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First, this is not a post about perpetual motion machines, although thinking about perpetual motion machines made me think of some issues. Something that is bothering me is the idea of a magnetic force not doing work. Well sort of. It’s completely clear to me that the magnetic field does no work since the magnetic force is always perpendicular to the displacement. \mathbf{F} = q( \mathbf{E} + \mathbf{v} \times \mathbf{B} ) and W = \int \mathbf{F} \cdot d \mathbf{x}
What’s made me confused is I’ve come across some claimed perpetual motion machines. I understand that true perpetual motion machines cannot exist because something that does work without the input of energy violates conservation of energy. But I’m hung up on what could be called a “perpetual motion machine” such as a water wheel, but using magnets. A water wheel can do work, but obviously energy is being put into it by the flowing water. When it comes to magnets, a magnet can indirectly do work such as lifting a paper clip or another magnet. But in that case I assume that the work is actually done by the electric field of displaced of moving charges(electrons) towards the magnet. The magnetic force changes the directions of the electrons towards the magnet, then the electric field from the electrons pulls the lattice of the wire with it, so it’s the electric field doing work. This brings up a question I’m struggling to answer. Could some arrangement of magnets then be put together to do work(even if it isn’t done directly by the magnetic field)? If so, when would it stop producing work? I know the energy density associated with a magnetic field, W = \frac{1} {2 \mu_o} \int B^2 d \tau which is attributed to the energy required to create the field, so I would think that the magnetic field would continue to diminish as work was being done. But could thermal excitation of the electrons from outside the system continue to provide energy to the electrons and therefore the magnetic field so that this thermal excitation would act as the water in the water wheel? What am I missing?
What’s made me confused is I’ve come across some claimed perpetual motion machines. I understand that true perpetual motion machines cannot exist because something that does work without the input of energy violates conservation of energy. But I’m hung up on what could be called a “perpetual motion machine” such as a water wheel, but using magnets. A water wheel can do work, but obviously energy is being put into it by the flowing water. When it comes to magnets, a magnet can indirectly do work such as lifting a paper clip or another magnet. But in that case I assume that the work is actually done by the electric field of displaced of moving charges(electrons) towards the magnet. The magnetic force changes the directions of the electrons towards the magnet, then the electric field from the electrons pulls the lattice of the wire with it, so it’s the electric field doing work. This brings up a question I’m struggling to answer. Could some arrangement of magnets then be put together to do work(even if it isn’t done directly by the magnetic field)? If so, when would it stop producing work? I know the energy density associated with a magnetic field, W = \frac{1} {2 \mu_o} \int B^2 d \tau which is attributed to the energy required to create the field, so I would think that the magnetic field would continue to diminish as work was being done. But could thermal excitation of the electrons from outside the system continue to provide energy to the electrons and therefore the magnetic field so that this thermal excitation would act as the water in the water wheel? What am I missing?