Why must a generator’s magnetic flux change in order to induce voltage?

A generator must experience a change in magnetic flux to induce a voltage because of the principles defined by Faraday’s law of induction.

According to this law, the magnitude of the electromotive force (voltage) induced in a circuit is directly proportional to the rate at which the magnetic flux cutting across that circuit changes over time. In an electric generator, this process typically involves rotating a rotor to create a time-varying magnetic field relative to the stator coils.12

As the magnetic field lines pass the sides of the coil, the flux linkage changes. If the magnetic flux were constant, there would be no rate of change ($d\Phi /dt=0$), and consequently, no voltage would be induced. Therefore, the motion of the generator—which ensures that the magnetic field encircled by the coil is constantly changing—is essential for the conversion of mechanical energy into electric energy.123