A rectangular coil of $N=50$ turns, each turn having an area $A=0.020{\text{m}}^2$, rotates with a constant angular speed $\omega =150{\text{rad s}}^{-1}$ in a uniform magnetic field $B=0.30\text{T}$ that is perpendicular to the axis of rotation. What is the maximum emf induced in the coil?

Step-by-step solution

1. For a rotating coil, the instantaneous emf is $\epsilon (t)=NBA\omega \sin \omega t$; the maximum occurs when $\sin \omega t=1$.
2. Thus ${\epsilon }_{\max }=NBA\omega$.
3. Insert the numbers: $NBA=50\times 0.30\text{T}\times 0.020{\text{m}}^2=0.30$.
4. Multiply by $\omega$: ${\epsilon }_{\max }=0.30\times 150=45\text{V}$.

Concept tested: Induced emf in a rotating coil

Published 14 September 2026 · How this solution was prepared and checked