Unanswered Question: Who Does Mechanical Work for Magnetism?

[Frank66]

May be a trivial question...
The forces that arise from the magnetic field are Lorentz forces that not make mechanical work.
When a piece of iron is attracted by a magnet is accelerated and its kinetic energy increases: Who does the work necessary?

 

[ghc]

I'm not sure about my answer, that's why I will formulate it in a question:
when a magnetic dipole with a magnetic moment \vec{\mu} is in a magnetic field \vec{B}, it has an energy E= -\vec{\mu}.\vec{B}. Now if \vec{B} is not uniform, there will be regions in space where the energy of the dipole is lower than in other regions and the dipole will move to that places, we call it virtual work, is that right?
The force exerted on the magnet dipole is \vec{F} = -\vec{\nabla}E, true?