almost the same, but the H-field will be weakened within said volume, because now the μ₀ permeability is substituded by a μ = μ₀*μ_r permeability ( H = B/μ , μ_r > 1 ).

Hence the said volume loose magnetic energy density, and this lost energy will be converted to mechanical energy.

 

[xareu]

Understood, thanks a lot Hesch