# How do electrical motors obey the conservation of energy?

Feynman introduces the concept of an electromagnetic motor with this diagram.

I believe I understand why the wire turns when there is current through it, because $$F = q(\mathbf{E} + \mathbf{v} \times \mathbf{B})$$, but I do not understand how this is allowed under conservation of energy.

Supposing I had a perfectly conducting wire, it seems I could close the loop and have an electron travel continuously around it, causing perpetual motion.

What am I missing? I suspect that my idea of closing the loop is wrongheaded, but would appreciate a principled explanation of why.

• I’m not really well versed on this subject but it is my understanding that perpetual motion machines violate the second law of thermodynamics not the first,?applies to conservation of energy – Bob D Jan 19 '20 at 6:56
• @BobD If I have a motor that turns my wheels and never stops (against friction), it gives me free energy, violating the first law, right? – Eli Rose Feb 24 '20 at 15:19
• You mean after taking the motor away the wheels move forever? – Bob D Feb 24 '20 at 15:23
• Nope, just a motor that doesn't stop, attached to a little car with wheels. – Eli Rose Feb 24 '20 at 15:57