What role do magnetic fields play in these energy transformations?

actually it is an extremely difficult Q.

until the 1800s people thought electricity and magnitism were different things

now we are (almost) certain that all magnetic effects are due to electric current. movement of electric charge.

it takes advance vector calculus to describe properly but the short answer is:

1) a static electric charge has NO magnetic effect

2) if a charge is moving it is a current, and another current can interact by what we name "the magnetic field

atoms have electrons which "spin" so a magnetic field can be produced

it takes months of physics to begin to understand the 1850s version

once you understand a little of that we realize it is NOT the complete answer. Einstein Special Relativity explains it with much higher and more difficult math

the practical things like electric motors and generators can be understood with the moving charge concept. but it requires 3 dimensional vector math to get numerical results.

in short the Electic currents interact with magnetic fields to produce forces on the wires

force on wires cause motion. force moving a distance is mechanical energy = work

volts * Amps = watts the unit of electric power

1 watt = 1 Joule of energy per second

it takes mechanical power to turn generators and produce current and voltage.

current and voltage in a motor use electric power to do mechanical energy. work = watts times time

The magnetic fields are approximately to tutor, that is thoroughly organic for it to alter into vulnerable earlier the polarities substitute from North to South, to South to North. everyone that has a compass might desire to word that the needle now no longer factors in direction of authentic North. there is historic info that this has befell earlier on our planet, do slightly analyze.