Which statement correctly describes how generated EMF scales with flux and speed (assuming other factors constant)?

• A. EMF is proportional to Φ^2 N.
• B. EMF is proportional to Φ / N.
• C. EMF is proportional to N / Φ.
• D. EMF is proportional to Φ N.

Answer: (D)

EMF in a generator comes from the coil linking changing magnetic flux as it rotates. The amount of EMF produced depends on how much flux links the coil (Φ) and how fast that flux is changing, which is tied to the rotation speed. If the number of turns is fixed, doubling the flux doubles the EMF, and doubling the speed also doubles the rate at which flux changes, so EMF scales linearly with speed as well. Since frequency of flux changes is proportional to speed (f ∝ N) and the EMF per cycle is proportional to Φ, the overall EMF is proportional to Φ times N. That makes the product ΦN the correct relationship. The other options imply incorrect dependencies, like EMF growing with Φ squared or decreasing with speed, which don’t fit how flux linkage and rotation drive generated EMF.