If we consider a steel ball falling under gravity in a cup (potential well) and being stopped at the bottom by an obstacle then energy conservation implies that the gravitational potential energy has first been transformed into kinetic energy and then in heat. After the experiment the potentiel well's height is decreased because there is a steel ball standing at the bottom. So I can repeat the experiment and each time I will extract less and less energy until I extract nothing when the well is filled up with balls. Now consider a magnet and a steel ball. The magnet accelerates the steel ball until they stick together and the kinetic energy is dissipated by heat emission. Energy conservation implies that the energy of the magnet+field+ball has changed (decreased by the amount of heat produced). My question is how is it decreased ? Is it the magnetic moment of the magnet which has been decreased, or should we take into account the induced magnetic moment in the steel ball to recompute the energy of the field ?
The problem can be simplified (for computation) but remains open if instead of a magnet and a steel ball one uses two coils, each one connected to a generator. If someone can write down the details of the calculus, it would be much appreciated. (Problem solved for the coils in Griffiths p211. The generators produce the energy dissipated by heat.) So it remains to solve the problem for a magnet and the steel ball. Is there a domain reconfiguration ?