A circular coil of 200 turns has radius 0.05 m and is rotating with constant angular speed 120 rad s\textsuperscript{-1} about an axis that makes an angle of 45° with a uniform magnetic field of 0.20 T that is perpendicular to the coil's plane. (i) Write the expression for the instantaneous induced emf. (ii) Calculate its maximum value.

Step-by-step solution

1. Compute the coil area: $A=\pi r^2=\pi (0.05{)}^2=7.854\times 10^{-3}{\text{ m}}^2$.
2. Determine the flux: $\Phi (t)=NBAsin\theta ,cos(\omega t)$, where $\theta =45^{\circ }$ and $\omega =120$ rad s\textsuperscript{-1}.
3. Differentiate to get emf: $\epsilon (t)=|dPhi/dt|=NBAsin\theta ,\omega ,sin(\omega t)$.
4. Maximum emf occurs when $sin(\omega t)=pm1$: ${\epsilon }_{\text{max}}=NBAsin\theta ,\omega$.
5. Insert the numbers: ${\epsilon }_{\text{max}}=200\times 0.20\times 7.854\times 10^{-3}\times 0.7071\times 120\approx 26.7\text{ V}$.

Concept tested: Faraday’s law with rotating coil at oblique angle

Published 18 September 2026 · How this solution was prepared and checked