A current-carrying conductor in a magnetic field experiences force. In a rotating machine, forces distributed around the rotor can combine into an electromagnetic torque about the shaft.

From force to torque

The direction of each conductor force follows the magnetic-force law. Its contribution to shaft torque depends on both the force and its lever arm about the rotation axis.

Changing current direction or magnetic-field direction reverses the corresponding force and can reverse the torque.

Dependence on field and current

In many simple machine models, torque has the proportional form

$$\tau=k\Phi I,$$

where $\Phi$ represents magnetic excitation, $I$ the torque-producing current and $k$ a machine constant.

Torque therefore requires both a magnetic field and current; increasing only one generally changes the torque in proportion while the linear model remains valid.

Motor and generator torque

In motor operation, electromagnetic torque drives the mechanical load. In generator operation, electromagnetic torque opposes the externally driven motion, consistent with conservation of energy and Lenz's law.

At steady speed, the electromagnetic torque balances the opposing load and loss torques. A torque imbalance produces angular acceleration.