The ratio of the peak emf induced in a coil of 50 turns and area A rotating at 50 Hz in a uniform magnetic field to that in a coil of 100 turns and the same area rotating at 100 Hz in the same field is
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 0.25
A coil of \( N \) turns and area \( A \) rotating with angular speed \( \omega=2\pi\nu \) in a uniform field \( B \) has a peak emf \( \varepsilon_0=NBA\omega \). Here \( B \) and \( A \) are the same for both coils, so the peak emf is proportional to \( N\nu \).
\( \begin{aligned} \frac{\varepsilon_1}{\varepsilon_2} &= \frac{N_1BA\,(2\pi\nu_1)}{N_2BA\,(2\pi\nu_2)} \\ &= \frac{N_1\nu_1}{N_2\nu_2} \\ &= \frac{50\times50\,\mathrm{Hz}}{100\times100\,\mathrm{Hz}} \\ &= 0.25 \end{aligned} \)