When does a motor or solenoid maximize and minimize power?
Motor
For a motor, the maximum power point is often where the efficiency is around half its maximum value. The rated output power of a motor remains constant, so its speed and torque are inversely related. As speed increases, available torque decreases proportionally, and vice versa. This relationship is typically shown in a motor performance curve, which also includes motor current draw (in Amps) and efficiency (in %).
Solenoid
For a solenoid, the power characteristics can vary based on the design and application, but generally, the power is maximized when the solenoid is operating at a specific point in its stroke length where the force and speed result in the highest power output .
\text{Power} = \text{Force} \times \text{Velocity}