How does magnetic flux affect the voltage generated by a DC generator?

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In a direct-current (DC) generator, the magnitude of the output voltage is directly proportional to the magnetic flux and the rotor speed.1

According to Faraday’s law of induction, the voltage (electromotive force) induced in a circuit is proportional to the rate of change of the magnetic flux that cuts across the circuit. In a DC generator, as the rotor turns, the coils experience a changing magnetic field, which induces this voltage.21

Because the output voltage depends on this flux, controlling the direct current in the field coils—which produces the magnetic field—is the standard method for regulating the generator's output voltage. If the field current is adjusted, the resulting change in magnetic flux directly alters the magnitude of the generated voltage.1