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?

 

[astrokreng]

The work done in this scenario is done by the magnetic field itself. The magnetic field exerts a force on the iron, causing it to move and gain kinetic energy. This work is done by the magnetic field through the Lorentz forces acting on the iron. So, in a way, the magnet is doing the work by exerting a force on the iron. However, it is important to note that this work is not considered mechanical work as it is not caused by a physical displacement of the object, but rather by the force exerted on it. This concept can be further explored through the principles of electromagnetism and the relationship between electricity and magnetism.