This might be pedantic, but there is only one electric field and one magnetic field, and they are linked. Everything operates against the same fields. By definition, a field takes on a value everywhere.
Electrons need a low resistance path relative to their voltage to move freely, and that’s what a circuit provides. The movement of electrons induces a magnetic field, which in turn powers the system.
The electric and magnetic energies are parts of the same force, and we take advantage of the batteries voltage to push electrons to create the magnetic field. The push of electrons is backwards from what we consider “classical” electricity flow (electrons go from negative to positive).
Putting a resistance on the circuit draws energy from the field induced from the moving electrons. This converts the electromagnet energy into heat, movement, vibration, etc. in other words: work.
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