Electrical machines use electromagnetic fields to transfer energy between electrical and mechanical systems.

In motor operation, electrical input produces electromagnetic torque and mechanical output. In generator operation, mechanical input produces induced voltage and electrical output.

Mechanical power

For a rotating shaft with torque $\tau$ and angular speed $\omega$, mechanical power is

$$P_{\mathrm{mech}}=\tau\omega.$$

Electrical and electromagnetic quantities

Current in magnetic fields can produce force and torque, while motion through magnetic flux can produce induced EMF. These are complementary aspects of the same electromagnetic coupling.

A machine can therefore often operate in either direction: the device that converts electrical power to mechanical power as a motor can convert mechanical power back to electrical power as a generator under different operating conditions.

Power balance

In an ideal conversion process,

$$P_{\mathrm{electrical}}=P_{\mathrm{mechanical}}.$$

Real machines also store some energy temporarily in fields and dissipate power through electrical resistance, magnetic-core loss, friction and other mechanisms.

The field is the intermediary: energy is not converted by an independent 'motor force' or 'generator force', but through the same electromagnetic laws in opposite power-flow directions.