A coil of N turns and area A spins in a magnetic field. The flux linkage is NΦ = NBA cosθ, largest when the coil faces the field and zero when its plane lies along the field. The induced e.m.f. is the rate of change of flux linkage, so it peaks exactly when the flux is changing fastest, a quarter turn out of step with the flux.
MissionWatch the e.m.f. reach its peak when the coil's plane is parallel to the field (flux linkage zero, changing fastest).Streak 0Best 0
The induced e.m.f. is greatest at the instant the plane of the coil is:
angle θ (normal to field)0°
flux linkage NΦ = NBA cosθ0.100 Wb
induced e.m.f.0.00 V
peak e.m.f. = NBAω0.40 V
Flux is maximum when the coil faces the field; the e.m.f. is then zero. A quarter turn later the flux is zero but changing fastest, so the e.m.f. peaks.