Does making a magnet move require more energy than a non-magnet?

Question

I know that electric fields store energy, with their energy in an infinetesimal volume being proportional to $E^2$ at that point. I also know that a moving magnet creates an electric field (consequence of Faraday's law of induction).

Together to me this seems to imply that if I have two pieces of iron, identical except for the first one being magnetised and I apply a force on them to make them move and give them $1\text{J}$ of energy each, the second one will end up with a higher velocity because some of the energy given to the first one will go to setting up the electric field around it so it'll end up having less kinetic energy, hence I'd need to do more work upon the magnet to give it the same velocity compared to the non-magnet. This seems very weird and non-intuitive to me so I was wondering if my intuitions need updating or I'm making an error somewhere.

Answer 1

Yes, making magnet move will generate disturbance in electromagnetic field, which will result in propagation of electromagnetic waves. These waves will carry energy and momentum, which will have to be supplied by you, when you move the magnet. Not something one usually thinks about when talking about magnets, but when you start talking about moving charges, you can get into things like Radiation Resistance, which describes loss of energy in antennas as a result of emitting radio-waves. Kinetic Inductance is another similar phenomenon. Usually used to describe difficulty in accelerating charges due to finite effective mass, but since effective mass of electrons in a solid includes effects due to electromagnetic coupling, this mass will also include effects due to emitting waves.

More generally, for non-relativistic electrons, the conjugate momentum, i.e. the bit that is conserved if space is translationally symmetric, is $m\mathbf{v}-q\mathbf{A}/c$ (libretext), where $m$ is mass, $\mathbf{v}$ is velocity, $c$ is speed of light, $q$ is charge and $\mathbf{A}$ is vector potential (of the electromagnetic field). So conservation of momentum for electron literally involves electromagnetic field. I am pretty sure similar expressions can be derived for particles with no electric charge but present magnetic dipole.

If you want to develop this a bit more, it might be good to get acquainted with Lagrangian/Hamiltonian mechanics. This will allow you to define what you mean by momentum and energy, and will provide you with better tools to understand coupling between charges/currents and fields.