Question

A rectangular coil of single turn, having area A, rotates in a uniform magnetic field B with an angular velocity $\omega$ about an axis perpendicular to the field. If initially the plane of the coil is perpendicular to the field, then the average induced emf when it has rotated through ${90}^o$ is:

• A. $\frac{\omega BA}{\pi }$
• B. $\frac{\omega BA}{2\pi }$
• C. $\frac{\omega BA}{4\pi }$
• D. $\frac{2\omega BA}{\pi }$

Answer 1

Answer: (D)

$\frac{2\omega BA}{\pi }$

Initially flux, $\varphi =BAcos0=BA$
After rotating through an angle ${90}^o$.
Flux through the coil is zero.
So, $\Delta \varphi =BA$

Angular speed $=w$, so, time period $=\frac{2\pi }{\omega }=T$

$\frac{T}{4}$ is time taken to rotate ${90}^o$.

So, $\frac{\Delta \varphi }{\Delta t}=\frac{BA}{T/4}=\frac{2BA\omega }{\pi }$