Flux Linkage In A Rotating Coil

A coil rotating in a uniform field experiences a sinusoidally varying flux, and Faraday's law gives a peak EMF (\varepsilon_0 = NBA\omega), where (\omega) is the angular speed of rotation. This is the operating principle of an AC generator. The frequency is 50 rev/s, so (\omega = 2\pi \times 50 = 100\pi \approx 314) rad/s. Substituting (N = 200), (B = 0.4) T, (A = 0.05) m^2 and (\omega = 314) rad/s gives (\varepsilon_0 = 200 \times 0.4 \times 0.05 \times 314 = 4 \times 314 = 1256) V. The option 628 V halves the result by using (\pi\times50) instead of (2\pi\times50). The option 400 V drops the angular-speed factor and keeps only (NBA) scaled. The option 200 V uses the turns count alone. This is the NCERT generator relation in which peak EMF scales with rotation rate, arising because the flux varies as (\Phi = NBA\cos\omega t) and its time derivative introduces the factor (\omega). The instantaneous EMF is therefore (\varepsilon = NBA\omega\sin\omega t), a pure sinusoid whose maximum is the peak value computed above and whose RMS value would be smaller by a factor of (\sqrt{2}). A plausibility check confirms the units (T·m^2·rad/s per turn, times turns) give volts, and a high peak is entirely reasonable for a many-turn coil spinning rapidly in a moderate field, which is why practical generators use many turns and high rotation speeds.